{"citation_context": " of Parameters in Linear Mixed-Effects Models.” Pharmaceutical Statistics 12, no. 3 (2013): 129–40. https://doi.org/10.1002/pst.1561 (https://doi.org/10.1002/pst.1561).", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": "10.1002/pst.1561", "external_url": "https://doi.org/10.1002/pst.1561", "kind": "doi_url", "post_id": 676832, "post_url": "https://stats.stackexchange.com/questions/676832/references-on-semiparametric-bootstrapping-in-mixed-multilevel-models", "product": "citations", "record_id": "Scientific-Citation-Graph:e178ec2a48552f3ad84a608e", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I am aware of some discussion of how to bootstrap residuals in (non-linear, but that's more coincidental) mixed effects models in Das and Krishen 1999. This is, again, from the pharmacometrics field like the 2013 paper you found (perhaps where they go their ideas from?).

\n

A search additionally let me find Meijer, van der Leeden and Busing 1995, which refers to a user manual for a software called MLA (I've never heard of) from 1994.

\n

That's still 15 years after the start of the bootstrap literature in 1979 and something like 38 to 45 from the beginnings of the jackknife (and mixed models have been around for about that long, too, I think). So there's definitely scope that someone did/published stuff before then. However, older stuff I found like

\n\n

is about resampling cases (i.e. hierachical units) rather than residuals, or

\n\n

where it's parametric bootstrapping of residuals.

\n", "answer_id": 676840, "answer_text": "I am aware of some discussion of how to bootstrap residuals in (non-linear, but that's more coincidental) mixed effects models in Das and Krishen 1999 (https://doi.org/10.1016/S0378-3758(98)00145-1). This is, again, from the pharmacometrics field like the 2013 paper you found (perhaps where they go their ideas from?).\n\n\n\n\nA search additionally let me find Meijer, van der Leeden and Busing 1995 (https://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/new7-2.pdf), which refers to a user manual for a software called MLA (I've never heard of) from 1994.\n\n\n\n\nThat's still 15 years after the start of the bootstrap literature (https://doi.org/10.1214%2Faos%2F1176344552) in 1979 and something like 38 to 45 from the beginnings of the jackknife (and mixed models have been around for about that long, too, I think). So there's definitely scope that someone did/published stuff before then. However, older stuff I found like\n\n\n\n\n\nJ. G. Bagaka. Two Level Nested Hierarchical Linear Model with Random\nIntercepts via the Bootstrap. PhD thesis, Michigan State University, East Lansing, MI, 1992. (Available from University Microfilms International, publication number AAT 9302972, http://www.umi.com (http://www.umi.com))\n\n\n\n\n\nis about resampling cases (i.e. hierachical units) rather than residuals, or\n\n\n\n\n\nBellmann, L., Breitung, J. and Wagner, J., 1989. Bias correction and bootstrapping of error component models for panel data: Theory and applications. Empirical Economics, 14(4), pp.329-342.\n\n\n\n\n\nwhere it's parametric bootstrapping of residuals.", "answer_url": "https://stats.stackexchange.com/a/676840", "author": "Björn", "author_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-11T07:33:29+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676832, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Björn", "profile_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "user_type": "registered"}, "created_at": "2026-08-11T07:33:29+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "32215905-FEAC-4501-8B2E-F8D1D6B1C236", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/32215905-FEAC-4501-8B2E-F8D1D6B1C236/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Björn", "profile_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "user_type": "registered"}, "created_at": "2026-08-11T07:43:14+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "3E76600E-590B-459B-BAD0-E785E7ABDDA0", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/3E76600E-590B-459B-BAD0-E785E7ABDDA0/view-source"}], "score": 4, "updated_at": "2026-08-11T07:43:14+00:00"}], "domain": "statistics", "external_links": ["http://www.umi.com", "https://doi.org/10.1002/pst.1561", "https://doi.org/10.1016/S0167-7152(02)00041-X", "https://doi.org/10.1016/S0378-3758(98)00145-1", "https://doi.org/10.1016/j.spl.2007.12.015", "https://doi.org/10.1214%2Faos%2F1176344552", "https://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/new7-2.pdf"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Ben Bolker", "question_author_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "question_author_user_type": "registered", "question_created_at": "2026-08-10T18:14:05+00:00", "question_html": "

I'm having a hard time finding primary references on semiparametric bootstrapping (i.e. residual bootstrapping) for multilevel/mixed models. This CV question refers to Shang and Cavanaugh (2008), but that paper doesn't provide anything going further back. I can't find anything in Chernick (2011) or Efron and Tibshirani (1994) (I haven't looked at Davis and Hinckley, but I would be surprised if there was anything there ...) The other references listed below are interesting, but not useful as far as I can tell.

\n

The basic question is how one should do residual-based bootstrapping for linear mixed models; do you resample both BLUPs/latent variables and residuals based on cluster-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta} - \\mathbf Z \\hat{\\mathbf b}$ (Morris 2002 says this doesn't work)? Simulate $\\mathbf b$ from the unconditional MVN distribution of latent variables (i.e., using the estimated random effects covariance matrices) and add those values to resampled cluster-level residuals and population-level predictions? Use resampled population-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta}$ added back to the population-level predictions?

\n

The last option seems to be what's recommended, but I would really like to see the original discussion/theoretical justification for this ...

\n
\n

Chernick, Michael R. Bootstrap Methods: A Guide for Practitioners and Researchers. John Wiley & Sons, 2011.

\n

Efron, Bradley, and R. J. Tibshirani. An Introduction to the Bootstrap. CRC Press, 1994.

\n

Morris, Jeffrey S. “The BLUPs Are Not ‘Best’ When It Comes to Bootstrapping.” Statistics & Probability Letters 56, no. 4 (2002): 425–30. https://doi.org/10.1016/S0167-7152(02)00041-X.

\n

Shang, Junfeng, and Joseph E. Cavanaugh. “An Assumption for the Development of Bootstrap Variants of the Akaike Information Criterion in Mixed Models.” Statistics & Probability Letters 78, no. 12 (2008): 1422–29. https://doi.org/10.1016/j.spl.2007.12.015.

\n

Thai, Hoai-Thu, France Mentré, Nicholas H. G. Holford, Christine Veyrat-Follet, and Emmanuelle Comets. “A Comparison of Bootstrap Approaches for Estimating Uncertainty of Parameters in Linear Mixed-Effects Models.” Pharmaceutical Statistics 12, no. 3 (2013): 129–40. https://doi.org/10.1002/pst.1561.

\n", "question_id": 676832, "question_license": "CC BY-SA 4.0", "question_score": 7, "question_text": "I'm having a hard time finding primary references on semiparametric bootstrapping (i.e. residual bootstrapping) for multilevel/mixed models. This CV question (https://stats.stackexchange.com/questions/29500/parametric-semiparametric-and-nonparametric-bootstrapping-for-mixed-models) refers to Shang and Cavanaugh (2008), but that paper doesn't provide anything going further back. I can't find anything in Chernick (2011) or Efron and Tibshirani (1994) (I haven't looked at Davis and Hinckley, but I would be surprised if there was anything there ...) The other references listed below are interesting, but not useful as far as I can tell.\n\n\n\n\nThe basic question is how one should do residual-based bootstrapping for linear mixed models; do you resample both BLUPs/latent variables and residuals based on cluster-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta} - \\mathbf Z \\hat{\\mathbf b}$ (Morris 2002 says this doesn't work)? Simulate $\\mathbf b$ from the unconditional MVN distribution of latent variables (i.e., using the estimated random effects covariance matrices) and add those values to resampled cluster-level residuals and population-level predictions? Use resampled population-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta}$ added back to the population-level predictions?\n\n\n\n\nThe last option seems to be what's recommended, but I would really like to see the original discussion/theoretical justification for this ...\n\n\n\n\n\n\n\nChernick, Michael R. Bootstrap Methods: A Guide for Practitioners and Researchers. John Wiley & Sons, 2011.\n\n\n\n\nEfron, Bradley, and R. J. Tibshirani. An Introduction to the Bootstrap. CRC Press, 1994.\n\n\n\n\nMorris, Jeffrey S. “The BLUPs Are Not ‘Best’ When It Comes to Bootstrapping.” Statistics & Probability Letters 56, no. 4 (2002): 425–30. https://doi.org/10.1016/S0167-7152(02)00041-X (https://doi.org/10.1016/S0167-7152(02)00041-X).\n\n\n\n\nShang, Junfeng, and Joseph E. Cavanaugh. “An Assumption for the Development of Bootstrap Variants of the Akaike Information Criterion in Mixed Models.” Statistics & Probability Letters 78, no. 12 (2008): 1422–29. https://doi.org/10.1016/j.spl.2007.12.015 (https://doi.org/10.1016/j.spl.2007.12.015).\n\n\n\n\nThai, Hoai-Thu, France Mentré, Nicholas H. G. Holford, Christine Veyrat-Follet, and Emmanuelle Comets. “A Comparison of Bootstrap Approaches for Estimating Uncertainty of Parameters in Linear Mixed-Effects Models.” Pharmaceutical Statistics 12, no. 3 (2013): 129–40. https://doi.org/10.1002/pst.1561 (https://doi.org/10.1002/pst.1561).", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ben Bolker", "profile_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "user_type": "registered"}, "created_at": "2026-08-10T18:14:05+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "D42FF201-3D9E-41EE-AD38-D701B246BD21", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/D42FF201-3D9E-41EE-AD38-D701B246BD21/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ben Bolker", "profile_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "user_type": "registered"}, "created_at": "2026-08-10T18:34:39+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "30821CFD-69CB-49E7-8636-CD19053C6EFF", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/30821CFD-69CB-49E7-8636-CD19053C6EFF/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-08-11T09:36:33+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "4D25C7FB-5C99-4487-BCBA-B001C9D9782A", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/4D25C7FB-5C99-4487-BCBA-B001C9D9782A/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676832/references-on-semiparametric-bootstrapping-in-mixed-multilevel-models", "split": "test", "split_group": "f66badcf3bceb0e03ae228ad9fa4fe002bfb6ea62c52876caa0f2adeb9118dde", "tags": ["mixed-model", "bootstrap"], "thread_id": "stats:676832", "title": "references on semiparametric bootstrapping in mixed/multilevel models"}} {"citation_context": " ‘Best’ When It Comes to Bootstrapping.” Statistics & Probability Letters 56, no. 4 (2002): 425–30. https://doi.org/10.1016/S0167-7152(02)00041-X (https://doi.org/10.1016/S0167-7152(02)00041-X).\n\n\n\n\nShang, Junfeng, and Joseph E. Cavanaugh. “An A", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": "10.1016/S0167-7152(02)00041-X", "external_url": "https://doi.org/10.1016/S0167-7152(02)00041-X", "kind": "doi_url", "post_id": 676832, "post_url": "https://stats.stackexchange.com/questions/676832/references-on-semiparametric-bootstrapping-in-mixed-multilevel-models", "product": "citations", "record_id": "Scientific-Citation-Graph:4e979a1e3ae27f6552248e4a", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I am aware of some discussion of how to bootstrap residuals in (non-linear, but that's more coincidental) mixed effects models in Das and Krishen 1999. This is, again, from the pharmacometrics field like the 2013 paper you found (perhaps where they go their ideas from?).

\n

A search additionally let me find Meijer, van der Leeden and Busing 1995, which refers to a user manual for a software called MLA (I've never heard of) from 1994.

\n

That's still 15 years after the start of the bootstrap literature in 1979 and something like 38 to 45 from the beginnings of the jackknife (and mixed models have been around for about that long, too, I think). So there's definitely scope that someone did/published stuff before then. However, older stuff I found like

\n\n

is about resampling cases (i.e. hierachical units) rather than residuals, or

\n\n

where it's parametric bootstrapping of residuals.

\n", "answer_id": 676840, "answer_text": "I am aware of some discussion of how to bootstrap residuals in (non-linear, but that's more coincidental) mixed effects models in Das and Krishen 1999 (https://doi.org/10.1016/S0378-3758(98)00145-1). This is, again, from the pharmacometrics field like the 2013 paper you found (perhaps where they go their ideas from?).\n\n\n\n\nA search additionally let me find Meijer, van der Leeden and Busing 1995 (https://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/new7-2.pdf), which refers to a user manual for a software called MLA (I've never heard of) from 1994.\n\n\n\n\nThat's still 15 years after the start of the bootstrap literature (https://doi.org/10.1214%2Faos%2F1176344552) in 1979 and something like 38 to 45 from the beginnings of the jackknife (and mixed models have been around for about that long, too, I think). So there's definitely scope that someone did/published stuff before then. However, older stuff I found like\n\n\n\n\n\nJ. G. Bagaka. Two Level Nested Hierarchical Linear Model with Random\nIntercepts via the Bootstrap. PhD thesis, Michigan State University, East Lansing, MI, 1992. (Available from University Microfilms International, publication number AAT 9302972, http://www.umi.com (http://www.umi.com))\n\n\n\n\n\nis about resampling cases (i.e. hierachical units) rather than residuals, or\n\n\n\n\n\nBellmann, L., Breitung, J. and Wagner, J., 1989. Bias correction and bootstrapping of error component models for panel data: Theory and applications. Empirical Economics, 14(4), pp.329-342.\n\n\n\n\n\nwhere it's parametric bootstrapping of residuals.", "answer_url": "https://stats.stackexchange.com/a/676840", "author": "Björn", "author_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-11T07:33:29+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676832, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Björn", "profile_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "user_type": "registered"}, "created_at": "2026-08-11T07:33:29+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "32215905-FEAC-4501-8B2E-F8D1D6B1C236", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/32215905-FEAC-4501-8B2E-F8D1D6B1C236/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Björn", "profile_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "user_type": "registered"}, "created_at": "2026-08-11T07:43:14+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "3E76600E-590B-459B-BAD0-E785E7ABDDA0", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/3E76600E-590B-459B-BAD0-E785E7ABDDA0/view-source"}], "score": 4, "updated_at": "2026-08-11T07:43:14+00:00"}], "domain": "statistics", "external_links": ["http://www.umi.com", "https://doi.org/10.1002/pst.1561", "https://doi.org/10.1016/S0167-7152(02)00041-X", "https://doi.org/10.1016/S0378-3758(98)00145-1", "https://doi.org/10.1016/j.spl.2007.12.015", "https://doi.org/10.1214%2Faos%2F1176344552", "https://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/new7-2.pdf"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Ben Bolker", "question_author_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "question_author_user_type": "registered", "question_created_at": "2026-08-10T18:14:05+00:00", "question_html": "

I'm having a hard time finding primary references on semiparametric bootstrapping (i.e. residual bootstrapping) for multilevel/mixed models. This CV question refers to Shang and Cavanaugh (2008), but that paper doesn't provide anything going further back. I can't find anything in Chernick (2011) or Efron and Tibshirani (1994) (I haven't looked at Davis and Hinckley, but I would be surprised if there was anything there ...) The other references listed below are interesting, but not useful as far as I can tell.

\n

The basic question is how one should do residual-based bootstrapping for linear mixed models; do you resample both BLUPs/latent variables and residuals based on cluster-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta} - \\mathbf Z \\hat{\\mathbf b}$ (Morris 2002 says this doesn't work)? Simulate $\\mathbf b$ from the unconditional MVN distribution of latent variables (i.e., using the estimated random effects covariance matrices) and add those values to resampled cluster-level residuals and population-level predictions? Use resampled population-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta}$ added back to the population-level predictions?

\n

The last option seems to be what's recommended, but I would really like to see the original discussion/theoretical justification for this ...

\n
\n

Chernick, Michael R. Bootstrap Methods: A Guide for Practitioners and Researchers. John Wiley & Sons, 2011.

\n

Efron, Bradley, and R. J. Tibshirani. An Introduction to the Bootstrap. CRC Press, 1994.

\n

Morris, Jeffrey S. “The BLUPs Are Not ‘Best’ When It Comes to Bootstrapping.” Statistics & Probability Letters 56, no. 4 (2002): 425–30. https://doi.org/10.1016/S0167-7152(02)00041-X.

\n

Shang, Junfeng, and Joseph E. Cavanaugh. “An Assumption for the Development of Bootstrap Variants of the Akaike Information Criterion in Mixed Models.” Statistics & Probability Letters 78, no. 12 (2008): 1422–29. https://doi.org/10.1016/j.spl.2007.12.015.

\n

Thai, Hoai-Thu, France Mentré, Nicholas H. G. Holford, Christine Veyrat-Follet, and Emmanuelle Comets. “A Comparison of Bootstrap Approaches for Estimating Uncertainty of Parameters in Linear Mixed-Effects Models.” Pharmaceutical Statistics 12, no. 3 (2013): 129–40. https://doi.org/10.1002/pst.1561.

\n", "question_id": 676832, "question_license": "CC BY-SA 4.0", "question_score": 7, "question_text": "I'm having a hard time finding primary references on semiparametric bootstrapping (i.e. residual bootstrapping) for multilevel/mixed models. This CV question (https://stats.stackexchange.com/questions/29500/parametric-semiparametric-and-nonparametric-bootstrapping-for-mixed-models) refers to Shang and Cavanaugh (2008), but that paper doesn't provide anything going further back. I can't find anything in Chernick (2011) or Efron and Tibshirani (1994) (I haven't looked at Davis and Hinckley, but I would be surprised if there was anything there ...) The other references listed below are interesting, but not useful as far as I can tell.\n\n\n\n\nThe basic question is how one should do residual-based bootstrapping for linear mixed models; do you resample both BLUPs/latent variables and residuals based on cluster-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta} - \\mathbf Z \\hat{\\mathbf b}$ (Morris 2002 says this doesn't work)? Simulate $\\mathbf b$ from the unconditional MVN distribution of latent variables (i.e., using the estimated random effects covariance matrices) and add those values to resampled cluster-level residuals and population-level predictions? Use resampled population-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta}$ added back to the population-level predictions?\n\n\n\n\nThe last option seems to be what's recommended, but I would really like to see the original discussion/theoretical justification for this ...\n\n\n\n\n\n\n\nChernick, Michael R. Bootstrap Methods: A Guide for Practitioners and Researchers. John Wiley & Sons, 2011.\n\n\n\n\nEfron, Bradley, and R. J. Tibshirani. An Introduction to the Bootstrap. CRC Press, 1994.\n\n\n\n\nMorris, Jeffrey S. “The BLUPs Are Not ‘Best’ When It Comes to Bootstrapping.” Statistics & Probability Letters 56, no. 4 (2002): 425–30. https://doi.org/10.1016/S0167-7152(02)00041-X (https://doi.org/10.1016/S0167-7152(02)00041-X).\n\n\n\n\nShang, Junfeng, and Joseph E. Cavanaugh. “An Assumption for the Development of Bootstrap Variants of the Akaike Information Criterion in Mixed Models.” Statistics & Probability Letters 78, no. 12 (2008): 1422–29. https://doi.org/10.1016/j.spl.2007.12.015 (https://doi.org/10.1016/j.spl.2007.12.015).\n\n\n\n\nThai, Hoai-Thu, France Mentré, Nicholas H. G. Holford, Christine Veyrat-Follet, and Emmanuelle Comets. “A Comparison of Bootstrap Approaches for Estimating Uncertainty of Parameters in Linear Mixed-Effects Models.” Pharmaceutical Statistics 12, no. 3 (2013): 129–40. https://doi.org/10.1002/pst.1561 (https://doi.org/10.1002/pst.1561).", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ben Bolker", "profile_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "user_type": "registered"}, "created_at": "2026-08-10T18:14:05+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "D42FF201-3D9E-41EE-AD38-D701B246BD21", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/D42FF201-3D9E-41EE-AD38-D701B246BD21/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ben Bolker", "profile_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "user_type": "registered"}, "created_at": "2026-08-10T18:34:39+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "30821CFD-69CB-49E7-8636-CD19053C6EFF", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/30821CFD-69CB-49E7-8636-CD19053C6EFF/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-08-11T09:36:33+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "4D25C7FB-5C99-4487-BCBA-B001C9D9782A", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/4D25C7FB-5C99-4487-BCBA-B001C9D9782A/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676832/references-on-semiparametric-bootstrapping-in-mixed-multilevel-models", "split": "test", "split_group": "f66badcf3bceb0e03ae228ad9fa4fe002bfb6ea62c52876caa0f2adeb9118dde", "tags": ["mixed-model", "bootstrap"], "thread_id": "stats:676832", "title": "references on semiparametric bootstrapping in mixed/multilevel models"}} {"citation_context": "nformation Criterion in Mixed Models.” Statistics & Probability Letters 78, no. 12 (2008): 1422–29. https://doi.org/10.1016/j.spl.2007.12.015 (https://doi.org/10.1016/j.spl.2007.12.015).\n\n\n\n\nThai, Hoai-Thu, France Mentré, Nicholas H. G. Holf", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": "10.1016/j.spl.2007.12.015", "external_url": "https://doi.org/10.1016/j.spl.2007.12.015", "kind": "doi_url", "post_id": 676832, "post_url": "https://stats.stackexchange.com/questions/676832/references-on-semiparametric-bootstrapping-in-mixed-multilevel-models", "product": "citations", "record_id": "Scientific-Citation-Graph:25ce8acee0777b3437a3a8cc", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I am aware of some discussion of how to bootstrap residuals in (non-linear, but that's more coincidental) mixed effects models in Das and Krishen 1999. This is, again, from the pharmacometrics field like the 2013 paper you found (perhaps where they go their ideas from?).

\n

A search additionally let me find Meijer, van der Leeden and Busing 1995, which refers to a user manual for a software called MLA (I've never heard of) from 1994.

\n

That's still 15 years after the start of the bootstrap literature in 1979 and something like 38 to 45 from the beginnings of the jackknife (and mixed models have been around for about that long, too, I think). So there's definitely scope that someone did/published stuff before then. However, older stuff I found like

\n\n

is about resampling cases (i.e. hierachical units) rather than residuals, or

\n\n

where it's parametric bootstrapping of residuals.

\n", "answer_id": 676840, "answer_text": "I am aware of some discussion of how to bootstrap residuals in (non-linear, but that's more coincidental) mixed effects models in Das and Krishen 1999 (https://doi.org/10.1016/S0378-3758(98)00145-1). This is, again, from the pharmacometrics field like the 2013 paper you found (perhaps where they go their ideas from?).\n\n\n\n\nA search additionally let me find Meijer, van der Leeden and Busing 1995 (https://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/new7-2.pdf), which refers to a user manual for a software called MLA (I've never heard of) from 1994.\n\n\n\n\nThat's still 15 years after the start of the bootstrap literature (https://doi.org/10.1214%2Faos%2F1176344552) in 1979 and something like 38 to 45 from the beginnings of the jackknife (and mixed models have been around for about that long, too, I think). So there's definitely scope that someone did/published stuff before then. However, older stuff I found like\n\n\n\n\n\nJ. G. Bagaka. Two Level Nested Hierarchical Linear Model with Random\nIntercepts via the Bootstrap. PhD thesis, Michigan State University, East Lansing, MI, 1992. (Available from University Microfilms International, publication number AAT 9302972, http://www.umi.com (http://www.umi.com))\n\n\n\n\n\nis about resampling cases (i.e. hierachical units) rather than residuals, or\n\n\n\n\n\nBellmann, L., Breitung, J. and Wagner, J., 1989. Bias correction and bootstrapping of error component models for panel data: Theory and applications. Empirical Economics, 14(4), pp.329-342.\n\n\n\n\n\nwhere it's parametric bootstrapping of residuals.", "answer_url": "https://stats.stackexchange.com/a/676840", "author": "Björn", "author_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-11T07:33:29+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676832, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Björn", "profile_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "user_type": "registered"}, "created_at": "2026-08-11T07:33:29+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "32215905-FEAC-4501-8B2E-F8D1D6B1C236", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/32215905-FEAC-4501-8B2E-F8D1D6B1C236/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Björn", "profile_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "user_type": "registered"}, "created_at": "2026-08-11T07:43:14+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "3E76600E-590B-459B-BAD0-E785E7ABDDA0", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/3E76600E-590B-459B-BAD0-E785E7ABDDA0/view-source"}], "score": 4, "updated_at": "2026-08-11T07:43:14+00:00"}], "domain": "statistics", "external_links": ["http://www.umi.com", "https://doi.org/10.1002/pst.1561", "https://doi.org/10.1016/S0167-7152(02)00041-X", "https://doi.org/10.1016/S0378-3758(98)00145-1", "https://doi.org/10.1016/j.spl.2007.12.015", "https://doi.org/10.1214%2Faos%2F1176344552", "https://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/new7-2.pdf"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Ben Bolker", "question_author_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "question_author_user_type": "registered", "question_created_at": "2026-08-10T18:14:05+00:00", "question_html": "

I'm having a hard time finding primary references on semiparametric bootstrapping (i.e. residual bootstrapping) for multilevel/mixed models. This CV question refers to Shang and Cavanaugh (2008), but that paper doesn't provide anything going further back. I can't find anything in Chernick (2011) or Efron and Tibshirani (1994) (I haven't looked at Davis and Hinckley, but I would be surprised if there was anything there ...) The other references listed below are interesting, but not useful as far as I can tell.

\n

The basic question is how one should do residual-based bootstrapping for linear mixed models; do you resample both BLUPs/latent variables and residuals based on cluster-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta} - \\mathbf Z \\hat{\\mathbf b}$ (Morris 2002 says this doesn't work)? Simulate $\\mathbf b$ from the unconditional MVN distribution of latent variables (i.e., using the estimated random effects covariance matrices) and add those values to resampled cluster-level residuals and population-level predictions? Use resampled population-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta}$ added back to the population-level predictions?

\n

The last option seems to be what's recommended, but I would really like to see the original discussion/theoretical justification for this ...

\n
\n

Chernick, Michael R. Bootstrap Methods: A Guide for Practitioners and Researchers. John Wiley & Sons, 2011.

\n

Efron, Bradley, and R. J. Tibshirani. An Introduction to the Bootstrap. CRC Press, 1994.

\n

Morris, Jeffrey S. “The BLUPs Are Not ‘Best’ When It Comes to Bootstrapping.” Statistics & Probability Letters 56, no. 4 (2002): 425–30. https://doi.org/10.1016/S0167-7152(02)00041-X.

\n

Shang, Junfeng, and Joseph E. Cavanaugh. “An Assumption for the Development of Bootstrap Variants of the Akaike Information Criterion in Mixed Models.” Statistics & Probability Letters 78, no. 12 (2008): 1422–29. https://doi.org/10.1016/j.spl.2007.12.015.

\n

Thai, Hoai-Thu, France Mentré, Nicholas H. G. Holford, Christine Veyrat-Follet, and Emmanuelle Comets. “A Comparison of Bootstrap Approaches for Estimating Uncertainty of Parameters in Linear Mixed-Effects Models.” Pharmaceutical Statistics 12, no. 3 (2013): 129–40. https://doi.org/10.1002/pst.1561.

\n", "question_id": 676832, "question_license": "CC BY-SA 4.0", "question_score": 7, "question_text": "I'm having a hard time finding primary references on semiparametric bootstrapping (i.e. residual bootstrapping) for multilevel/mixed models. This CV question (https://stats.stackexchange.com/questions/29500/parametric-semiparametric-and-nonparametric-bootstrapping-for-mixed-models) refers to Shang and Cavanaugh (2008), but that paper doesn't provide anything going further back. I can't find anything in Chernick (2011) or Efron and Tibshirani (1994) (I haven't looked at Davis and Hinckley, but I would be surprised if there was anything there ...) The other references listed below are interesting, but not useful as far as I can tell.\n\n\n\n\nThe basic question is how one should do residual-based bootstrapping for linear mixed models; do you resample both BLUPs/latent variables and residuals based on cluster-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta} - \\mathbf Z \\hat{\\mathbf b}$ (Morris 2002 says this doesn't work)? Simulate $\\mathbf b$ from the unconditional MVN distribution of latent variables (i.e., using the estimated random effects covariance matrices) and add those values to resampled cluster-level residuals and population-level predictions? Use resampled population-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta}$ added back to the population-level predictions?\n\n\n\n\nThe last option seems to be what's recommended, but I would really like to see the original discussion/theoretical justification for this ...\n\n\n\n\n\n\n\nChernick, Michael R. Bootstrap Methods: A Guide for Practitioners and Researchers. John Wiley & Sons, 2011.\n\n\n\n\nEfron, Bradley, and R. J. Tibshirani. An Introduction to the Bootstrap. CRC Press, 1994.\n\n\n\n\nMorris, Jeffrey S. “The BLUPs Are Not ‘Best’ When It Comes to Bootstrapping.” Statistics & Probability Letters 56, no. 4 (2002): 425–30. https://doi.org/10.1016/S0167-7152(02)00041-X (https://doi.org/10.1016/S0167-7152(02)00041-X).\n\n\n\n\nShang, Junfeng, and Joseph E. Cavanaugh. “An Assumption for the Development of Bootstrap Variants of the Akaike Information Criterion in Mixed Models.” Statistics & Probability Letters 78, no. 12 (2008): 1422–29. https://doi.org/10.1016/j.spl.2007.12.015 (https://doi.org/10.1016/j.spl.2007.12.015).\n\n\n\n\nThai, Hoai-Thu, France Mentré, Nicholas H. G. Holford, Christine Veyrat-Follet, and Emmanuelle Comets. “A Comparison of Bootstrap Approaches for Estimating Uncertainty of Parameters in Linear Mixed-Effects Models.” Pharmaceutical Statistics 12, no. 3 (2013): 129–40. https://doi.org/10.1002/pst.1561 (https://doi.org/10.1002/pst.1561).", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ben Bolker", "profile_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "user_type": "registered"}, "created_at": "2026-08-10T18:14:05+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "D42FF201-3D9E-41EE-AD38-D701B246BD21", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/D42FF201-3D9E-41EE-AD38-D701B246BD21/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ben Bolker", "profile_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "user_type": "registered"}, "created_at": "2026-08-10T18:34:39+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "30821CFD-69CB-49E7-8636-CD19053C6EFF", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/30821CFD-69CB-49E7-8636-CD19053C6EFF/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-08-11T09:36:33+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "4D25C7FB-5C99-4487-BCBA-B001C9D9782A", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/4D25C7FB-5C99-4487-BCBA-B001C9D9782A/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676832/references-on-semiparametric-bootstrapping-in-mixed-multilevel-models", "split": "test", "split_group": "f66badcf3bceb0e03ae228ad9fa4fe002bfb6ea62c52876caa0f2adeb9118dde", "tags": ["mixed-model", "bootstrap"], "thread_id": "stats:676832", "title": "references on semiparametric bootstrapping in mixed/multilevel models"}} {"citation_context": "ing, MI, 1992. (Available from University Microfilms International, publication number AAT 9302972, http://www.umi.com (http://www.umi.com))\n\n\n\n\n\nis about resampling cases (i.e. hierachical units) rather than residuals", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "http://www.umi.com", "kind": "external_url", "post_id": 676840, "post_url": "https://stats.stackexchange.com/a/676840", "product": "citations", "record_id": "Scientific-Citation-Graph:56763de51a893de781feaf9e", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I am aware of some discussion of how to bootstrap residuals in (non-linear, but that's more coincidental) mixed effects models in Das and Krishen 1999. This is, again, from the pharmacometrics field like the 2013 paper you found (perhaps where they go their ideas from?).

\n

A search additionally let me find Meijer, van der Leeden and Busing 1995, which refers to a user manual for a software called MLA (I've never heard of) from 1994.

\n

That's still 15 years after the start of the bootstrap literature in 1979 and something like 38 to 45 from the beginnings of the jackknife (and mixed models have been around for about that long, too, I think). So there's definitely scope that someone did/published stuff before then. However, older stuff I found like

\n\n

is about resampling cases (i.e. hierachical units) rather than residuals, or

\n\n

where it's parametric bootstrapping of residuals.

\n", "answer_id": 676840, "answer_text": "I am aware of some discussion of how to bootstrap residuals in (non-linear, but that's more coincidental) mixed effects models in Das and Krishen 1999 (https://doi.org/10.1016/S0378-3758(98)00145-1). This is, again, from the pharmacometrics field like the 2013 paper you found (perhaps where they go their ideas from?).\n\n\n\n\nA search additionally let me find Meijer, van der Leeden and Busing 1995 (https://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/new7-2.pdf), which refers to a user manual for a software called MLA (I've never heard of) from 1994.\n\n\n\n\nThat's still 15 years after the start of the bootstrap literature (https://doi.org/10.1214%2Faos%2F1176344552) in 1979 and something like 38 to 45 from the beginnings of the jackknife (and mixed models have been around for about that long, too, I think). So there's definitely scope that someone did/published stuff before then. However, older stuff I found like\n\n\n\n\n\nJ. G. Bagaka. Two Level Nested Hierarchical Linear Model with Random\nIntercepts via the Bootstrap. PhD thesis, Michigan State University, East Lansing, MI, 1992. (Available from University Microfilms International, publication number AAT 9302972, http://www.umi.com (http://www.umi.com))\n\n\n\n\n\nis about resampling cases (i.e. hierachical units) rather than residuals, or\n\n\n\n\n\nBellmann, L., Breitung, J. and Wagner, J., 1989. Bias correction and bootstrapping of error component models for panel data: Theory and applications. Empirical Economics, 14(4), pp.329-342.\n\n\n\n\n\nwhere it's parametric bootstrapping of residuals.", "answer_url": "https://stats.stackexchange.com/a/676840", "author": "Björn", "author_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-11T07:33:29+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676832, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Björn", "profile_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "user_type": "registered"}, "created_at": "2026-08-11T07:33:29+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "32215905-FEAC-4501-8B2E-F8D1D6B1C236", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/32215905-FEAC-4501-8B2E-F8D1D6B1C236/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Björn", "profile_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "user_type": "registered"}, "created_at": "2026-08-11T07:43:14+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "3E76600E-590B-459B-BAD0-E785E7ABDDA0", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/3E76600E-590B-459B-BAD0-E785E7ABDDA0/view-source"}], "score": 4, "updated_at": "2026-08-11T07:43:14+00:00"}], "domain": "statistics", "external_links": ["http://www.umi.com", "https://doi.org/10.1002/pst.1561", "https://doi.org/10.1016/S0167-7152(02)00041-X", "https://doi.org/10.1016/S0378-3758(98)00145-1", "https://doi.org/10.1016/j.spl.2007.12.015", "https://doi.org/10.1214%2Faos%2F1176344552", "https://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/new7-2.pdf"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Ben Bolker", "question_author_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "question_author_user_type": "registered", "question_created_at": "2026-08-10T18:14:05+00:00", "question_html": "

I'm having a hard time finding primary references on semiparametric bootstrapping (i.e. residual bootstrapping) for multilevel/mixed models. This CV question refers to Shang and Cavanaugh (2008), but that paper doesn't provide anything going further back. I can't find anything in Chernick (2011) or Efron and Tibshirani (1994) (I haven't looked at Davis and Hinckley, but I would be surprised if there was anything there ...) The other references listed below are interesting, but not useful as far as I can tell.

\n

The basic question is how one should do residual-based bootstrapping for linear mixed models; do you resample both BLUPs/latent variables and residuals based on cluster-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta} - \\mathbf Z \\hat{\\mathbf b}$ (Morris 2002 says this doesn't work)? Simulate $\\mathbf b$ from the unconditional MVN distribution of latent variables (i.e., using the estimated random effects covariance matrices) and add those values to resampled cluster-level residuals and population-level predictions? Use resampled population-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta}$ added back to the population-level predictions?

\n

The last option seems to be what's recommended, but I would really like to see the original discussion/theoretical justification for this ...

\n
\n

Chernick, Michael R. Bootstrap Methods: A Guide for Practitioners and Researchers. John Wiley & Sons, 2011.

\n

Efron, Bradley, and R. J. Tibshirani. An Introduction to the Bootstrap. CRC Press, 1994.

\n

Morris, Jeffrey S. “The BLUPs Are Not ‘Best’ When It Comes to Bootstrapping.” Statistics & Probability Letters 56, no. 4 (2002): 425–30. https://doi.org/10.1016/S0167-7152(02)00041-X.

\n

Shang, Junfeng, and Joseph E. Cavanaugh. “An Assumption for the Development of Bootstrap Variants of the Akaike Information Criterion in Mixed Models.” Statistics & Probability Letters 78, no. 12 (2008): 1422–29. https://doi.org/10.1016/j.spl.2007.12.015.

\n

Thai, Hoai-Thu, France Mentré, Nicholas H. G. Holford, Christine Veyrat-Follet, and Emmanuelle Comets. “A Comparison of Bootstrap Approaches for Estimating Uncertainty of Parameters in Linear Mixed-Effects Models.” Pharmaceutical Statistics 12, no. 3 (2013): 129–40. https://doi.org/10.1002/pst.1561.

\n", "question_id": 676832, "question_license": "CC BY-SA 4.0", "question_score": 7, "question_text": "I'm having a hard time finding primary references on semiparametric bootstrapping (i.e. residual bootstrapping) for multilevel/mixed models. This CV question (https://stats.stackexchange.com/questions/29500/parametric-semiparametric-and-nonparametric-bootstrapping-for-mixed-models) refers to Shang and Cavanaugh (2008), but that paper doesn't provide anything going further back. I can't find anything in Chernick (2011) or Efron and Tibshirani (1994) (I haven't looked at Davis and Hinckley, but I would be surprised if there was anything there ...) The other references listed below are interesting, but not useful as far as I can tell.\n\n\n\n\nThe basic question is how one should do residual-based bootstrapping for linear mixed models; do you resample both BLUPs/latent variables and residuals based on cluster-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta} - \\mathbf Z \\hat{\\mathbf b}$ (Morris 2002 says this doesn't work)? Simulate $\\mathbf b$ from the unconditional MVN distribution of latent variables (i.e., using the estimated random effects covariance matrices) and add those values to resampled cluster-level residuals and population-level predictions? Use resampled population-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta}$ added back to the population-level predictions?\n\n\n\n\nThe last option seems to be what's recommended, but I would really like to see the original discussion/theoretical justification for this ...\n\n\n\n\n\n\n\nChernick, Michael R. Bootstrap Methods: A Guide for Practitioners and Researchers. John Wiley & Sons, 2011.\n\n\n\n\nEfron, Bradley, and R. J. Tibshirani. An Introduction to the Bootstrap. CRC Press, 1994.\n\n\n\n\nMorris, Jeffrey S. “The BLUPs Are Not ‘Best’ When It Comes to Bootstrapping.” Statistics & Probability Letters 56, no. 4 (2002): 425–30. https://doi.org/10.1016/S0167-7152(02)00041-X (https://doi.org/10.1016/S0167-7152(02)00041-X).\n\n\n\n\nShang, Junfeng, and Joseph E. Cavanaugh. “An Assumption for the Development of Bootstrap Variants of the Akaike Information Criterion in Mixed Models.” Statistics & Probability Letters 78, no. 12 (2008): 1422–29. https://doi.org/10.1016/j.spl.2007.12.015 (https://doi.org/10.1016/j.spl.2007.12.015).\n\n\n\n\nThai, Hoai-Thu, France Mentré, Nicholas H. G. Holford, Christine Veyrat-Follet, and Emmanuelle Comets. “A Comparison of Bootstrap Approaches for Estimating Uncertainty of Parameters in Linear Mixed-Effects Models.” Pharmaceutical Statistics 12, no. 3 (2013): 129–40. https://doi.org/10.1002/pst.1561 (https://doi.org/10.1002/pst.1561).", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ben Bolker", "profile_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "user_type": "registered"}, "created_at": "2026-08-10T18:14:05+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "D42FF201-3D9E-41EE-AD38-D701B246BD21", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/D42FF201-3D9E-41EE-AD38-D701B246BD21/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ben Bolker", "profile_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "user_type": "registered"}, "created_at": "2026-08-10T18:34:39+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "30821CFD-69CB-49E7-8636-CD19053C6EFF", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/30821CFD-69CB-49E7-8636-CD19053C6EFF/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-08-11T09:36:33+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "4D25C7FB-5C99-4487-BCBA-B001C9D9782A", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/4D25C7FB-5C99-4487-BCBA-B001C9D9782A/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676832/references-on-semiparametric-bootstrapping-in-mixed-multilevel-models", "split": "test", "split_group": "f66badcf3bceb0e03ae228ad9fa4fe002bfb6ea62c52876caa0f2adeb9118dde", "tags": ["mixed-model", "bootstrap"], "thread_id": "stats:676832", "title": "references on semiparametric bootstrapping in mixed/multilevel models"}} {"citation_context": "siduals in (non-linear, but that's more coincidental) mixed effects models in Das and Krishen 1999 (https://doi.org/10.1016/S0378-3758(98)00145-1). This is, again, from the pharmacometrics field like the 2013 paper you found (perhaps where they ", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": "10.1016/S0378-3758(98)00145-1", "external_url": "https://doi.org/10.1016/S0378-3758(98)00145-1", "kind": "doi_url", "post_id": 676840, "post_url": "https://stats.stackexchange.com/a/676840", "product": "citations", "record_id": "Scientific-Citation-Graph:4391ea4cec3feea7ecb8d025", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I am aware of some discussion of how to bootstrap residuals in (non-linear, but that's more coincidental) mixed effects models in Das and Krishen 1999. This is, again, from the pharmacometrics field like the 2013 paper you found (perhaps where they go their ideas from?).

\n

A search additionally let me find Meijer, van der Leeden and Busing 1995, which refers to a user manual for a software called MLA (I've never heard of) from 1994.

\n

That's still 15 years after the start of the bootstrap literature in 1979 and something like 38 to 45 from the beginnings of the jackknife (and mixed models have been around for about that long, too, I think). So there's definitely scope that someone did/published stuff before then. However, older stuff I found like

\n\n

is about resampling cases (i.e. hierachical units) rather than residuals, or

\n\n

where it's parametric bootstrapping of residuals.

\n", "answer_id": 676840, "answer_text": "I am aware of some discussion of how to bootstrap residuals in (non-linear, but that's more coincidental) mixed effects models in Das and Krishen 1999 (https://doi.org/10.1016/S0378-3758(98)00145-1). This is, again, from the pharmacometrics field like the 2013 paper you found (perhaps where they go their ideas from?).\n\n\n\n\nA search additionally let me find Meijer, van der Leeden and Busing 1995 (https://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/new7-2.pdf), which refers to a user manual for a software called MLA (I've never heard of) from 1994.\n\n\n\n\nThat's still 15 years after the start of the bootstrap literature (https://doi.org/10.1214%2Faos%2F1176344552) in 1979 and something like 38 to 45 from the beginnings of the jackknife (and mixed models have been around for about that long, too, I think). So there's definitely scope that someone did/published stuff before then. However, older stuff I found like\n\n\n\n\n\nJ. G. Bagaka. Two Level Nested Hierarchical Linear Model with Random\nIntercepts via the Bootstrap. PhD thesis, Michigan State University, East Lansing, MI, 1992. (Available from University Microfilms International, publication number AAT 9302972, http://www.umi.com (http://www.umi.com))\n\n\n\n\n\nis about resampling cases (i.e. hierachical units) rather than residuals, or\n\n\n\n\n\nBellmann, L., Breitung, J. and Wagner, J., 1989. Bias correction and bootstrapping of error component models for panel data: Theory and applications. Empirical Economics, 14(4), pp.329-342.\n\n\n\n\n\nwhere it's parametric bootstrapping of residuals.", "answer_url": "https://stats.stackexchange.com/a/676840", "author": "Björn", "author_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-11T07:33:29+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676832, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Björn", "profile_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "user_type": "registered"}, "created_at": "2026-08-11T07:33:29+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "32215905-FEAC-4501-8B2E-F8D1D6B1C236", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/32215905-FEAC-4501-8B2E-F8D1D6B1C236/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Björn", "profile_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "user_type": "registered"}, "created_at": "2026-08-11T07:43:14+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "3E76600E-590B-459B-BAD0-E785E7ABDDA0", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/3E76600E-590B-459B-BAD0-E785E7ABDDA0/view-source"}], "score": 4, "updated_at": "2026-08-11T07:43:14+00:00"}], "domain": "statistics", "external_links": ["http://www.umi.com", "https://doi.org/10.1002/pst.1561", "https://doi.org/10.1016/S0167-7152(02)00041-X", "https://doi.org/10.1016/S0378-3758(98)00145-1", "https://doi.org/10.1016/j.spl.2007.12.015", "https://doi.org/10.1214%2Faos%2F1176344552", "https://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/new7-2.pdf"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Ben Bolker", "question_author_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "question_author_user_type": "registered", "question_created_at": "2026-08-10T18:14:05+00:00", "question_html": "

I'm having a hard time finding primary references on semiparametric bootstrapping (i.e. residual bootstrapping) for multilevel/mixed models. This CV question refers to Shang and Cavanaugh (2008), but that paper doesn't provide anything going further back. I can't find anything in Chernick (2011) or Efron and Tibshirani (1994) (I haven't looked at Davis and Hinckley, but I would be surprised if there was anything there ...) The other references listed below are interesting, but not useful as far as I can tell.

\n

The basic question is how one should do residual-based bootstrapping for linear mixed models; do you resample both BLUPs/latent variables and residuals based on cluster-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta} - \\mathbf Z \\hat{\\mathbf b}$ (Morris 2002 says this doesn't work)? Simulate $\\mathbf b$ from the unconditional MVN distribution of latent variables (i.e., using the estimated random effects covariance matrices) and add those values to resampled cluster-level residuals and population-level predictions? Use resampled population-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta}$ added back to the population-level predictions?

\n

The last option seems to be what's recommended, but I would really like to see the original discussion/theoretical justification for this ...

\n
\n

Chernick, Michael R. Bootstrap Methods: A Guide for Practitioners and Researchers. John Wiley & Sons, 2011.

\n

Efron, Bradley, and R. J. Tibshirani. An Introduction to the Bootstrap. CRC Press, 1994.

\n

Morris, Jeffrey S. “The BLUPs Are Not ‘Best’ When It Comes to Bootstrapping.” Statistics & Probability Letters 56, no. 4 (2002): 425–30. https://doi.org/10.1016/S0167-7152(02)00041-X.

\n

Shang, Junfeng, and Joseph E. Cavanaugh. “An Assumption for the Development of Bootstrap Variants of the Akaike Information Criterion in Mixed Models.” Statistics & Probability Letters 78, no. 12 (2008): 1422–29. https://doi.org/10.1016/j.spl.2007.12.015.

\n

Thai, Hoai-Thu, France Mentré, Nicholas H. G. Holford, Christine Veyrat-Follet, and Emmanuelle Comets. “A Comparison of Bootstrap Approaches for Estimating Uncertainty of Parameters in Linear Mixed-Effects Models.” Pharmaceutical Statistics 12, no. 3 (2013): 129–40. https://doi.org/10.1002/pst.1561.

\n", "question_id": 676832, "question_license": "CC BY-SA 4.0", "question_score": 7, "question_text": "I'm having a hard time finding primary references on semiparametric bootstrapping (i.e. residual bootstrapping) for multilevel/mixed models. This CV question (https://stats.stackexchange.com/questions/29500/parametric-semiparametric-and-nonparametric-bootstrapping-for-mixed-models) refers to Shang and Cavanaugh (2008), but that paper doesn't provide anything going further back. I can't find anything in Chernick (2011) or Efron and Tibshirani (1994) (I haven't looked at Davis and Hinckley, but I would be surprised if there was anything there ...) The other references listed below are interesting, but not useful as far as I can tell.\n\n\n\n\nThe basic question is how one should do residual-based bootstrapping for linear mixed models; do you resample both BLUPs/latent variables and residuals based on cluster-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta} - \\mathbf Z \\hat{\\mathbf b}$ (Morris 2002 says this doesn't work)? Simulate $\\mathbf b$ from the unconditional MVN distribution of latent variables (i.e., using the estimated random effects covariance matrices) and add those values to resampled cluster-level residuals and population-level predictions? Use resampled population-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta}$ added back to the population-level predictions?\n\n\n\n\nThe last option seems to be what's recommended, but I would really like to see the original discussion/theoretical justification for this ...\n\n\n\n\n\n\n\nChernick, Michael R. Bootstrap Methods: A Guide for Practitioners and Researchers. John Wiley & Sons, 2011.\n\n\n\n\nEfron, Bradley, and R. J. Tibshirani. An Introduction to the Bootstrap. CRC Press, 1994.\n\n\n\n\nMorris, Jeffrey S. “The BLUPs Are Not ‘Best’ When It Comes to Bootstrapping.” Statistics & Probability Letters 56, no. 4 (2002): 425–30. https://doi.org/10.1016/S0167-7152(02)00041-X (https://doi.org/10.1016/S0167-7152(02)00041-X).\n\n\n\n\nShang, Junfeng, and Joseph E. Cavanaugh. “An Assumption for the Development of Bootstrap Variants of the Akaike Information Criterion in Mixed Models.” Statistics & Probability Letters 78, no. 12 (2008): 1422–29. https://doi.org/10.1016/j.spl.2007.12.015 (https://doi.org/10.1016/j.spl.2007.12.015).\n\n\n\n\nThai, Hoai-Thu, France Mentré, Nicholas H. G. Holford, Christine Veyrat-Follet, and Emmanuelle Comets. “A Comparison of Bootstrap Approaches for Estimating Uncertainty of Parameters in Linear Mixed-Effects Models.” Pharmaceutical Statistics 12, no. 3 (2013): 129–40. https://doi.org/10.1002/pst.1561 (https://doi.org/10.1002/pst.1561).", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ben Bolker", "profile_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "user_type": "registered"}, "created_at": "2026-08-10T18:14:05+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "D42FF201-3D9E-41EE-AD38-D701B246BD21", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/D42FF201-3D9E-41EE-AD38-D701B246BD21/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ben Bolker", "profile_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "user_type": "registered"}, "created_at": "2026-08-10T18:34:39+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "30821CFD-69CB-49E7-8636-CD19053C6EFF", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/30821CFD-69CB-49E7-8636-CD19053C6EFF/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-08-11T09:36:33+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "4D25C7FB-5C99-4487-BCBA-B001C9D9782A", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/4D25C7FB-5C99-4487-BCBA-B001C9D9782A/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676832/references-on-semiparametric-bootstrapping-in-mixed-multilevel-models", "split": "test", "split_group": "f66badcf3bceb0e03ae228ad9fa4fe002bfb6ea62c52876caa0f2adeb9118dde", "tags": ["mixed-model", "bootstrap"], "thread_id": "stats:676832", "title": "references on semiparametric bootstrapping in mixed/multilevel models"}} {"citation_context": "e never heard of) from 1994.\n\n\n\n\nThat's still 15 years after the start of the bootstrap literature (https://doi.org/10.1214%2Faos%2F1176344552) in 1979 and something like 38 to 45 from the beginnings of the jackknife (and mixed models have be", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": "10.1214/aos/1176344552", "external_url": "https://doi.org/10.1214%2Faos%2F1176344552", "kind": "doi_url", "post_id": 676840, "post_url": "https://stats.stackexchange.com/a/676840", "product": "citations", "record_id": "Scientific-Citation-Graph:ca2b4c1c1d5ad037352b3e25", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I am aware of some discussion of how to bootstrap residuals in (non-linear, but that's more coincidental) mixed effects models in Das and Krishen 1999. This is, again, from the pharmacometrics field like the 2013 paper you found (perhaps where they go their ideas from?).

\n

A search additionally let me find Meijer, van der Leeden and Busing 1995, which refers to a user manual for a software called MLA (I've never heard of) from 1994.

\n

That's still 15 years after the start of the bootstrap literature in 1979 and something like 38 to 45 from the beginnings of the jackknife (and mixed models have been around for about that long, too, I think). So there's definitely scope that someone did/published stuff before then. However, older stuff I found like

\n\n

is about resampling cases (i.e. hierachical units) rather than residuals, or

\n\n

where it's parametric bootstrapping of residuals.

\n", "answer_id": 676840, "answer_text": "I am aware of some discussion of how to bootstrap residuals in (non-linear, but that's more coincidental) mixed effects models in Das and Krishen 1999 (https://doi.org/10.1016/S0378-3758(98)00145-1). This is, again, from the pharmacometrics field like the 2013 paper you found (perhaps where they go their ideas from?).\n\n\n\n\nA search additionally let me find Meijer, van der Leeden and Busing 1995 (https://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/new7-2.pdf), which refers to a user manual for a software called MLA (I've never heard of) from 1994.\n\n\n\n\nThat's still 15 years after the start of the bootstrap literature (https://doi.org/10.1214%2Faos%2F1176344552) in 1979 and something like 38 to 45 from the beginnings of the jackknife (and mixed models have been around for about that long, too, I think). So there's definitely scope that someone did/published stuff before then. However, older stuff I found like\n\n\n\n\n\nJ. G. Bagaka. Two Level Nested Hierarchical Linear Model with Random\nIntercepts via the Bootstrap. PhD thesis, Michigan State University, East Lansing, MI, 1992. (Available from University Microfilms International, publication number AAT 9302972, http://www.umi.com (http://www.umi.com))\n\n\n\n\n\nis about resampling cases (i.e. hierachical units) rather than residuals, or\n\n\n\n\n\nBellmann, L., Breitung, J. and Wagner, J., 1989. Bias correction and bootstrapping of error component models for panel data: Theory and applications. Empirical Economics, 14(4), pp.329-342.\n\n\n\n\n\nwhere it's parametric bootstrapping of residuals.", "answer_url": "https://stats.stackexchange.com/a/676840", "author": "Björn", "author_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-11T07:33:29+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676832, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Björn", "profile_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "user_type": "registered"}, "created_at": "2026-08-11T07:33:29+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "32215905-FEAC-4501-8B2E-F8D1D6B1C236", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/32215905-FEAC-4501-8B2E-F8D1D6B1C236/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Björn", "profile_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "user_type": "registered"}, "created_at": "2026-08-11T07:43:14+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "3E76600E-590B-459B-BAD0-E785E7ABDDA0", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/3E76600E-590B-459B-BAD0-E785E7ABDDA0/view-source"}], "score": 4, "updated_at": "2026-08-11T07:43:14+00:00"}], "domain": "statistics", "external_links": ["http://www.umi.com", "https://doi.org/10.1002/pst.1561", "https://doi.org/10.1016/S0167-7152(02)00041-X", "https://doi.org/10.1016/S0378-3758(98)00145-1", "https://doi.org/10.1016/j.spl.2007.12.015", "https://doi.org/10.1214%2Faos%2F1176344552", "https://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/new7-2.pdf"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Ben Bolker", "question_author_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "question_author_user_type": "registered", "question_created_at": "2026-08-10T18:14:05+00:00", "question_html": "

I'm having a hard time finding primary references on semiparametric bootstrapping (i.e. residual bootstrapping) for multilevel/mixed models. This CV question refers to Shang and Cavanaugh (2008), but that paper doesn't provide anything going further back. I can't find anything in Chernick (2011) or Efron and Tibshirani (1994) (I haven't looked at Davis and Hinckley, but I would be surprised if there was anything there ...) The other references listed below are interesting, but not useful as far as I can tell.

\n

The basic question is how one should do residual-based bootstrapping for linear mixed models; do you resample both BLUPs/latent variables and residuals based on cluster-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta} - \\mathbf Z \\hat{\\mathbf b}$ (Morris 2002 says this doesn't work)? Simulate $\\mathbf b$ from the unconditional MVN distribution of latent variables (i.e., using the estimated random effects covariance matrices) and add those values to resampled cluster-level residuals and population-level predictions? Use resampled population-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta}$ added back to the population-level predictions?

\n

The last option seems to be what's recommended, but I would really like to see the original discussion/theoretical justification for this ...

\n
\n

Chernick, Michael R. Bootstrap Methods: A Guide for Practitioners and Researchers. John Wiley & Sons, 2011.

\n

Efron, Bradley, and R. J. Tibshirani. An Introduction to the Bootstrap. CRC Press, 1994.

\n

Morris, Jeffrey S. “The BLUPs Are Not ‘Best’ When It Comes to Bootstrapping.” Statistics & Probability Letters 56, no. 4 (2002): 425–30. https://doi.org/10.1016/S0167-7152(02)00041-X.

\n

Shang, Junfeng, and Joseph E. Cavanaugh. “An Assumption for the Development of Bootstrap Variants of the Akaike Information Criterion in Mixed Models.” Statistics & Probability Letters 78, no. 12 (2008): 1422–29. https://doi.org/10.1016/j.spl.2007.12.015.

\n

Thai, Hoai-Thu, France Mentré, Nicholas H. G. Holford, Christine Veyrat-Follet, and Emmanuelle Comets. “A Comparison of Bootstrap Approaches for Estimating Uncertainty of Parameters in Linear Mixed-Effects Models.” Pharmaceutical Statistics 12, no. 3 (2013): 129–40. https://doi.org/10.1002/pst.1561.

\n", "question_id": 676832, "question_license": "CC BY-SA 4.0", "question_score": 7, "question_text": "I'm having a hard time finding primary references on semiparametric bootstrapping (i.e. residual bootstrapping) for multilevel/mixed models. This CV question (https://stats.stackexchange.com/questions/29500/parametric-semiparametric-and-nonparametric-bootstrapping-for-mixed-models) refers to Shang and Cavanaugh (2008), but that paper doesn't provide anything going further back. I can't find anything in Chernick (2011) or Efron and Tibshirani (1994) (I haven't looked at Davis and Hinckley, but I would be surprised if there was anything there ...) The other references listed below are interesting, but not useful as far as I can tell.\n\n\n\n\nThe basic question is how one should do residual-based bootstrapping for linear mixed models; do you resample both BLUPs/latent variables and residuals based on cluster-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta} - \\mathbf Z \\hat{\\mathbf b}$ (Morris 2002 says this doesn't work)? Simulate $\\mathbf b$ from the unconditional MVN distribution of latent variables (i.e., using the estimated random effects covariance matrices) and add those values to resampled cluster-level residuals and population-level predictions? Use resampled population-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta}$ added back to the population-level predictions?\n\n\n\n\nThe last option seems to be what's recommended, but I would really like to see the original discussion/theoretical justification for this ...\n\n\n\n\n\n\n\nChernick, Michael R. Bootstrap Methods: A Guide for Practitioners and Researchers. John Wiley & Sons, 2011.\n\n\n\n\nEfron, Bradley, and R. J. Tibshirani. An Introduction to the Bootstrap. CRC Press, 1994.\n\n\n\n\nMorris, Jeffrey S. “The BLUPs Are Not ‘Best’ When It Comes to Bootstrapping.” Statistics & Probability Letters 56, no. 4 (2002): 425–30. https://doi.org/10.1016/S0167-7152(02)00041-X (https://doi.org/10.1016/S0167-7152(02)00041-X).\n\n\n\n\nShang, Junfeng, and Joseph E. Cavanaugh. “An Assumption for the Development of Bootstrap Variants of the Akaike Information Criterion in Mixed Models.” Statistics & Probability Letters 78, no. 12 (2008): 1422–29. https://doi.org/10.1016/j.spl.2007.12.015 (https://doi.org/10.1016/j.spl.2007.12.015).\n\n\n\n\nThai, Hoai-Thu, France Mentré, Nicholas H. G. Holford, Christine Veyrat-Follet, and Emmanuelle Comets. “A Comparison of Bootstrap Approaches for Estimating Uncertainty of Parameters in Linear Mixed-Effects Models.” Pharmaceutical Statistics 12, no. 3 (2013): 129–40. https://doi.org/10.1002/pst.1561 (https://doi.org/10.1002/pst.1561).", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ben Bolker", "profile_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "user_type": "registered"}, "created_at": "2026-08-10T18:14:05+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "D42FF201-3D9E-41EE-AD38-D701B246BD21", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/D42FF201-3D9E-41EE-AD38-D701B246BD21/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ben Bolker", "profile_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "user_type": "registered"}, "created_at": "2026-08-10T18:34:39+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "30821CFD-69CB-49E7-8636-CD19053C6EFF", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/30821CFD-69CB-49E7-8636-CD19053C6EFF/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-08-11T09:36:33+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "4D25C7FB-5C99-4487-BCBA-B001C9D9782A", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/4D25C7FB-5C99-4487-BCBA-B001C9D9782A/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676832/references-on-semiparametric-bootstrapping-in-mixed-multilevel-models", "split": "test", "split_group": "f66badcf3bceb0e03ae228ad9fa4fe002bfb6ea62c52876caa0f2adeb9118dde", "tags": ["mixed-model", "bootstrap"], "thread_id": "stats:676832", "title": "references on semiparametric bootstrapping in mixed/multilevel models"}} {"citation_context": "o their ideas from?).\n\n\n\n\nA search additionally let me find Meijer, van der Leeden and Busing 1995 (https://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/new7-2.pdf), which refers to a user manual for a software called MLA (I've never heard of) from 1994.\n\n\n\n\nThat", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/new7-2.pdf", "kind": "external_url", "post_id": 676840, "post_url": "https://stats.stackexchange.com/a/676840", "product": "citations", "record_id": "Scientific-Citation-Graph:1fd5c6079e4666d1eea6c9df", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I am aware of some discussion of how to bootstrap residuals in (non-linear, but that's more coincidental) mixed effects models in Das and Krishen 1999. This is, again, from the pharmacometrics field like the 2013 paper you found (perhaps where they go their ideas from?).

\n

A search additionally let me find Meijer, van der Leeden and Busing 1995, which refers to a user manual for a software called MLA (I've never heard of) from 1994.

\n

That's still 15 years after the start of the bootstrap literature in 1979 and something like 38 to 45 from the beginnings of the jackknife (and mixed models have been around for about that long, too, I think). So there's definitely scope that someone did/published stuff before then. However, older stuff I found like

\n\n

is about resampling cases (i.e. hierachical units) rather than residuals, or

\n\n

where it's parametric bootstrapping of residuals.

\n", "answer_id": 676840, "answer_text": "I am aware of some discussion of how to bootstrap residuals in (non-linear, but that's more coincidental) mixed effects models in Das and Krishen 1999 (https://doi.org/10.1016/S0378-3758(98)00145-1). This is, again, from the pharmacometrics field like the 2013 paper you found (perhaps where they go their ideas from?).\n\n\n\n\nA search additionally let me find Meijer, van der Leeden and Busing 1995 (https://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/new7-2.pdf), which refers to a user manual for a software called MLA (I've never heard of) from 1994.\n\n\n\n\nThat's still 15 years after the start of the bootstrap literature (https://doi.org/10.1214%2Faos%2F1176344552) in 1979 and something like 38 to 45 from the beginnings of the jackknife (and mixed models have been around for about that long, too, I think). So there's definitely scope that someone did/published stuff before then. However, older stuff I found like\n\n\n\n\n\nJ. G. Bagaka. Two Level Nested Hierarchical Linear Model with Random\nIntercepts via the Bootstrap. PhD thesis, Michigan State University, East Lansing, MI, 1992. (Available from University Microfilms International, publication number AAT 9302972, http://www.umi.com (http://www.umi.com))\n\n\n\n\n\nis about resampling cases (i.e. hierachical units) rather than residuals, or\n\n\n\n\n\nBellmann, L., Breitung, J. and Wagner, J., 1989. Bias correction and bootstrapping of error component models for panel data: Theory and applications. Empirical Economics, 14(4), pp.329-342.\n\n\n\n\n\nwhere it's parametric bootstrapping of residuals.", "answer_url": "https://stats.stackexchange.com/a/676840", "author": "Björn", "author_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-11T07:33:29+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676832, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Björn", "profile_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "user_type": "registered"}, "created_at": "2026-08-11T07:33:29+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "32215905-FEAC-4501-8B2E-F8D1D6B1C236", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/32215905-FEAC-4501-8B2E-F8D1D6B1C236/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Björn", "profile_url": "https://stats.stackexchange.com/users/86652/bj%c3%b6rn", "user_type": "registered"}, "created_at": "2026-08-11T07:43:14+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "3E76600E-590B-459B-BAD0-E785E7ABDDA0", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/3E76600E-590B-459B-BAD0-E785E7ABDDA0/view-source"}], "score": 4, "updated_at": "2026-08-11T07:43:14+00:00"}], "domain": "statistics", "external_links": ["http://www.umi.com", "https://doi.org/10.1002/pst.1561", "https://doi.org/10.1016/S0167-7152(02)00041-X", "https://doi.org/10.1016/S0378-3758(98)00145-1", "https://doi.org/10.1016/j.spl.2007.12.015", "https://doi.org/10.1214%2Faos%2F1176344552", "https://www.bristol.ac.uk/media-library/sites/cmm/migrated/documents/new7-2.pdf"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Ben Bolker", "question_author_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "question_author_user_type": "registered", "question_created_at": "2026-08-10T18:14:05+00:00", "question_html": "

I'm having a hard time finding primary references on semiparametric bootstrapping (i.e. residual bootstrapping) for multilevel/mixed models. This CV question refers to Shang and Cavanaugh (2008), but that paper doesn't provide anything going further back. I can't find anything in Chernick (2011) or Efron and Tibshirani (1994) (I haven't looked at Davis and Hinckley, but I would be surprised if there was anything there ...) The other references listed below are interesting, but not useful as far as I can tell.

\n

The basic question is how one should do residual-based bootstrapping for linear mixed models; do you resample both BLUPs/latent variables and residuals based on cluster-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta} - \\mathbf Z \\hat{\\mathbf b}$ (Morris 2002 says this doesn't work)? Simulate $\\mathbf b$ from the unconditional MVN distribution of latent variables (i.e., using the estimated random effects covariance matrices) and add those values to resampled cluster-level residuals and population-level predictions? Use resampled population-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta}$ added back to the population-level predictions?

\n

The last option seems to be what's recommended, but I would really like to see the original discussion/theoretical justification for this ...

\n
\n

Chernick, Michael R. Bootstrap Methods: A Guide for Practitioners and Researchers. John Wiley & Sons, 2011.

\n

Efron, Bradley, and R. J. Tibshirani. An Introduction to the Bootstrap. CRC Press, 1994.

\n

Morris, Jeffrey S. “The BLUPs Are Not ‘Best’ When It Comes to Bootstrapping.” Statistics & Probability Letters 56, no. 4 (2002): 425–30. https://doi.org/10.1016/S0167-7152(02)00041-X.

\n

Shang, Junfeng, and Joseph E. Cavanaugh. “An Assumption for the Development of Bootstrap Variants of the Akaike Information Criterion in Mixed Models.” Statistics & Probability Letters 78, no. 12 (2008): 1422–29. https://doi.org/10.1016/j.spl.2007.12.015.

\n

Thai, Hoai-Thu, France Mentré, Nicholas H. G. Holford, Christine Veyrat-Follet, and Emmanuelle Comets. “A Comparison of Bootstrap Approaches for Estimating Uncertainty of Parameters in Linear Mixed-Effects Models.” Pharmaceutical Statistics 12, no. 3 (2013): 129–40. https://doi.org/10.1002/pst.1561.

\n", "question_id": 676832, "question_license": "CC BY-SA 4.0", "question_score": 7, "question_text": "I'm having a hard time finding primary references on semiparametric bootstrapping (i.e. residual bootstrapping) for multilevel/mixed models. This CV question (https://stats.stackexchange.com/questions/29500/parametric-semiparametric-and-nonparametric-bootstrapping-for-mixed-models) refers to Shang and Cavanaugh (2008), but that paper doesn't provide anything going further back. I can't find anything in Chernick (2011) or Efron and Tibshirani (1994) (I haven't looked at Davis and Hinckley, but I would be surprised if there was anything there ...) The other references listed below are interesting, but not useful as far as I can tell.\n\n\n\n\nThe basic question is how one should do residual-based bootstrapping for linear mixed models; do you resample both BLUPs/latent variables and residuals based on cluster-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta} - \\mathbf Z \\hat{\\mathbf b}$ (Morris 2002 says this doesn't work)? Simulate $\\mathbf b$ from the unconditional MVN distribution of latent variables (i.e., using the estimated random effects covariance matrices) and add those values to resampled cluster-level residuals and population-level predictions? Use resampled population-level residuals $\\mathbf y - \\mathbf X \\hat{\\boldsymbol \\beta}$ added back to the population-level predictions?\n\n\n\n\nThe last option seems to be what's recommended, but I would really like to see the original discussion/theoretical justification for this ...\n\n\n\n\n\n\n\nChernick, Michael R. Bootstrap Methods: A Guide for Practitioners and Researchers. John Wiley & Sons, 2011.\n\n\n\n\nEfron, Bradley, and R. J. Tibshirani. An Introduction to the Bootstrap. CRC Press, 1994.\n\n\n\n\nMorris, Jeffrey S. “The BLUPs Are Not ‘Best’ When It Comes to Bootstrapping.” Statistics & Probability Letters 56, no. 4 (2002): 425–30. https://doi.org/10.1016/S0167-7152(02)00041-X (https://doi.org/10.1016/S0167-7152(02)00041-X).\n\n\n\n\nShang, Junfeng, and Joseph E. Cavanaugh. “An Assumption for the Development of Bootstrap Variants of the Akaike Information Criterion in Mixed Models.” Statistics & Probability Letters 78, no. 12 (2008): 1422–29. https://doi.org/10.1016/j.spl.2007.12.015 (https://doi.org/10.1016/j.spl.2007.12.015).\n\n\n\n\nThai, Hoai-Thu, France Mentré, Nicholas H. G. Holford, Christine Veyrat-Follet, and Emmanuelle Comets. “A Comparison of Bootstrap Approaches for Estimating Uncertainty of Parameters in Linear Mixed-Effects Models.” Pharmaceutical Statistics 12, no. 3 (2013): 129–40. https://doi.org/10.1002/pst.1561 (https://doi.org/10.1002/pst.1561).", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ben Bolker", "profile_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "user_type": "registered"}, "created_at": "2026-08-10T18:14:05+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "D42FF201-3D9E-41EE-AD38-D701B246BD21", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/D42FF201-3D9E-41EE-AD38-D701B246BD21/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ben Bolker", "profile_url": "https://stats.stackexchange.com/users/2126/ben-bolker", "user_type": "registered"}, "created_at": "2026-08-10T18:34:39+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "30821CFD-69CB-49E7-8636-CD19053C6EFF", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/30821CFD-69CB-49E7-8636-CD19053C6EFF/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-08-11T09:36:33+00:00", "raw_file": "raw/codex_api_v1/4f74c7234d8d68222a97a637c85bc14d5aa045a3d3f336d95a6178b29bc656cd_1790825248437413600_0.json", "raw_sha256": "8385102f4bd0517d9240ab820144fa12ccb111d0c4dd000e66bdc0e0ba0294fe", "revision_guid": "4D25C7FB-5C99-4487-BCBA-B001C9D9782A", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/4D25C7FB-5C99-4487-BCBA-B001C9D9782A/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676832/references-on-semiparametric-bootstrapping-in-mixed-multilevel-models", "split": "test", "split_group": "f66badcf3bceb0e03ae228ad9fa4fe002bfb6ea62c52876caa0f2adeb9118dde", "tags": ["mixed-model", "bootstrap"], "thread_id": "stats:676832", "title": "references on semiparametric bootstrapping in mixed/multilevel models"}} {"citation_context": "3$mer)\n\n\n\n\n\nJust the lmer component predictive curve.\n[image: enter image description here; source: https://i.sstatic.net/H3mCUZgO.jpg] (https://i.sstatic.net/H3mCUZgO.jpg)\n\n\n\n\n> check_model(temp3) Throws an error, so it seems it is i", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://i.sstatic.net/H3mCUZgO.jpg", "kind": "external_url", "post_id": 676893, "post_url": "https://stats.stackexchange.com/questions/676893/is-this-the-correct-specification-for-gamm4-splines-where-species-are-short-te", "product": "citations", "record_id": "Scientific-Citation-Graph:2da8973d04b632a88f1d2010", "split": "test", "thread": {"accepted_answer_id": 676895, "answers": [{"answer_html": "

I would suggest you look at a changing a couple of things:

\n
    \n

  1. The distribution of Age is quite skewed, with some data squished up around 0 age. I would suggest trying to spread these values by out transforming Age, say via a square root transformation.

    \n

    If you look at the smooth of Age, most of the smooth is supported by by a few unique time points - the whole right hand side of the plot. Those unique ages are having a potentially bigger influence on the shape of the function than the ages that are all squished up at the left of the x axis. Spreading out the ages allows all the data to influence the smooth more evenly. You can still present the results on the Age scale, What we want to avoid is unnecessary wiggles because the smooth adapted to widely spaced values on the original scale.

    \n
    2. \n

  2. The fs smooths by Taxon aren't really doing much because they are very restricted in terms of basis functions.

    \n
    3. \n

  3. There is potential for an identifiability issue as you include a Taxon random intercept through the fs smooths, and then again through the ranef structure.

    \n

    Identifiability refers to the model's ability to unique identify (estimate a value for) each parameter in the model. You are including a random intercept for taxon through the random argument and the fs basis also includes a random intercept term for taxon. As you have included the same variable in the model twice, the model has no way of knowing how to apportion variance in the response between these terms. This will often cause estimation problems and even if the models fit OK, you will likely have larger standard errors than if you didn't have the identifiability problem.

    \n
    4. \n

  4. You will have to explain what you are trying or aiming to do rather than show what you did and ask if it is OK; it is not clear what the aim of the analysis, what model you are trying to fit, or how the data are structured, etc. (what is To Fa for example?).

    \n
    5. \n
\n

Unless you think the mean of Asfc for individual taxa changes over time smoothly, then there is no reason to use the taxon specific fs smooths. The random effect structure you propose seems reasonable, except I'm unclear from your description if you have multiple observations of Asfc per Facet? Or is facet informative in some way (inside vs top surface for example). If you don't have multiple observations per facet, you don't need the lowermost level in your ranef structure I believe. If individual taxa have different mean values of complexity (which I understand to be true broadly, but perhaps not in your specific group of taxa) then I think you do need Taxon at the highest level of the random effect structure.

\n

Finally, your model assume that the response Acsf values are conditional distributed Gaussian, meaning any value, negative or positive, is possible. If it is measuring complexity, that implies to me that negative values of the response are not observable, which would suggest the Gaussian is not appropriate. But perhaps this is not the case; the partial residuals don't look too bad, but proper model diagnostics would be need to confirm this. You also might need to consider the problem of temporal autocorrelation, although the Age smooth will help with that to some extent.

\n
\n

As an aside, how do I only plot the first plot?

\n
\n

Use the select argument to gratia' draw() function. This is a generic function so you need to look at the help for the gam method.

\n", "answer_id": 676895, "answer_text": "I would suggest you look at a changing a couple of things:\n\n\n\n\n\n\n\nThe distribution of Age is quite skewed, with some data squished up around 0 age. I would suggest trying to spread these values by out transforming Age, say via a square root transformation.\n\n\n\n\nIf you look at the smooth of Age, most of the smooth is supported by by a few unique time points - the whole right hand side of the plot. Those unique ages are having a potentially bigger influence on the shape of the function than the ages that are all squished up at the left of the x axis. Spreading out the ages allows all the data to influence the smooth more evenly. You can still present the results on the Age scale, What we want to avoid is unnecessary wiggles because the smooth adapted to widely spaced values on the original scale.\n\n\n\n\n\n\n\n\n\nThe fs smooths by Taxon aren't really doing much because they are very restricted in terms of basis functions.\n\n\n\n\n\n\n\n\n\nThere is potential for an identifiability issue as you include a Taxon random intercept through the fs smooths, and then again through the ranef structure.\n\n\n\n\nIdentifiability refers to the model's ability to unique identify (estimate a value for) each parameter in the model. You are including a random intercept for taxon through the random argument and the fs basis also includes a random intercept term for taxon. As you have included the same variable in the model twice, the model has no way of knowing how to apportion variance in the response between these terms. This will often cause estimation problems and even if the models fit OK, you will likely have larger standard errors than if you didn't have the identifiability problem.\n\n\n\n\n\n\n\n\n\nYou will have to explain what you are trying or aiming to do rather than show what you did and ask if it is OK; it is not clear what the aim of the analysis, what model you are trying to fit, or how the data are structured, etc. (what is To Fa for example?).\n\n\n\n\n\n\n\n\nUnless you think the mean of Asfc for individual taxa changes over time smoothly, then there is no reason to use the taxon specific fs smooths. The random effect structure you propose seems reasonable, except I'm unclear from your description if you have multiple observations of Asfc per Facet? Or is facet informative in some way (inside vs top surface for example). If you don't have multiple observations per facet, you don't need the lowermost level in your ranef structure I believe. If individual taxa have different mean values of complexity (which I understand to be true broadly, but perhaps not in your specific group of taxa) then I think you do need Taxon at the highest level of the random effect structure.\n\n\n\n\nFinally, your model assume that the response Acsf values are conditional distributed Gaussian, meaning any value, negative or positive, is possible. If it is measuring complexity, that implies to me that negative values of the response are not observable, which would suggest the Gaussian is not appropriate. But perhaps this is not the case; the partial residuals don't look too bad, but proper model diagnostics would be need to confirm this. You also might need to consider the problem of temporal autocorrelation, although the Age smooth will help with that to some extent.\n\n\n\n\n\n\n\nAs an aside, how do I only plot the first plot?\n\n\n\n\n\n\n\nUse the select argument to gratia' draw() function. This is a generic function so you need to look at the help for the gam method (https://gavinsimpson.github.io/gratia/reference/draw.gam.html).", "answer_url": "https://stats.stackexchange.com/a/676895", "author": "Gavin Simpson", "author_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-17T09:31:11+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676893, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Gavin Simpson", "profile_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "user_type": "registered"}, "created_at": "2026-08-17T09:31:11+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "344FFDF7-D995-42B0-B0C3-7BDBCFF41311", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/344FFDF7-D995-42B0-B0C3-7BDBCFF41311/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Gavin Simpson", "profile_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "user_type": "registered"}, "created_at": "2026-08-18T07:38:43+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "7758802C-386E-40D4-A5C5-B896DDCE2569", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/7758802C-386E-40D4-A5C5-B896DDCE2569/view-source"}], "score": 5, "updated_at": "2026-08-18T07:38:43+00:00"}], "domain": "statistics", "external_links": ["https://gavinsimpson.github.io/gratia/reference/draw.gam.html", "https://i.sstatic.net/H3mCUZgO.jpg", "https://i.sstatic.net/IXmEOkWk.jpg", "https://i.sstatic.net/KnHUkWbG.jpg", "https://i.sstatic.net/M6wP2hpB.jpg", "https://i.sstatic.net/UmccNppE.jpg", "https://i.sstatic.net/gYiJQdTI.jpg", "https://i.sstatic.net/iV7wvyRj.jpg"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "MrSwaggins", "question_author_url": "https://stats.stackexchange.com/users/331950/mrswaggins", "question_author_user_type": "registered", "question_created_at": "2026-08-17T05:08:58+00:00", "question_html": "

I have ~1400 measurements of teeth from ~40 species (taxon) that go back in time ~35mya (Age).\nThe data is noisy, so there is repetition in measurements from specimens that requires nesting as a random effect.

\n

I wish to see if there are trends in this data through time. I can see the trends as individual taxon boxplots if I roughly order them by time, but I would highly prefer Age as a continuous variable and the repetition accounted for.

\n

The problem is that taxa (i.e. species) generally exist for 1my or less, and there are large gaps, so if I understand gamms properly (not a given here lol) then the smoothing splines will be (in my simple terms) trying to extrapolate/estimate the curves for a species across the entire dataset where they don't really exist. I have tried to compensate for this using factor smoothing for taxon.

\n

To cut to the point after much testing and fiddling, I came up with this:

\n
temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs = "tp") + s(Age, taxon, bs = "fs", k = 3), data = df, random = ~(1|taxon/Specimen/To/Fa))\ntemp4 <- gamm4(Asfc ~ s(Age, k = 8, bs = "tp") + s(Age, taxon, bs = "fs", k = 3), data = df, random = ~(1|Specimen/To/Fa))\ndraw(temp3$gam, residuals = TRUE)\n
\n

And I get something like this:\n\"gamm4

\n

For this data am I "gamm-ing" correctly? The second plot suggests errr no, or is that just the intercept and slope for taxon influence?

\n

Should taxon be in the random effect structure? There are many specimens of each taxon.

\n

As an aside, how do I only plot the first plot?

\n

------ Edit for clarification from questions (and comments) below ------

\n

Each measurement is in this example a "complexity" value of a single facet (Fa has four levels), from a tooth (To has 8 levels). There are 1 to 8 measurements per Specimen requiring it to be a random effect. Each Specimen does belong to a species, though Species may or may not require nesting, or inclusion in the model per se, since most species have a single value for age, or are spread over 0.5 million years at most, it is highly correlated to Age and may be superfluous. Asfc is continuous, well normalised, and is considered gaussian.

\n

This is an updated model with model check based on comments : gamm4(Asfc ~ s(sqrtAge, k = 8, bs ="tp"), data = df, random = ~(1|Specimen/ToothNoLR/Facet))\n\"newGamm\"

\n

\"checkgamm\"

\n

RE check_model() I'm doing this to look for verifiable trends, not for prediction. I realise the large gaps would make the latter difficult, so this is more exploratory to see if a signal is present.

\n
$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3606.394\nRandom effects:\n Groups                   Name         Std.Dev.\n Facet:ToothNoLR:Specimen (Intercept)  0.4767  \n ToothNoLR:Specimen       (Intercept)  0.3814  \n Specimen                 (Intercept)  0.6024  \n Xr                       s(sqrt(Age)) 7.7972  \n Residual                              0.4563  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen, 1430; ToothNoLR:Specimen, 542; Specimen, 421; Xr, 6\nFixed Effects:\n    X(Intercept)  Xs(sqrt(Age))Fx1  \n        0.008243         -0.872465  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n5.56  total = 6.56 \n\nlmer.REML score: 3606.394     \n\nattr(,"class")\n[1] "gamm4" "list" \n
\n

------ 2nd edit updating random effect structure ------\nHere is the model with taxon added. The CI's are worse, but I suspect it is a "truer" model. gamm4(Asfc ~ s(sqrt(Age), k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))

\n

\"REtaxonadded\"

\n

The check shows a more even spread of residuals.

\n

\"retaxoncheck\"

\n

These are the new results.

\n
> temp3 <- gamm4(Asfc ~ s(sqrt(Age), k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.052\nRandom effects:\n Groups                         Name         Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept)  0.4786  \n ToothNoLR:Specimen:taxon       (Intercept)  0.3614  \n Specimen:taxon                 (Intercept)  0.5246  \n taxon                          (Intercept)  0.4379  \n Xr                             s(sqrt(Age)) 4.5753  \n Residual                                    0.4561  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\n    X(Intercept)  Xs(sqrt(Age))Fx1  \n        -0.04013          -0.01014  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n4.3  total = 5.3 \n\nlmer.REML score: 3566.053\n
\n

Compare them to the results where Age is not sqrt()'ed

\n
> temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.762\nRandom effects:\n Groups                         Name        Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4651  \n ToothNoLR:Specimen:taxon       (Intercept) 0.3611  \n Specimen:taxon                 (Intercept) 0.5317  \n taxon                          (Intercept) 0.3790  \n Xr                             s(Age)      7.4438  \n Residual                                   0.4692  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\nX(Intercept)    Xs(Age)Fx1  \n    -0.04286      -0.98535  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(Age, k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n4.77  total = 5.77 \n\nlmer.REML score: 3566.762 \n
\n

I would appreciate any help in interpreting all this.

\n

------ Edit ------\nIn reply to the posterior predictive check. Removal of Facet.\n\"enter\ntemp3 without Facet in nesting, temp4 with Facet in nesting.

\n
> compare_performance(temp3, temp4)\n# Comparison of Model Performance Indices\n\nName  | Model |  AIC (weights) |  BIC (weights) |    R2 |  RMSE | Sigma\n-----------------------------------------------------------------------\ntemp3 | gamm4 | 4031.8 (0.475) | 4065.0 (0.484) | 0.049 | 0.572 | 0.573\ntemp4 | gamm4 | 4031.6 (0.525) | 4064.8 (0.516) | 0.049 | 0.274 | 0.275\n
\n

------ quick edit ------\nSo, yes, when I check $mer I get these results, and it appears to be(?), the missing "components" to complete the response?:

\n
> model_performance(temp3$mer)\n# Indices of model performance\n\nAIC    |   AICc |    BIC | R2 (cond.) | R2 (marg.) |   ICC |  RMSE | Sigma\n--------------------------------------------------------------------------\n3581.9 | 3582.0 | 3618.9 |      0.579 |  1.298e-04 | 0.579 | 0.572 | 0.660\n\n> icc(temp3$mer, by_group = TRUE)\n\nGroup                    |   ICC\n--------------------------------\nToothNoLR:Specimen:taxon | 0.127\nSpecimen:taxon           | 0.267\ntaxon                    | 0.185\n> check_model(temp3$mer)\n
\n

Just the lmer component predictive curve.\n\"enter

\n

> check_model(temp3) Throws an error, so it seems it is incapable of incorporating both $mer and $gam into the check.

\n", "question_id": 676893, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "I have ~1400 measurements of teeth from ~40 species (taxon) that go back in time ~35mya (Age).\nThe data is noisy, so there is repetition in measurements from specimens that requires nesting as a random effect.\n\n\n\n\nI wish to see if there are trends in this data through time. I can see the trends as individual taxon boxplots if I roughly order them by time, but I would highly prefer Age as a continuous variable and the repetition accounted for.\n\n\n\n\nThe problem is that taxa (i.e. species) generally exist for 1my or less, and there are large gaps, so if I understand gamms properly (not a given here lol) then the smoothing splines will be (in my simple terms) trying to extrapolate/estimate the curves for a species across the entire dataset where they don't really exist. I have tried to compensate for this using factor smoothing for taxon.\n\n\n\n\nTo cut to the point after much testing and fiddling, I came up with this:\n\n\n\n\ntemp3 <- gamm4(Asfc ~ s(Age, k = 8, bs = \"tp\") + s(Age, taxon, bs = \"fs\", k = 3), data = df, random = ~(1|taxon/Specimen/To/Fa))\ntemp4 <- gamm4(Asfc ~ s(Age, k = 8, bs = \"tp\") + s(Age, taxon, bs = \"fs\", k = 3), data = df, random = ~(1|Specimen/To/Fa))\ndraw(temp3$gam, residuals = TRUE)\n\n\n\n\n\nAnd I get something like this:\n[image: gamm4 plot; source: https://i.sstatic.net/M6wP2hpB.jpg] (https://i.sstatic.net/M6wP2hpB.jpg)\n\n\n\n\nFor this data am I \"gamm-ing\" correctly? The second plot suggests errr no, or is that just the intercept and slope for taxon influence?\n\n\n\n\nShould taxon be in the random effect structure? There are many specimens of each taxon.\n\n\n\n\nAs an aside, how do I only plot the first plot?\n\n\n\n\n------ Edit for clarification from questions (and comments) below ------\n\n\n\n\nEach measurement is in this example a \"complexity\" value of a single facet (Fa has four levels), from a tooth (To has 8 levels). There are 1 to 8 measurements per Specimen requiring it to be a random effect. Each Specimen does belong to a species, though Species may or may not require nesting, or inclusion in the model per se, since most species have a single value for age, or are spread over 0.5 million years at most, it is highly correlated to Age and may be superfluous. Asfc is continuous, well normalised, and is considered gaussian.\n\n\n\n\nThis is an updated model with model check based on comments : gamm4(Asfc ~ s(sqrtAge, k = 8, bs =\"tp\"), data = df, random = ~(1|Specimen/ToothNoLR/Facet))\n[image: newGamm; source: https://i.sstatic.net/UmccNppE.jpg] (https://i.sstatic.net/UmccNppE.jpg)\n\n\n\n\n[image: checkgamm; source: https://i.sstatic.net/gYiJQdTI.jpg] (https://i.sstatic.net/gYiJQdTI.jpg)\n\n\n\n\nRE check_model() I'm doing this to look for verifiable trends, not for prediction. I realise the large gaps would make the latter difficult, so this is more exploratory to see if a signal is present.\n\n\n\n\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3606.394\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen (Intercept) 0.4767 \n ToothNoLR:Specimen (Intercept) 0.3814 \n Specimen (Intercept) 0.6024 \n Xr s(sqrt(Age)) 7.7972 \n Residual 0.4563 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen, 1430; ToothNoLR:Specimen, 542; Specimen, 421; Xr, 6\nFixed Effects:\n X(Intercept) Xs(sqrt(Age))Fx1 \n 0.008243 -0.872465 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n5.56 total = 6.56 \n\nlmer.REML score: 3606.394 \n\nattr(,\"class\")\n[1] \"gamm4\" \"list\" \n\n\n\n\n\n------ 2nd edit updating random effect structure ------\nHere is the model with taxon added. The CI's are worse, but I suspect it is a \"truer\" model. gamm4(Asfc ~ s(sqrt(Age), k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n\n\n\n\n[image: REtaxonadded; source: https://i.sstatic.net/KnHUkWbG.jpg] (https://i.sstatic.net/KnHUkWbG.jpg)\n\n\n\n\nThe check shows a more even spread of residuals.\n\n\n\n\n[image: retaxoncheck; source: https://i.sstatic.net/IXmEOkWk.jpg] (https://i.sstatic.net/IXmEOkWk.jpg)\n\n\n\n\nThese are the new results.\n\n\n\n\n> temp3 <- gamm4(Asfc ~ s(sqrt(Age), k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.052\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4786 \n ToothNoLR:Specimen:taxon (Intercept) 0.3614 \n Specimen:taxon (Intercept) 0.5246 \n taxon (Intercept) 0.4379 \n Xr s(sqrt(Age)) 4.5753 \n Residual 0.4561 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\n X(Intercept) Xs(sqrt(Age))Fx1 \n -0.04013 -0.01014 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n4.3 total = 5.3 \n\nlmer.REML score: 3566.053\n\n\n\n\n\nCompare them to the results where Age is not sqrt()'ed\n\n\n\n\n> temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.762\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4651 \n ToothNoLR:Specimen:taxon (Intercept) 0.3611 \n Specimen:taxon (Intercept) 0.5317 \n taxon (Intercept) 0.3790 \n Xr s(Age) 7.4438 \n Residual 0.4692 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\nX(Intercept) Xs(Age)Fx1 \n -0.04286 -0.98535 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(Age, k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n4.77 total = 5.77 \n\nlmer.REML score: 3566.762 \n\n\n\n\n\nI would appreciate any help in interpreting all this.\n\n\n\n\n------ Edit ------\nIn reply to the posterior predictive check. Removal of Facet.\n[image: enter image description here; source: https://i.sstatic.net/iV7wvyRj.jpg] (https://i.sstatic.net/iV7wvyRj.jpg)\ntemp3 without Facet in nesting, temp4 with Facet in nesting.\n\n\n\n\n> compare_performance(temp3, temp4)\n# Comparison of Model Performance Indices\n\nName | Model | AIC (weights) | BIC (weights) | R2 | RMSE | Sigma\n-----------------------------------------------------------------------\ntemp3 | gamm4 | 4031.8 (0.475) | 4065.0 (0.484) | 0.049 | 0.572 | 0.573\ntemp4 | gamm4 | 4031.6 (0.525) | 4064.8 (0.516) | 0.049 | 0.274 | 0.275\n\n\n\n\n\n------ quick edit ------\nSo, yes, when I check $mer I get these results, and it appears to be(?), the missing \"components\" to complete the response?:\n\n\n\n\n> model_performance(temp3$mer)\n# Indices of model performance\n\nAIC | AICc | BIC | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma\n--------------------------------------------------------------------------\n3581.9 | 3582.0 | 3618.9 | 0.579 | 1.298e-04 | 0.579 | 0.572 | 0.660\n\n> icc(temp3$mer, by_group = TRUE)\n\nGroup | ICC\n--------------------------------\nToothNoLR:Specimen:taxon | 0.127\nSpecimen:taxon | 0.267\ntaxon | 0.185\n> check_model(temp3$mer)\n\n\n\n\n\nJust the lmer component predictive curve.\n[image: enter image description here; source: https://i.sstatic.net/H3mCUZgO.jpg] (https://i.sstatic.net/H3mCUZgO.jpg)\n\n\n\n\n> check_model(temp3) Throws an error, so it seems it is incapable of incorporating both $mer and $gam into the check.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MrSwaggins", "profile_url": "https://stats.stackexchange.com/users/331950/mrswaggins", "user_type": "registered"}, "created_at": "2026-08-17T05:08:58+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": 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"correctness_verified": false, "doi": null, "external_url": "https://i.sstatic.net/IXmEOkWk.jpg", "kind": "external_url", "post_id": 676893, "post_url": "https://stats.stackexchange.com/questions/676893/is-this-the-correct-specification-for-gamm4-splines-where-species-are-short-te", "product": "citations", "record_id": "Scientific-Citation-Graph:f92c8403e593c3c708b45095", "split": "test", "thread": {"accepted_answer_id": 676895, "answers": [{"answer_html": "

I would suggest you look at a changing a couple of things:

\n
    \n

  1. The distribution of Age is quite skewed, with some data squished up around 0 age. I would suggest trying to spread these values by out transforming Age, say via a square root transformation.

    \n

    If you look at the smooth of Age, most of the smooth is supported by by a few unique time points - the whole right hand side of the plot. Those unique ages are having a potentially bigger influence on the shape of the function than the ages that are all squished up at the left of the x axis. Spreading out the ages allows all the data to influence the smooth more evenly. You can still present the results on the Age scale, What we want to avoid is unnecessary wiggles because the smooth adapted to widely spaced values on the original scale.

    \n
    2. \n

  2. The fs smooths by Taxon aren't really doing much because they are very restricted in terms of basis functions.

    \n
    3. \n

  3. There is potential for an identifiability issue as you include a Taxon random intercept through the fs smooths, and then again through the ranef structure.

    \n

    Identifiability refers to the model's ability to unique identify (estimate a value for) each parameter in the model. You are including a random intercept for taxon through the random argument and the fs basis also includes a random intercept term for taxon. As you have included the same variable in the model twice, the model has no way of knowing how to apportion variance in the response between these terms. This will often cause estimation problems and even if the models fit OK, you will likely have larger standard errors than if you didn't have the identifiability problem.

    \n
    4. \n

  4. You will have to explain what you are trying or aiming to do rather than show what you did and ask if it is OK; it is not clear what the aim of the analysis, what model you are trying to fit, or how the data are structured, etc. (what is To Fa for example?).

    \n
    5. \n
\n

Unless you think the mean of Asfc for individual taxa changes over time smoothly, then there is no reason to use the taxon specific fs smooths. The random effect structure you propose seems reasonable, except I'm unclear from your description if you have multiple observations of Asfc per Facet? Or is facet informative in some way (inside vs top surface for example). If you don't have multiple observations per facet, you don't need the lowermost level in your ranef structure I believe. If individual taxa have different mean values of complexity (which I understand to be true broadly, but perhaps not in your specific group of taxa) then I think you do need Taxon at the highest level of the random effect structure.

\n

Finally, your model assume that the response Acsf values are conditional distributed Gaussian, meaning any value, negative or positive, is possible. If it is measuring complexity, that implies to me that negative values of the response are not observable, which would suggest the Gaussian is not appropriate. But perhaps this is not the case; the partial residuals don't look too bad, but proper model diagnostics would be need to confirm this. You also might need to consider the problem of temporal autocorrelation, although the Age smooth will help with that to some extent.

\n
\n

As an aside, how do I only plot the first plot?

\n
\n

Use the select argument to gratia' draw() function. This is a generic function so you need to look at the help for the gam method.

\n", "answer_id": 676895, "answer_text": "I would suggest you look at a changing a couple of things:\n\n\n\n\n\n\n\nThe distribution of Age is quite skewed, with some data squished up around 0 age. I would suggest trying to spread these values by out transforming Age, say via a square root transformation.\n\n\n\n\nIf you look at the smooth of Age, most of the smooth is supported by by a few unique time points - the whole right hand side of the plot. Those unique ages are having a potentially bigger influence on the shape of the function than the ages that are all squished up at the left of the x axis. Spreading out the ages allows all the data to influence the smooth more evenly. You can still present the results on the Age scale, What we want to avoid is unnecessary wiggles because the smooth adapted to widely spaced values on the original scale.\n\n\n\n\n\n\n\n\n\nThe fs smooths by Taxon aren't really doing much because they are very restricted in terms of basis functions.\n\n\n\n\n\n\n\n\n\nThere is potential for an identifiability issue as you include a Taxon random intercept through the fs smooths, and then again through the ranef structure.\n\n\n\n\nIdentifiability refers to the model's ability to unique identify (estimate a value for) each parameter in the model. You are including a random intercept for taxon through the random argument and the fs basis also includes a random intercept term for taxon. As you have included the same variable in the model twice, the model has no way of knowing how to apportion variance in the response between these terms. This will often cause estimation problems and even if the models fit OK, you will likely have larger standard errors than if you didn't have the identifiability problem.\n\n\n\n\n\n\n\n\n\nYou will have to explain what you are trying or aiming to do rather than show what you did and ask if it is OK; it is not clear what the aim of the analysis, what model you are trying to fit, or how the data are structured, etc. (what is To Fa for example?).\n\n\n\n\n\n\n\n\nUnless you think the mean of Asfc for individual taxa changes over time smoothly, then there is no reason to use the taxon specific fs smooths. The random effect structure you propose seems reasonable, except I'm unclear from your description if you have multiple observations of Asfc per Facet? Or is facet informative in some way (inside vs top surface for example). If you don't have multiple observations per facet, you don't need the lowermost level in your ranef structure I believe. If individual taxa have different mean values of complexity (which I understand to be true broadly, but perhaps not in your specific group of taxa) then I think you do need Taxon at the highest level of the random effect structure.\n\n\n\n\nFinally, your model assume that the response Acsf values are conditional distributed Gaussian, meaning any value, negative or positive, is possible. If it is measuring complexity, that implies to me that negative values of the response are not observable, which would suggest the Gaussian is not appropriate. But perhaps this is not the case; the partial residuals don't look too bad, but proper model diagnostics would be need to confirm this. You also might need to consider the problem of temporal autocorrelation, although the Age smooth will help with that to some extent.\n\n\n\n\n\n\n\nAs an aside, how do I only plot the first plot?\n\n\n\n\n\n\n\nUse the select argument to gratia' draw() function. This is a generic function so you need to look at the help for the gam method (https://gavinsimpson.github.io/gratia/reference/draw.gam.html).", "answer_url": "https://stats.stackexchange.com/a/676895", "author": "Gavin Simpson", "author_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-17T09:31:11+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676893, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Gavin Simpson", "profile_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "user_type": "registered"}, "created_at": "2026-08-17T09:31:11+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "344FFDF7-D995-42B0-B0C3-7BDBCFF41311", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/344FFDF7-D995-42B0-B0C3-7BDBCFF41311/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Gavin Simpson", "profile_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "user_type": "registered"}, "created_at": "2026-08-18T07:38:43+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "7758802C-386E-40D4-A5C5-B896DDCE2569", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/7758802C-386E-40D4-A5C5-B896DDCE2569/view-source"}], "score": 5, "updated_at": "2026-08-18T07:38:43+00:00"}], "domain": "statistics", "external_links": ["https://gavinsimpson.github.io/gratia/reference/draw.gam.html", "https://i.sstatic.net/H3mCUZgO.jpg", "https://i.sstatic.net/IXmEOkWk.jpg", "https://i.sstatic.net/KnHUkWbG.jpg", "https://i.sstatic.net/M6wP2hpB.jpg", "https://i.sstatic.net/UmccNppE.jpg", "https://i.sstatic.net/gYiJQdTI.jpg", "https://i.sstatic.net/iV7wvyRj.jpg"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "MrSwaggins", "question_author_url": "https://stats.stackexchange.com/users/331950/mrswaggins", "question_author_user_type": "registered", "question_created_at": "2026-08-17T05:08:58+00:00", "question_html": "

I have ~1400 measurements of teeth from ~40 species (taxon) that go back in time ~35mya (Age).\nThe data is noisy, so there is repetition in measurements from specimens that requires nesting as a random effect.

\n

I wish to see if there are trends in this data through time. I can see the trends as individual taxon boxplots if I roughly order them by time, but I would highly prefer Age as a continuous variable and the repetition accounted for.

\n

The problem is that taxa (i.e. species) generally exist for 1my or less, and there are large gaps, so if I understand gamms properly (not a given here lol) then the smoothing splines will be (in my simple terms) trying to extrapolate/estimate the curves for a species across the entire dataset where they don't really exist. I have tried to compensate for this using factor smoothing for taxon.

\n

To cut to the point after much testing and fiddling, I came up with this:

\n
temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs = "tp") + s(Age, taxon, bs = "fs", k = 3), data = df, random = ~(1|taxon/Specimen/To/Fa))\ntemp4 <- gamm4(Asfc ~ s(Age, k = 8, bs = "tp") + s(Age, taxon, bs = "fs", k = 3), data = df, random = ~(1|Specimen/To/Fa))\ndraw(temp3$gam, residuals = TRUE)\n
\n

And I get something like this:\n\"gamm4

\n

For this data am I "gamm-ing" correctly? The second plot suggests errr no, or is that just the intercept and slope for taxon influence?

\n

Should taxon be in the random effect structure? There are many specimens of each taxon.

\n

As an aside, how do I only plot the first plot?

\n

------ Edit for clarification from questions (and comments) below ------

\n

Each measurement is in this example a "complexity" value of a single facet (Fa has four levels), from a tooth (To has 8 levels). There are 1 to 8 measurements per Specimen requiring it to be a random effect. Each Specimen does belong to a species, though Species may or may not require nesting, or inclusion in the model per se, since most species have a single value for age, or are spread over 0.5 million years at most, it is highly correlated to Age and may be superfluous. Asfc is continuous, well normalised, and is considered gaussian.

\n

This is an updated model with model check based on comments : gamm4(Asfc ~ s(sqrtAge, k = 8, bs ="tp"), data = df, random = ~(1|Specimen/ToothNoLR/Facet))\n\"newGamm\"

\n

\"checkgamm\"

\n

RE check_model() I'm doing this to look for verifiable trends, not for prediction. I realise the large gaps would make the latter difficult, so this is more exploratory to see if a signal is present.

\n
$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3606.394\nRandom effects:\n Groups                   Name         Std.Dev.\n Facet:ToothNoLR:Specimen (Intercept)  0.4767  \n ToothNoLR:Specimen       (Intercept)  0.3814  \n Specimen                 (Intercept)  0.6024  \n Xr                       s(sqrt(Age)) 7.7972  \n Residual                              0.4563  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen, 1430; ToothNoLR:Specimen, 542; Specimen, 421; Xr, 6\nFixed Effects:\n    X(Intercept)  Xs(sqrt(Age))Fx1  \n        0.008243         -0.872465  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n5.56  total = 6.56 \n\nlmer.REML score: 3606.394     \n\nattr(,"class")\n[1] "gamm4" "list" \n
\n

------ 2nd edit updating random effect structure ------\nHere is the model with taxon added. The CI's are worse, but I suspect it is a "truer" model. gamm4(Asfc ~ s(sqrt(Age), k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))

\n

\"REtaxonadded\"

\n

The check shows a more even spread of residuals.

\n

\"retaxoncheck\"

\n

These are the new results.

\n
> temp3 <- gamm4(Asfc ~ s(sqrt(Age), k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.052\nRandom effects:\n Groups                         Name         Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept)  0.4786  \n ToothNoLR:Specimen:taxon       (Intercept)  0.3614  \n Specimen:taxon                 (Intercept)  0.5246  \n taxon                          (Intercept)  0.4379  \n Xr                             s(sqrt(Age)) 4.5753  \n Residual                                    0.4561  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\n    X(Intercept)  Xs(sqrt(Age))Fx1  \n        -0.04013          -0.01014  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n4.3  total = 5.3 \n\nlmer.REML score: 3566.053\n
\n

Compare them to the results where Age is not sqrt()'ed

\n
> temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.762\nRandom effects:\n Groups                         Name        Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4651  \n ToothNoLR:Specimen:taxon       (Intercept) 0.3611  \n Specimen:taxon                 (Intercept) 0.5317  \n taxon                          (Intercept) 0.3790  \n Xr                             s(Age)      7.4438  \n Residual                                   0.4692  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\nX(Intercept)    Xs(Age)Fx1  \n    -0.04286      -0.98535  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(Age, k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n4.77  total = 5.77 \n\nlmer.REML score: 3566.762 \n
\n

I would appreciate any help in interpreting all this.

\n

------ Edit ------\nIn reply to the posterior predictive check. Removal of Facet.\n\"enter\ntemp3 without Facet in nesting, temp4 with Facet in nesting.

\n
> compare_performance(temp3, temp4)\n# Comparison of Model Performance Indices\n\nName  | Model |  AIC (weights) |  BIC (weights) |    R2 |  RMSE | Sigma\n-----------------------------------------------------------------------\ntemp3 | gamm4 | 4031.8 (0.475) | 4065.0 (0.484) | 0.049 | 0.572 | 0.573\ntemp4 | gamm4 | 4031.6 (0.525) | 4064.8 (0.516) | 0.049 | 0.274 | 0.275\n
\n

------ quick edit ------\nSo, yes, when I check $mer I get these results, and it appears to be(?), the missing "components" to complete the response?:

\n
> model_performance(temp3$mer)\n# Indices of model performance\n\nAIC    |   AICc |    BIC | R2 (cond.) | R2 (marg.) |   ICC |  RMSE | Sigma\n--------------------------------------------------------------------------\n3581.9 | 3582.0 | 3618.9 |      0.579 |  1.298e-04 | 0.579 | 0.572 | 0.660\n\n> icc(temp3$mer, by_group = TRUE)\n\nGroup                    |   ICC\n--------------------------------\nToothNoLR:Specimen:taxon | 0.127\nSpecimen:taxon           | 0.267\ntaxon                    | 0.185\n> check_model(temp3$mer)\n
\n

Just the lmer component predictive curve.\n\"enter

\n

> check_model(temp3) Throws an error, so it seems it is incapable of incorporating both $mer and $gam into the check.

\n", "question_id": 676893, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "I have ~1400 measurements of teeth from ~40 species (taxon) that go back in time ~35mya (Age).\nThe data is noisy, so there is repetition in measurements from specimens that requires nesting as a random effect.\n\n\n\n\nI wish to see if there are trends in this data through time. I can see the trends as individual taxon boxplots if I roughly order them by time, but I would highly prefer Age as a continuous variable and the repetition accounted for.\n\n\n\n\nThe problem is that taxa (i.e. species) generally exist for 1my or less, and there are large gaps, so if I understand gamms properly (not a given here lol) then the smoothing splines will be (in my simple terms) trying to extrapolate/estimate the curves for a species across the entire dataset where they don't really exist. I have tried to compensate for this using factor smoothing for taxon.\n\n\n\n\nTo cut to the point after much testing and fiddling, I came up with this:\n\n\n\n\ntemp3 <- gamm4(Asfc ~ s(Age, k = 8, bs = \"tp\") + s(Age, taxon, bs = \"fs\", k = 3), data = df, random = ~(1|taxon/Specimen/To/Fa))\ntemp4 <- gamm4(Asfc ~ s(Age, k = 8, bs = \"tp\") + s(Age, taxon, bs = \"fs\", k = 3), data = df, random = ~(1|Specimen/To/Fa))\ndraw(temp3$gam, residuals = TRUE)\n\n\n\n\n\nAnd I get something like this:\n[image: gamm4 plot; source: https://i.sstatic.net/M6wP2hpB.jpg] (https://i.sstatic.net/M6wP2hpB.jpg)\n\n\n\n\nFor this data am I \"gamm-ing\" correctly? The second plot suggests errr no, or is that just the intercept and slope for taxon influence?\n\n\n\n\nShould taxon be in the random effect structure? There are many specimens of each taxon.\n\n\n\n\nAs an aside, how do I only plot the first plot?\n\n\n\n\n------ Edit for clarification from questions (and comments) below ------\n\n\n\n\nEach measurement is in this example a \"complexity\" value of a single facet (Fa has four levels), from a tooth (To has 8 levels). There are 1 to 8 measurements per Specimen requiring it to be a random effect. Each Specimen does belong to a species, though Species may or may not require nesting, or inclusion in the model per se, since most species have a single value for age, or are spread over 0.5 million years at most, it is highly correlated to Age and may be superfluous. Asfc is continuous, well normalised, and is considered gaussian.\n\n\n\n\nThis is an updated model with model check based on comments : gamm4(Asfc ~ s(sqrtAge, k = 8, bs =\"tp\"), data = df, random = ~(1|Specimen/ToothNoLR/Facet))\n[image: newGamm; source: https://i.sstatic.net/UmccNppE.jpg] (https://i.sstatic.net/UmccNppE.jpg)\n\n\n\n\n[image: checkgamm; source: https://i.sstatic.net/gYiJQdTI.jpg] (https://i.sstatic.net/gYiJQdTI.jpg)\n\n\n\n\nRE check_model() I'm doing this to look for verifiable trends, not for prediction. I realise the large gaps would make the latter difficult, so this is more exploratory to see if a signal is present.\n\n\n\n\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3606.394\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen (Intercept) 0.4767 \n ToothNoLR:Specimen (Intercept) 0.3814 \n Specimen (Intercept) 0.6024 \n Xr s(sqrt(Age)) 7.7972 \n Residual 0.4563 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen, 1430; ToothNoLR:Specimen, 542; Specimen, 421; Xr, 6\nFixed Effects:\n X(Intercept) Xs(sqrt(Age))Fx1 \n 0.008243 -0.872465 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n5.56 total = 6.56 \n\nlmer.REML score: 3606.394 \n\nattr(,\"class\")\n[1] \"gamm4\" \"list\" \n\n\n\n\n\n------ 2nd edit updating random effect structure ------\nHere is the model with taxon added. The CI's are worse, but I suspect it is a \"truer\" model. gamm4(Asfc ~ s(sqrt(Age), k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n\n\n\n\n[image: REtaxonadded; source: https://i.sstatic.net/KnHUkWbG.jpg] (https://i.sstatic.net/KnHUkWbG.jpg)\n\n\n\n\nThe check shows a more even spread of residuals.\n\n\n\n\n[image: retaxoncheck; source: https://i.sstatic.net/IXmEOkWk.jpg] (https://i.sstatic.net/IXmEOkWk.jpg)\n\n\n\n\nThese are the new results.\n\n\n\n\n> temp3 <- gamm4(Asfc ~ s(sqrt(Age), k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.052\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4786 \n ToothNoLR:Specimen:taxon (Intercept) 0.3614 \n Specimen:taxon (Intercept) 0.5246 \n taxon (Intercept) 0.4379 \n Xr s(sqrt(Age)) 4.5753 \n Residual 0.4561 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\n X(Intercept) Xs(sqrt(Age))Fx1 \n -0.04013 -0.01014 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n4.3 total = 5.3 \n\nlmer.REML score: 3566.053\n\n\n\n\n\nCompare them to the results where Age is not sqrt()'ed\n\n\n\n\n> temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.762\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4651 \n ToothNoLR:Specimen:taxon (Intercept) 0.3611 \n Specimen:taxon (Intercept) 0.5317 \n taxon (Intercept) 0.3790 \n Xr s(Age) 7.4438 \n Residual 0.4692 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\nX(Intercept) Xs(Age)Fx1 \n -0.04286 -0.98535 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(Age, k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n4.77 total = 5.77 \n\nlmer.REML score: 3566.762 \n\n\n\n\n\nI would appreciate any help in interpreting all this.\n\n\n\n\n------ Edit ------\nIn reply to the posterior predictive check. Removal of Facet.\n[image: enter image description here; source: https://i.sstatic.net/iV7wvyRj.jpg] (https://i.sstatic.net/iV7wvyRj.jpg)\ntemp3 without Facet in nesting, temp4 with Facet in nesting.\n\n\n\n\n> compare_performance(temp3, temp4)\n# Comparison of Model Performance Indices\n\nName | Model | AIC (weights) | BIC (weights) | R2 | RMSE | Sigma\n-----------------------------------------------------------------------\ntemp3 | gamm4 | 4031.8 (0.475) | 4065.0 (0.484) | 0.049 | 0.572 | 0.573\ntemp4 | gamm4 | 4031.6 (0.525) | 4064.8 (0.516) | 0.049 | 0.274 | 0.275\n\n\n\n\n\n------ quick edit ------\nSo, yes, when I check $mer I get these results, and it appears to be(?), the missing \"components\" to complete the response?:\n\n\n\n\n> model_performance(temp3$mer)\n# Indices of model performance\n\nAIC | AICc | BIC | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma\n--------------------------------------------------------------------------\n3581.9 | 3582.0 | 3618.9 | 0.579 | 1.298e-04 | 0.579 | 0.572 | 0.660\n\n> icc(temp3$mer, by_group = TRUE)\n\nGroup | ICC\n--------------------------------\nToothNoLR:Specimen:taxon | 0.127\nSpecimen:taxon | 0.267\ntaxon | 0.185\n> check_model(temp3$mer)\n\n\n\n\n\nJust the lmer component predictive curve.\n[image: enter image description here; source: https://i.sstatic.net/H3mCUZgO.jpg] (https://i.sstatic.net/H3mCUZgO.jpg)\n\n\n\n\n> check_model(temp3) Throws an error, so it seems it is incapable of incorporating both $mer and $gam into the check.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MrSwaggins", "profile_url": "https://stats.stackexchange.com/users/331950/mrswaggins", "user_type": "registered"}, "created_at": "2026-08-17T05:08:58+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": 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"revision_url": "https://stats.stackexchange.com/revisions/8D79A3B0-2AE6-4E89-94B4-B4BB66830EE2/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676893/is-this-the-correct-specification-for-gamm4-splines-where-species-are-short-te", "split": "test", "split_group": "61409f7f49db16a90eedb3018c6f3602d4fb05c1b06859ec9e29c98cb27d345b", "tags": ["time-series", "lme4-nlme", "trend", "gamm4"], "thread_id": "stats:676893", "title": "Is this the correct specification for gamm4() splines where Species are short term, but time period is very long?"}} {"citation_context": " =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n\n\n\n\n[image: REtaxonadded; source: https://i.sstatic.net/KnHUkWbG.jpg] (https://i.sstatic.net/KnHUkWbG.jpg)\n\n\n\n\nThe check shows a more even spread of residuals.\n\n\n\n\n[ima", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://i.sstatic.net/KnHUkWbG.jpg", "kind": "external_url", "post_id": 676893, "post_url": "https://stats.stackexchange.com/questions/676893/is-this-the-correct-specification-for-gamm4-splines-where-species-are-short-te", "product": "citations", "record_id": "Scientific-Citation-Graph:ed7bc6f9e144eb6daeec1574", "split": "test", "thread": {"accepted_answer_id": 676895, "answers": [{"answer_html": "

I would suggest you look at a changing a couple of things:

\n
    \n

  1. The distribution of Age is quite skewed, with some data squished up around 0 age. I would suggest trying to spread these values by out transforming Age, say via a square root transformation.

    \n

    If you look at the smooth of Age, most of the smooth is supported by by a few unique time points - the whole right hand side of the plot. Those unique ages are having a potentially bigger influence on the shape of the function than the ages that are all squished up at the left of the x axis. Spreading out the ages allows all the data to influence the smooth more evenly. You can still present the results on the Age scale, What we want to avoid is unnecessary wiggles because the smooth adapted to widely spaced values on the original scale.

    \n
    2. \n

  2. The fs smooths by Taxon aren't really doing much because they are very restricted in terms of basis functions.

    \n
    3. \n

  3. There is potential for an identifiability issue as you include a Taxon random intercept through the fs smooths, and then again through the ranef structure.

    \n

    Identifiability refers to the model's ability to unique identify (estimate a value for) each parameter in the model. You are including a random intercept for taxon through the random argument and the fs basis also includes a random intercept term for taxon. As you have included the same variable in the model twice, the model has no way of knowing how to apportion variance in the response between these terms. This will often cause estimation problems and even if the models fit OK, you will likely have larger standard errors than if you didn't have the identifiability problem.

    \n
    4. \n

  4. You will have to explain what you are trying or aiming to do rather than show what you did and ask if it is OK; it is not clear what the aim of the analysis, what model you are trying to fit, or how the data are structured, etc. (what is To Fa for example?).

    \n
    5. \n
\n

Unless you think the mean of Asfc for individual taxa changes over time smoothly, then there is no reason to use the taxon specific fs smooths. The random effect structure you propose seems reasonable, except I'm unclear from your description if you have multiple observations of Asfc per Facet? Or is facet informative in some way (inside vs top surface for example). If you don't have multiple observations per facet, you don't need the lowermost level in your ranef structure I believe. If individual taxa have different mean values of complexity (which I understand to be true broadly, but perhaps not in your specific group of taxa) then I think you do need Taxon at the highest level of the random effect structure.

\n

Finally, your model assume that the response Acsf values are conditional distributed Gaussian, meaning any value, negative or positive, is possible. If it is measuring complexity, that implies to me that negative values of the response are not observable, which would suggest the Gaussian is not appropriate. But perhaps this is not the case; the partial residuals don't look too bad, but proper model diagnostics would be need to confirm this. You also might need to consider the problem of temporal autocorrelation, although the Age smooth will help with that to some extent.

\n
\n

As an aside, how do I only plot the first plot?

\n
\n

Use the select argument to gratia' draw() function. This is a generic function so you need to look at the help for the gam method.

\n", "answer_id": 676895, "answer_text": "I would suggest you look at a changing a couple of things:\n\n\n\n\n\n\n\nThe distribution of Age is quite skewed, with some data squished up around 0 age. I would suggest trying to spread these values by out transforming Age, say via a square root transformation.\n\n\n\n\nIf you look at the smooth of Age, most of the smooth is supported by by a few unique time points - the whole right hand side of the plot. Those unique ages are having a potentially bigger influence on the shape of the function than the ages that are all squished up at the left of the x axis. Spreading out the ages allows all the data to influence the smooth more evenly. You can still present the results on the Age scale, What we want to avoid is unnecessary wiggles because the smooth adapted to widely spaced values on the original scale.\n\n\n\n\n\n\n\n\n\nThe fs smooths by Taxon aren't really doing much because they are very restricted in terms of basis functions.\n\n\n\n\n\n\n\n\n\nThere is potential for an identifiability issue as you include a Taxon random intercept through the fs smooths, and then again through the ranef structure.\n\n\n\n\nIdentifiability refers to the model's ability to unique identify (estimate a value for) each parameter in the model. You are including a random intercept for taxon through the random argument and the fs basis also includes a random intercept term for taxon. As you have included the same variable in the model twice, the model has no way of knowing how to apportion variance in the response between these terms. This will often cause estimation problems and even if the models fit OK, you will likely have larger standard errors than if you didn't have the identifiability problem.\n\n\n\n\n\n\n\n\n\nYou will have to explain what you are trying or aiming to do rather than show what you did and ask if it is OK; it is not clear what the aim of the analysis, what model you are trying to fit, or how the data are structured, etc. (what is To Fa for example?).\n\n\n\n\n\n\n\n\nUnless you think the mean of Asfc for individual taxa changes over time smoothly, then there is no reason to use the taxon specific fs smooths. The random effect structure you propose seems reasonable, except I'm unclear from your description if you have multiple observations of Asfc per Facet? Or is facet informative in some way (inside vs top surface for example). If you don't have multiple observations per facet, you don't need the lowermost level in your ranef structure I believe. If individual taxa have different mean values of complexity (which I understand to be true broadly, but perhaps not in your specific group of taxa) then I think you do need Taxon at the highest level of the random effect structure.\n\n\n\n\nFinally, your model assume that the response Acsf values are conditional distributed Gaussian, meaning any value, negative or positive, is possible. If it is measuring complexity, that implies to me that negative values of the response are not observable, which would suggest the Gaussian is not appropriate. But perhaps this is not the case; the partial residuals don't look too bad, but proper model diagnostics would be need to confirm this. You also might need to consider the problem of temporal autocorrelation, although the Age smooth will help with that to some extent.\n\n\n\n\n\n\n\nAs an aside, how do I only plot the first plot?\n\n\n\n\n\n\n\nUse the select argument to gratia' draw() function. This is a generic function so you need to look at the help for the gam method (https://gavinsimpson.github.io/gratia/reference/draw.gam.html).", "answer_url": "https://stats.stackexchange.com/a/676895", "author": "Gavin Simpson", "author_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-17T09:31:11+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676893, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Gavin Simpson", "profile_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "user_type": "registered"}, "created_at": "2026-08-17T09:31:11+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "344FFDF7-D995-42B0-B0C3-7BDBCFF41311", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/344FFDF7-D995-42B0-B0C3-7BDBCFF41311/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Gavin Simpson", "profile_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "user_type": "registered"}, "created_at": "2026-08-18T07:38:43+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "7758802C-386E-40D4-A5C5-B896DDCE2569", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/7758802C-386E-40D4-A5C5-B896DDCE2569/view-source"}], "score": 5, "updated_at": "2026-08-18T07:38:43+00:00"}], "domain": "statistics", "external_links": ["https://gavinsimpson.github.io/gratia/reference/draw.gam.html", "https://i.sstatic.net/H3mCUZgO.jpg", "https://i.sstatic.net/IXmEOkWk.jpg", "https://i.sstatic.net/KnHUkWbG.jpg", "https://i.sstatic.net/M6wP2hpB.jpg", "https://i.sstatic.net/UmccNppE.jpg", "https://i.sstatic.net/gYiJQdTI.jpg", "https://i.sstatic.net/iV7wvyRj.jpg"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "MrSwaggins", "question_author_url": "https://stats.stackexchange.com/users/331950/mrswaggins", "question_author_user_type": "registered", "question_created_at": "2026-08-17T05:08:58+00:00", "question_html": "

I have ~1400 measurements of teeth from ~40 species (taxon) that go back in time ~35mya (Age).\nThe data is noisy, so there is repetition in measurements from specimens that requires nesting as a random effect.

\n

I wish to see if there are trends in this data through time. I can see the trends as individual taxon boxplots if I roughly order them by time, but I would highly prefer Age as a continuous variable and the repetition accounted for.

\n

The problem is that taxa (i.e. species) generally exist for 1my or less, and there are large gaps, so if I understand gamms properly (not a given here lol) then the smoothing splines will be (in my simple terms) trying to extrapolate/estimate the curves for a species across the entire dataset where they don't really exist. I have tried to compensate for this using factor smoothing for taxon.

\n

To cut to the point after much testing and fiddling, I came up with this:

\n
temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs = "tp") + s(Age, taxon, bs = "fs", k = 3), data = df, random = ~(1|taxon/Specimen/To/Fa))\ntemp4 <- gamm4(Asfc ~ s(Age, k = 8, bs = "tp") + s(Age, taxon, bs = "fs", k = 3), data = df, random = ~(1|Specimen/To/Fa))\ndraw(temp3$gam, residuals = TRUE)\n
\n

And I get something like this:\n\"gamm4

\n

For this data am I "gamm-ing" correctly? The second plot suggests errr no, or is that just the intercept and slope for taxon influence?

\n

Should taxon be in the random effect structure? There are many specimens of each taxon.

\n

As an aside, how do I only plot the first plot?

\n

------ Edit for clarification from questions (and comments) below ------

\n

Each measurement is in this example a "complexity" value of a single facet (Fa has four levels), from a tooth (To has 8 levels). There are 1 to 8 measurements per Specimen requiring it to be a random effect. Each Specimen does belong to a species, though Species may or may not require nesting, or inclusion in the model per se, since most species have a single value for age, or are spread over 0.5 million years at most, it is highly correlated to Age and may be superfluous. Asfc is continuous, well normalised, and is considered gaussian.

\n

This is an updated model with model check based on comments : gamm4(Asfc ~ s(sqrtAge, k = 8, bs ="tp"), data = df, random = ~(1|Specimen/ToothNoLR/Facet))\n\"newGamm\"

\n

\"checkgamm\"

\n

RE check_model() I'm doing this to look for verifiable trends, not for prediction. I realise the large gaps would make the latter difficult, so this is more exploratory to see if a signal is present.

\n
$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3606.394\nRandom effects:\n Groups                   Name         Std.Dev.\n Facet:ToothNoLR:Specimen (Intercept)  0.4767  \n ToothNoLR:Specimen       (Intercept)  0.3814  \n Specimen                 (Intercept)  0.6024  \n Xr                       s(sqrt(Age)) 7.7972  \n Residual                              0.4563  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen, 1430; ToothNoLR:Specimen, 542; Specimen, 421; Xr, 6\nFixed Effects:\n    X(Intercept)  Xs(sqrt(Age))Fx1  \n        0.008243         -0.872465  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n5.56  total = 6.56 \n\nlmer.REML score: 3606.394     \n\nattr(,"class")\n[1] "gamm4" "list" \n
\n

------ 2nd edit updating random effect structure ------\nHere is the model with taxon added. The CI's are worse, but I suspect it is a "truer" model. gamm4(Asfc ~ s(sqrt(Age), k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))

\n

\"REtaxonadded\"

\n

The check shows a more even spread of residuals.

\n

\"retaxoncheck\"

\n

These are the new results.

\n
> temp3 <- gamm4(Asfc ~ s(sqrt(Age), k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.052\nRandom effects:\n Groups                         Name         Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept)  0.4786  \n ToothNoLR:Specimen:taxon       (Intercept)  0.3614  \n Specimen:taxon                 (Intercept)  0.5246  \n taxon                          (Intercept)  0.4379  \n Xr                             s(sqrt(Age)) 4.5753  \n Residual                                    0.4561  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\n    X(Intercept)  Xs(sqrt(Age))Fx1  \n        -0.04013          -0.01014  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n4.3  total = 5.3 \n\nlmer.REML score: 3566.053\n
\n

Compare them to the results where Age is not sqrt()'ed

\n
> temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.762\nRandom effects:\n Groups                         Name        Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4651  \n ToothNoLR:Specimen:taxon       (Intercept) 0.3611  \n Specimen:taxon                 (Intercept) 0.5317  \n taxon                          (Intercept) 0.3790  \n Xr                             s(Age)      7.4438  \n Residual                                   0.4692  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\nX(Intercept)    Xs(Age)Fx1  \n    -0.04286      -0.98535  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(Age, k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n4.77  total = 5.77 \n\nlmer.REML score: 3566.762 \n
\n

I would appreciate any help in interpreting all this.

\n

------ Edit ------\nIn reply to the posterior predictive check. Removal of Facet.\n\"enter\ntemp3 without Facet in nesting, temp4 with Facet in nesting.

\n
> compare_performance(temp3, temp4)\n# Comparison of Model Performance Indices\n\nName  | Model |  AIC (weights) |  BIC (weights) |    R2 |  RMSE | Sigma\n-----------------------------------------------------------------------\ntemp3 | gamm4 | 4031.8 (0.475) | 4065.0 (0.484) | 0.049 | 0.572 | 0.573\ntemp4 | gamm4 | 4031.6 (0.525) | 4064.8 (0.516) | 0.049 | 0.274 | 0.275\n
\n

------ quick edit ------\nSo, yes, when I check $mer I get these results, and it appears to be(?), the missing "components" to complete the response?:

\n
> model_performance(temp3$mer)\n# Indices of model performance\n\nAIC    |   AICc |    BIC | R2 (cond.) | R2 (marg.) |   ICC |  RMSE | Sigma\n--------------------------------------------------------------------------\n3581.9 | 3582.0 | 3618.9 |      0.579 |  1.298e-04 | 0.579 | 0.572 | 0.660\n\n> icc(temp3$mer, by_group = TRUE)\n\nGroup                    |   ICC\n--------------------------------\nToothNoLR:Specimen:taxon | 0.127\nSpecimen:taxon           | 0.267\ntaxon                    | 0.185\n> check_model(temp3$mer)\n
\n

Just the lmer component predictive curve.\n\"enter

\n

> check_model(temp3) Throws an error, so it seems it is incapable of incorporating both $mer and $gam into the check.

\n", "question_id": 676893, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "I have ~1400 measurements of teeth from ~40 species (taxon) that go back in time ~35mya (Age).\nThe data is noisy, so there is repetition in measurements from specimens that requires nesting as a random effect.\n\n\n\n\nI wish to see if there are trends in this data through time. I can see the trends as individual taxon boxplots if I roughly order them by time, but I would highly prefer Age as a continuous variable and the repetition accounted for.\n\n\n\n\nThe problem is that taxa (i.e. species) generally exist for 1my or less, and there are large gaps, so if I understand gamms properly (not a given here lol) then the smoothing splines will be (in my simple terms) trying to extrapolate/estimate the curves for a species across the entire dataset where they don't really exist. I have tried to compensate for this using factor smoothing for taxon.\n\n\n\n\nTo cut to the point after much testing and fiddling, I came up with this:\n\n\n\n\ntemp3 <- gamm4(Asfc ~ s(Age, k = 8, bs = \"tp\") + s(Age, taxon, bs = \"fs\", k = 3), data = df, random = ~(1|taxon/Specimen/To/Fa))\ntemp4 <- gamm4(Asfc ~ s(Age, k = 8, bs = \"tp\") + s(Age, taxon, bs = \"fs\", k = 3), data = df, random = ~(1|Specimen/To/Fa))\ndraw(temp3$gam, residuals = TRUE)\n\n\n\n\n\nAnd I get something like this:\n[image: gamm4 plot; source: https://i.sstatic.net/M6wP2hpB.jpg] (https://i.sstatic.net/M6wP2hpB.jpg)\n\n\n\n\nFor this data am I \"gamm-ing\" correctly? The second plot suggests errr no, or is that just the intercept and slope for taxon influence?\n\n\n\n\nShould taxon be in the random effect structure? There are many specimens of each taxon.\n\n\n\n\nAs an aside, how do I only plot the first plot?\n\n\n\n\n------ Edit for clarification from questions (and comments) below ------\n\n\n\n\nEach measurement is in this example a \"complexity\" value of a single facet (Fa has four levels), from a tooth (To has 8 levels). There are 1 to 8 measurements per Specimen requiring it to be a random effect. Each Specimen does belong to a species, though Species may or may not require nesting, or inclusion in the model per se, since most species have a single value for age, or are spread over 0.5 million years at most, it is highly correlated to Age and may be superfluous. Asfc is continuous, well normalised, and is considered gaussian.\n\n\n\n\nThis is an updated model with model check based on comments : gamm4(Asfc ~ s(sqrtAge, k = 8, bs =\"tp\"), data = df, random = ~(1|Specimen/ToothNoLR/Facet))\n[image: newGamm; source: https://i.sstatic.net/UmccNppE.jpg] (https://i.sstatic.net/UmccNppE.jpg)\n\n\n\n\n[image: checkgamm; source: https://i.sstatic.net/gYiJQdTI.jpg] (https://i.sstatic.net/gYiJQdTI.jpg)\n\n\n\n\nRE check_model() I'm doing this to look for verifiable trends, not for prediction. I realise the large gaps would make the latter difficult, so this is more exploratory to see if a signal is present.\n\n\n\n\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3606.394\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen (Intercept) 0.4767 \n ToothNoLR:Specimen (Intercept) 0.3814 \n Specimen (Intercept) 0.6024 \n Xr s(sqrt(Age)) 7.7972 \n Residual 0.4563 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen, 1430; ToothNoLR:Specimen, 542; Specimen, 421; Xr, 6\nFixed Effects:\n X(Intercept) Xs(sqrt(Age))Fx1 \n 0.008243 -0.872465 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n5.56 total = 6.56 \n\nlmer.REML score: 3606.394 \n\nattr(,\"class\")\n[1] \"gamm4\" \"list\" \n\n\n\n\n\n------ 2nd edit updating random effect structure ------\nHere is the model with taxon added. The CI's are worse, but I suspect it is a \"truer\" model. gamm4(Asfc ~ s(sqrt(Age), k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n\n\n\n\n[image: REtaxonadded; source: https://i.sstatic.net/KnHUkWbG.jpg] (https://i.sstatic.net/KnHUkWbG.jpg)\n\n\n\n\nThe check shows a more even spread of residuals.\n\n\n\n\n[image: retaxoncheck; source: https://i.sstatic.net/IXmEOkWk.jpg] (https://i.sstatic.net/IXmEOkWk.jpg)\n\n\n\n\nThese are the new results.\n\n\n\n\n> temp3 <- gamm4(Asfc ~ s(sqrt(Age), k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.052\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4786 \n ToothNoLR:Specimen:taxon (Intercept) 0.3614 \n Specimen:taxon (Intercept) 0.5246 \n taxon (Intercept) 0.4379 \n Xr s(sqrt(Age)) 4.5753 \n Residual 0.4561 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\n X(Intercept) Xs(sqrt(Age))Fx1 \n -0.04013 -0.01014 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n4.3 total = 5.3 \n\nlmer.REML score: 3566.053\n\n\n\n\n\nCompare them to the results where Age is not sqrt()'ed\n\n\n\n\n> temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.762\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4651 \n ToothNoLR:Specimen:taxon (Intercept) 0.3611 \n Specimen:taxon (Intercept) 0.5317 \n taxon (Intercept) 0.3790 \n Xr s(Age) 7.4438 \n Residual 0.4692 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\nX(Intercept) Xs(Age)Fx1 \n -0.04286 -0.98535 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(Age, k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n4.77 total = 5.77 \n\nlmer.REML score: 3566.762 \n\n\n\n\n\nI would appreciate any help in interpreting all this.\n\n\n\n\n------ Edit ------\nIn reply to the posterior predictive check. Removal of Facet.\n[image: enter image description here; source: https://i.sstatic.net/iV7wvyRj.jpg] (https://i.sstatic.net/iV7wvyRj.jpg)\ntemp3 without Facet in nesting, temp4 with Facet in nesting.\n\n\n\n\n> compare_performance(temp3, temp4)\n# Comparison of Model Performance Indices\n\nName | Model | AIC (weights) | BIC (weights) | R2 | RMSE | Sigma\n-----------------------------------------------------------------------\ntemp3 | gamm4 | 4031.8 (0.475) | 4065.0 (0.484) | 0.049 | 0.572 | 0.573\ntemp4 | gamm4 | 4031.6 (0.525) | 4064.8 (0.516) | 0.049 | 0.274 | 0.275\n\n\n\n\n\n------ quick edit ------\nSo, yes, when I check $mer I get these results, and it appears to be(?), the missing \"components\" to complete the response?:\n\n\n\n\n> model_performance(temp3$mer)\n# Indices of model performance\n\nAIC | AICc | BIC | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma\n--------------------------------------------------------------------------\n3581.9 | 3582.0 | 3618.9 | 0.579 | 1.298e-04 | 0.579 | 0.572 | 0.660\n\n> icc(temp3$mer, by_group = TRUE)\n\nGroup | ICC\n--------------------------------\nToothNoLR:Specimen:taxon | 0.127\nSpecimen:taxon | 0.267\ntaxon | 0.185\n> check_model(temp3$mer)\n\n\n\n\n\nJust the lmer component predictive curve.\n[image: enter image description here; source: https://i.sstatic.net/H3mCUZgO.jpg] (https://i.sstatic.net/H3mCUZgO.jpg)\n\n\n\n\n> check_model(temp3) Throws an error, so it seems it is incapable of incorporating both $mer and $gam into the check.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MrSwaggins", "profile_url": "https://stats.stackexchange.com/users/331950/mrswaggins", "user_type": "registered"}, "created_at": "2026-08-17T05:08:58+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": 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"revision_url": "https://stats.stackexchange.com/revisions/8D79A3B0-2AE6-4E89-94B4-B4BB66830EE2/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676893/is-this-the-correct-specification-for-gamm4-splines-where-species-are-short-te", "split": "test", "split_group": "61409f7f49db16a90eedb3018c6f3602d4fb05c1b06859ec9e29c98cb27d345b", "tags": ["time-series", "lme4-nlme", "trend", "gamm4"], "thread_id": "stats:676893", "title": "Is this the correct specification for gamm4() splines where Species are short term, but time period is very long?"}} {"citation_context": ")\ndraw(temp3$gam, residuals = TRUE)\n\n\n\n\n\nAnd I get something like this:\n[image: gamm4 plot; source: https://i.sstatic.net/M6wP2hpB.jpg] (https://i.sstatic.net/M6wP2hpB.jpg)\n\n\n\n\nFor this data am I \"gamm-ing\" correctly? The second plot ", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://i.sstatic.net/M6wP2hpB.jpg", "kind": "external_url", "post_id": 676893, "post_url": "https://stats.stackexchange.com/questions/676893/is-this-the-correct-specification-for-gamm4-splines-where-species-are-short-te", "product": "citations", "record_id": "Scientific-Citation-Graph:e759f499b183876d3236e2e4", "split": "test", "thread": {"accepted_answer_id": 676895, "answers": [{"answer_html": "

I would suggest you look at a changing a couple of things:

\n
    \n

  1. The distribution of Age is quite skewed, with some data squished up around 0 age. I would suggest trying to spread these values by out transforming Age, say via a square root transformation.

    \n

    If you look at the smooth of Age, most of the smooth is supported by by a few unique time points - the whole right hand side of the plot. Those unique ages are having a potentially bigger influence on the shape of the function than the ages that are all squished up at the left of the x axis. Spreading out the ages allows all the data to influence the smooth more evenly. You can still present the results on the Age scale, What we want to avoid is unnecessary wiggles because the smooth adapted to widely spaced values on the original scale.

    \n
    2. \n

  2. The fs smooths by Taxon aren't really doing much because they are very restricted in terms of basis functions.

    \n
    3. \n

  3. There is potential for an identifiability issue as you include a Taxon random intercept through the fs smooths, and then again through the ranef structure.

    \n

    Identifiability refers to the model's ability to unique identify (estimate a value for) each parameter in the model. You are including a random intercept for taxon through the random argument and the fs basis also includes a random intercept term for taxon. As you have included the same variable in the model twice, the model has no way of knowing how to apportion variance in the response between these terms. This will often cause estimation problems and even if the models fit OK, you will likely have larger standard errors than if you didn't have the identifiability problem.

    \n
    4. \n

  4. You will have to explain what you are trying or aiming to do rather than show what you did and ask if it is OK; it is not clear what the aim of the analysis, what model you are trying to fit, or how the data are structured, etc. (what is To Fa for example?).

    \n
    5. \n
\n

Unless you think the mean of Asfc for individual taxa changes over time smoothly, then there is no reason to use the taxon specific fs smooths. The random effect structure you propose seems reasonable, except I'm unclear from your description if you have multiple observations of Asfc per Facet? Or is facet informative in some way (inside vs top surface for example). If you don't have multiple observations per facet, you don't need the lowermost level in your ranef structure I believe. If individual taxa have different mean values of complexity (which I understand to be true broadly, but perhaps not in your specific group of taxa) then I think you do need Taxon at the highest level of the random effect structure.

\n

Finally, your model assume that the response Acsf values are conditional distributed Gaussian, meaning any value, negative or positive, is possible. If it is measuring complexity, that implies to me that negative values of the response are not observable, which would suggest the Gaussian is not appropriate. But perhaps this is not the case; the partial residuals don't look too bad, but proper model diagnostics would be need to confirm this. You also might need to consider the problem of temporal autocorrelation, although the Age smooth will help with that to some extent.

\n
\n

As an aside, how do I only plot the first plot?

\n
\n

Use the select argument to gratia' draw() function. This is a generic function so you need to look at the help for the gam method.

\n", "answer_id": 676895, "answer_text": "I would suggest you look at a changing a couple of things:\n\n\n\n\n\n\n\nThe distribution of Age is quite skewed, with some data squished up around 0 age. I would suggest trying to spread these values by out transforming Age, say via a square root transformation.\n\n\n\n\nIf you look at the smooth of Age, most of the smooth is supported by by a few unique time points - the whole right hand side of the plot. Those unique ages are having a potentially bigger influence on the shape of the function than the ages that are all squished up at the left of the x axis. Spreading out the ages allows all the data to influence the smooth more evenly. You can still present the results on the Age scale, What we want to avoid is unnecessary wiggles because the smooth adapted to widely spaced values on the original scale.\n\n\n\n\n\n\n\n\n\nThe fs smooths by Taxon aren't really doing much because they are very restricted in terms of basis functions.\n\n\n\n\n\n\n\n\n\nThere is potential for an identifiability issue as you include a Taxon random intercept through the fs smooths, and then again through the ranef structure.\n\n\n\n\nIdentifiability refers to the model's ability to unique identify (estimate a value for) each parameter in the model. You are including a random intercept for taxon through the random argument and the fs basis also includes a random intercept term for taxon. As you have included the same variable in the model twice, the model has no way of knowing how to apportion variance in the response between these terms. This will often cause estimation problems and even if the models fit OK, you will likely have larger standard errors than if you didn't have the identifiability problem.\n\n\n\n\n\n\n\n\n\nYou will have to explain what you are trying or aiming to do rather than show what you did and ask if it is OK; it is not clear what the aim of the analysis, what model you are trying to fit, or how the data are structured, etc. (what is To Fa for example?).\n\n\n\n\n\n\n\n\nUnless you think the mean of Asfc for individual taxa changes over time smoothly, then there is no reason to use the taxon specific fs smooths. The random effect structure you propose seems reasonable, except I'm unclear from your description if you have multiple observations of Asfc per Facet? Or is facet informative in some way (inside vs top surface for example). If you don't have multiple observations per facet, you don't need the lowermost level in your ranef structure I believe. If individual taxa have different mean values of complexity (which I understand to be true broadly, but perhaps not in your specific group of taxa) then I think you do need Taxon at the highest level of the random effect structure.\n\n\n\n\nFinally, your model assume that the response Acsf values are conditional distributed Gaussian, meaning any value, negative or positive, is possible. If it is measuring complexity, that implies to me that negative values of the response are not observable, which would suggest the Gaussian is not appropriate. But perhaps this is not the case; the partial residuals don't look too bad, but proper model diagnostics would be need to confirm this. You also might need to consider the problem of temporal autocorrelation, although the Age smooth will help with that to some extent.\n\n\n\n\n\n\n\nAs an aside, how do I only plot the first plot?\n\n\n\n\n\n\n\nUse the select argument to gratia' draw() function. This is a generic function so you need to look at the help for the gam method (https://gavinsimpson.github.io/gratia/reference/draw.gam.html).", "answer_url": "https://stats.stackexchange.com/a/676895", "author": "Gavin Simpson", "author_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-17T09:31:11+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676893, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Gavin Simpson", "profile_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "user_type": "registered"}, "created_at": "2026-08-17T09:31:11+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "344FFDF7-D995-42B0-B0C3-7BDBCFF41311", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/344FFDF7-D995-42B0-B0C3-7BDBCFF41311/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Gavin Simpson", "profile_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "user_type": "registered"}, "created_at": "2026-08-18T07:38:43+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "7758802C-386E-40D4-A5C5-B896DDCE2569", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/7758802C-386E-40D4-A5C5-B896DDCE2569/view-source"}], "score": 5, "updated_at": "2026-08-18T07:38:43+00:00"}], "domain": "statistics", "external_links": ["https://gavinsimpson.github.io/gratia/reference/draw.gam.html", "https://i.sstatic.net/H3mCUZgO.jpg", "https://i.sstatic.net/IXmEOkWk.jpg", "https://i.sstatic.net/KnHUkWbG.jpg", "https://i.sstatic.net/M6wP2hpB.jpg", "https://i.sstatic.net/UmccNppE.jpg", "https://i.sstatic.net/gYiJQdTI.jpg", "https://i.sstatic.net/iV7wvyRj.jpg"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "MrSwaggins", "question_author_url": "https://stats.stackexchange.com/users/331950/mrswaggins", "question_author_user_type": "registered", "question_created_at": "2026-08-17T05:08:58+00:00", "question_html": "

I have ~1400 measurements of teeth from ~40 species (taxon) that go back in time ~35mya (Age).\nThe data is noisy, so there is repetition in measurements from specimens that requires nesting as a random effect.

\n

I wish to see if there are trends in this data through time. I can see the trends as individual taxon boxplots if I roughly order them by time, but I would highly prefer Age as a continuous variable and the repetition accounted for.

\n

The problem is that taxa (i.e. species) generally exist for 1my or less, and there are large gaps, so if I understand gamms properly (not a given here lol) then the smoothing splines will be (in my simple terms) trying to extrapolate/estimate the curves for a species across the entire dataset where they don't really exist. I have tried to compensate for this using factor smoothing for taxon.

\n

To cut to the point after much testing and fiddling, I came up with this:

\n
temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs = "tp") + s(Age, taxon, bs = "fs", k = 3), data = df, random = ~(1|taxon/Specimen/To/Fa))\ntemp4 <- gamm4(Asfc ~ s(Age, k = 8, bs = "tp") + s(Age, taxon, bs = "fs", k = 3), data = df, random = ~(1|Specimen/To/Fa))\ndraw(temp3$gam, residuals = TRUE)\n
\n

And I get something like this:\n\"gamm4

\n

For this data am I "gamm-ing" correctly? The second plot suggests errr no, or is that just the intercept and slope for taxon influence?

\n

Should taxon be in the random effect structure? There are many specimens of each taxon.

\n

As an aside, how do I only plot the first plot?

\n

------ Edit for clarification from questions (and comments) below ------

\n

Each measurement is in this example a "complexity" value of a single facet (Fa has four levels), from a tooth (To has 8 levels). There are 1 to 8 measurements per Specimen requiring it to be a random effect. Each Specimen does belong to a species, though Species may or may not require nesting, or inclusion in the model per se, since most species have a single value for age, or are spread over 0.5 million years at most, it is highly correlated to Age and may be superfluous. Asfc is continuous, well normalised, and is considered gaussian.

\n

This is an updated model with model check based on comments : gamm4(Asfc ~ s(sqrtAge, k = 8, bs ="tp"), data = df, random = ~(1|Specimen/ToothNoLR/Facet))\n\"newGamm\"

\n

\"checkgamm\"

\n

RE check_model() I'm doing this to look for verifiable trends, not for prediction. I realise the large gaps would make the latter difficult, so this is more exploratory to see if a signal is present.

\n
$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3606.394\nRandom effects:\n Groups                   Name         Std.Dev.\n Facet:ToothNoLR:Specimen (Intercept)  0.4767  \n ToothNoLR:Specimen       (Intercept)  0.3814  \n Specimen                 (Intercept)  0.6024  \n Xr                       s(sqrt(Age)) 7.7972  \n Residual                              0.4563  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen, 1430; ToothNoLR:Specimen, 542; Specimen, 421; Xr, 6\nFixed Effects:\n    X(Intercept)  Xs(sqrt(Age))Fx1  \n        0.008243         -0.872465  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n5.56  total = 6.56 \n\nlmer.REML score: 3606.394     \n\nattr(,"class")\n[1] "gamm4" "list" \n
\n

------ 2nd edit updating random effect structure ------\nHere is the model with taxon added. The CI's are worse, but I suspect it is a "truer" model. gamm4(Asfc ~ s(sqrt(Age), k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))

\n

\"REtaxonadded\"

\n

The check shows a more even spread of residuals.

\n

\"retaxoncheck\"

\n

These are the new results.

\n
> temp3 <- gamm4(Asfc ~ s(sqrt(Age), k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.052\nRandom effects:\n Groups                         Name         Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept)  0.4786  \n ToothNoLR:Specimen:taxon       (Intercept)  0.3614  \n Specimen:taxon                 (Intercept)  0.5246  \n taxon                          (Intercept)  0.4379  \n Xr                             s(sqrt(Age)) 4.5753  \n Residual                                    0.4561  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\n    X(Intercept)  Xs(sqrt(Age))Fx1  \n        -0.04013          -0.01014  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n4.3  total = 5.3 \n\nlmer.REML score: 3566.053\n
\n

Compare them to the results where Age is not sqrt()'ed

\n
> temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.762\nRandom effects:\n Groups                         Name        Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4651  \n ToothNoLR:Specimen:taxon       (Intercept) 0.3611  \n Specimen:taxon                 (Intercept) 0.5317  \n taxon                          (Intercept) 0.3790  \n Xr                             s(Age)      7.4438  \n Residual                                   0.4692  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\nX(Intercept)    Xs(Age)Fx1  \n    -0.04286      -0.98535  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(Age, k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n4.77  total = 5.77 \n\nlmer.REML score: 3566.762 \n
\n

I would appreciate any help in interpreting all this.

\n

------ Edit ------\nIn reply to the posterior predictive check. Removal of Facet.\n\"enter\ntemp3 without Facet in nesting, temp4 with Facet in nesting.

\n
> compare_performance(temp3, temp4)\n# Comparison of Model Performance Indices\n\nName  | Model |  AIC (weights) |  BIC (weights) |    R2 |  RMSE | Sigma\n-----------------------------------------------------------------------\ntemp3 | gamm4 | 4031.8 (0.475) | 4065.0 (0.484) | 0.049 | 0.572 | 0.573\ntemp4 | gamm4 | 4031.6 (0.525) | 4064.8 (0.516) | 0.049 | 0.274 | 0.275\n
\n

------ quick edit ------\nSo, yes, when I check $mer I get these results, and it appears to be(?), the missing "components" to complete the response?:

\n
> model_performance(temp3$mer)\n# Indices of model performance\n\nAIC    |   AICc |    BIC | R2 (cond.) | R2 (marg.) |   ICC |  RMSE | Sigma\n--------------------------------------------------------------------------\n3581.9 | 3582.0 | 3618.9 |      0.579 |  1.298e-04 | 0.579 | 0.572 | 0.660\n\n> icc(temp3$mer, by_group = TRUE)\n\nGroup                    |   ICC\n--------------------------------\nToothNoLR:Specimen:taxon | 0.127\nSpecimen:taxon           | 0.267\ntaxon                    | 0.185\n> check_model(temp3$mer)\n
\n

Just the lmer component predictive curve.\n\"enter

\n

> check_model(temp3) Throws an error, so it seems it is incapable of incorporating both $mer and $gam into the check.

\n", "question_id": 676893, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "I have ~1400 measurements of teeth from ~40 species (taxon) that go back in time ~35mya (Age).\nThe data is noisy, so there is repetition in measurements from specimens that requires nesting as a random effect.\n\n\n\n\nI wish to see if there are trends in this data through time. I can see the trends as individual taxon boxplots if I roughly order them by time, but I would highly prefer Age as a continuous variable and the repetition accounted for.\n\n\n\n\nThe problem is that taxa (i.e. species) generally exist for 1my or less, and there are large gaps, so if I understand gamms properly (not a given here lol) then the smoothing splines will be (in my simple terms) trying to extrapolate/estimate the curves for a species across the entire dataset where they don't really exist. I have tried to compensate for this using factor smoothing for taxon.\n\n\n\n\nTo cut to the point after much testing and fiddling, I came up with this:\n\n\n\n\ntemp3 <- gamm4(Asfc ~ s(Age, k = 8, bs = \"tp\") + s(Age, taxon, bs = \"fs\", k = 3), data = df, random = ~(1|taxon/Specimen/To/Fa))\ntemp4 <- gamm4(Asfc ~ s(Age, k = 8, bs = \"tp\") + s(Age, taxon, bs = \"fs\", k = 3), data = df, random = ~(1|Specimen/To/Fa))\ndraw(temp3$gam, residuals = TRUE)\n\n\n\n\n\nAnd I get something like this:\n[image: gamm4 plot; source: https://i.sstatic.net/M6wP2hpB.jpg] (https://i.sstatic.net/M6wP2hpB.jpg)\n\n\n\n\nFor this data am I \"gamm-ing\" correctly? The second plot suggests errr no, or is that just the intercept and slope for taxon influence?\n\n\n\n\nShould taxon be in the random effect structure? There are many specimens of each taxon.\n\n\n\n\nAs an aside, how do I only plot the first plot?\n\n\n\n\n------ Edit for clarification from questions (and comments) below ------\n\n\n\n\nEach measurement is in this example a \"complexity\" value of a single facet (Fa has four levels), from a tooth (To has 8 levels). There are 1 to 8 measurements per Specimen requiring it to be a random effect. Each Specimen does belong to a species, though Species may or may not require nesting, or inclusion in the model per se, since most species have a single value for age, or are spread over 0.5 million years at most, it is highly correlated to Age and may be superfluous. Asfc is continuous, well normalised, and is considered gaussian.\n\n\n\n\nThis is an updated model with model check based on comments : gamm4(Asfc ~ s(sqrtAge, k = 8, bs =\"tp\"), data = df, random = ~(1|Specimen/ToothNoLR/Facet))\n[image: newGamm; source: https://i.sstatic.net/UmccNppE.jpg] (https://i.sstatic.net/UmccNppE.jpg)\n\n\n\n\n[image: checkgamm; source: https://i.sstatic.net/gYiJQdTI.jpg] (https://i.sstatic.net/gYiJQdTI.jpg)\n\n\n\n\nRE check_model() I'm doing this to look for verifiable trends, not for prediction. I realise the large gaps would make the latter difficult, so this is more exploratory to see if a signal is present.\n\n\n\n\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3606.394\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen (Intercept) 0.4767 \n ToothNoLR:Specimen (Intercept) 0.3814 \n Specimen (Intercept) 0.6024 \n Xr s(sqrt(Age)) 7.7972 \n Residual 0.4563 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen, 1430; ToothNoLR:Specimen, 542; Specimen, 421; Xr, 6\nFixed Effects:\n X(Intercept) Xs(sqrt(Age))Fx1 \n 0.008243 -0.872465 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n5.56 total = 6.56 \n\nlmer.REML score: 3606.394 \n\nattr(,\"class\")\n[1] \"gamm4\" \"list\" \n\n\n\n\n\n------ 2nd edit updating random effect structure ------\nHere is the model with taxon added. The CI's are worse, but I suspect it is a \"truer\" model. gamm4(Asfc ~ s(sqrt(Age), k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n\n\n\n\n[image: REtaxonadded; source: https://i.sstatic.net/KnHUkWbG.jpg] (https://i.sstatic.net/KnHUkWbG.jpg)\n\n\n\n\nThe check shows a more even spread of residuals.\n\n\n\n\n[image: retaxoncheck; source: https://i.sstatic.net/IXmEOkWk.jpg] (https://i.sstatic.net/IXmEOkWk.jpg)\n\n\n\n\nThese are the new results.\n\n\n\n\n> temp3 <- gamm4(Asfc ~ s(sqrt(Age), k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.052\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4786 \n ToothNoLR:Specimen:taxon (Intercept) 0.3614 \n Specimen:taxon (Intercept) 0.5246 \n taxon (Intercept) 0.4379 \n Xr s(sqrt(Age)) 4.5753 \n Residual 0.4561 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\n X(Intercept) Xs(sqrt(Age))Fx1 \n -0.04013 -0.01014 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n4.3 total = 5.3 \n\nlmer.REML score: 3566.053\n\n\n\n\n\nCompare them to the results where Age is not sqrt()'ed\n\n\n\n\n> temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.762\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4651 \n ToothNoLR:Specimen:taxon (Intercept) 0.3611 \n Specimen:taxon (Intercept) 0.5317 \n taxon (Intercept) 0.3790 \n Xr s(Age) 7.4438 \n Residual 0.4692 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\nX(Intercept) Xs(Age)Fx1 \n -0.04286 -0.98535 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(Age, k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n4.77 total = 5.77 \n\nlmer.REML score: 3566.762 \n\n\n\n\n\nI would appreciate any help in interpreting all this.\n\n\n\n\n------ Edit ------\nIn reply to the posterior predictive check. Removal of Facet.\n[image: enter image description here; source: https://i.sstatic.net/iV7wvyRj.jpg] (https://i.sstatic.net/iV7wvyRj.jpg)\ntemp3 without Facet in nesting, temp4 with Facet in nesting.\n\n\n\n\n> compare_performance(temp3, temp4)\n# Comparison of Model Performance Indices\n\nName | Model | AIC (weights) | BIC (weights) | R2 | RMSE | Sigma\n-----------------------------------------------------------------------\ntemp3 | gamm4 | 4031.8 (0.475) | 4065.0 (0.484) | 0.049 | 0.572 | 0.573\ntemp4 | gamm4 | 4031.6 (0.525) | 4064.8 (0.516) | 0.049 | 0.274 | 0.275\n\n\n\n\n\n------ quick edit ------\nSo, yes, when I check $mer I get these results, and it appears to be(?), the missing \"components\" to complete the response?:\n\n\n\n\n> model_performance(temp3$mer)\n# Indices of model performance\n\nAIC | AICc | BIC | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma\n--------------------------------------------------------------------------\n3581.9 | 3582.0 | 3618.9 | 0.579 | 1.298e-04 | 0.579 | 0.572 | 0.660\n\n> icc(temp3$mer, by_group = TRUE)\n\nGroup | ICC\n--------------------------------\nToothNoLR:Specimen:taxon | 0.127\nSpecimen:taxon | 0.267\ntaxon | 0.185\n> check_model(temp3$mer)\n\n\n\n\n\nJust the lmer component predictive curve.\n[image: enter image description here; source: https://i.sstatic.net/H3mCUZgO.jpg] (https://i.sstatic.net/H3mCUZgO.jpg)\n\n\n\n\n> check_model(temp3) Throws an error, so it seems it is incapable of incorporating both $mer and $gam into the check.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MrSwaggins", "profile_url": "https://stats.stackexchange.com/users/331950/mrswaggins", "user_type": "registered"}, "created_at": "2026-08-17T05:08:58+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": 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I would suggest you look at a changing a couple of things:

\n
    \n

  1. The distribution of Age is quite skewed, with some data squished up around 0 age. I would suggest trying to spread these values by out transforming Age, say via a square root transformation.

    \n

    If you look at the smooth of Age, most of the smooth is supported by by a few unique time points - the whole right hand side of the plot. Those unique ages are having a potentially bigger influence on the shape of the function than the ages that are all squished up at the left of the x axis. Spreading out the ages allows all the data to influence the smooth more evenly. You can still present the results on the Age scale, What we want to avoid is unnecessary wiggles because the smooth adapted to widely spaced values on the original scale.

    \n
    2. \n

  2. The fs smooths by Taxon aren't really doing much because they are very restricted in terms of basis functions.

    \n
    3. \n

  3. There is potential for an identifiability issue as you include a Taxon random intercept through the fs smooths, and then again through the ranef structure.

    \n

    Identifiability refers to the model's ability to unique identify (estimate a value for) each parameter in the model. You are including a random intercept for taxon through the random argument and the fs basis also includes a random intercept term for taxon. As you have included the same variable in the model twice, the model has no way of knowing how to apportion variance in the response between these terms. This will often cause estimation problems and even if the models fit OK, you will likely have larger standard errors than if you didn't have the identifiability problem.

    \n
    4. \n

  4. You will have to explain what you are trying or aiming to do rather than show what you did and ask if it is OK; it is not clear what the aim of the analysis, what model you are trying to fit, or how the data are structured, etc. (what is To Fa for example?).

    \n
    5. \n
\n

Unless you think the mean of Asfc for individual taxa changes over time smoothly, then there is no reason to use the taxon specific fs smooths. The random effect structure you propose seems reasonable, except I'm unclear from your description if you have multiple observations of Asfc per Facet? Or is facet informative in some way (inside vs top surface for example). If you don't have multiple observations per facet, you don't need the lowermost level in your ranef structure I believe. If individual taxa have different mean values of complexity (which I understand to be true broadly, but perhaps not in your specific group of taxa) then I think you do need Taxon at the highest level of the random effect structure.

\n

Finally, your model assume that the response Acsf values are conditional distributed Gaussian, meaning any value, negative or positive, is possible. If it is measuring complexity, that implies to me that negative values of the response are not observable, which would suggest the Gaussian is not appropriate. But perhaps this is not the case; the partial residuals don't look too bad, but proper model diagnostics would be need to confirm this. You also might need to consider the problem of temporal autocorrelation, although the Age smooth will help with that to some extent.

\n
\n

As an aside, how do I only plot the first plot?

\n
\n

Use the select argument to gratia' draw() function. This is a generic function so you need to look at the help for the gam method.

\n", "answer_id": 676895, "answer_text": "I would suggest you look at a changing a couple of things:\n\n\n\n\n\n\n\nThe distribution of Age is quite skewed, with some data squished up around 0 age. I would suggest trying to spread these values by out transforming Age, say via a square root transformation.\n\n\n\n\nIf you look at the smooth of Age, most of the smooth is supported by by a few unique time points - the whole right hand side of the plot. Those unique ages are having a potentially bigger influence on the shape of the function than the ages that are all squished up at the left of the x axis. Spreading out the ages allows all the data to influence the smooth more evenly. You can still present the results on the Age scale, What we want to avoid is unnecessary wiggles because the smooth adapted to widely spaced values on the original scale.\n\n\n\n\n\n\n\n\n\nThe fs smooths by Taxon aren't really doing much because they are very restricted in terms of basis functions.\n\n\n\n\n\n\n\n\n\nThere is potential for an identifiability issue as you include a Taxon random intercept through the fs smooths, and then again through the ranef structure.\n\n\n\n\nIdentifiability refers to the model's ability to unique identify (estimate a value for) each parameter in the model. You are including a random intercept for taxon through the random argument and the fs basis also includes a random intercept term for taxon. As you have included the same variable in the model twice, the model has no way of knowing how to apportion variance in the response between these terms. This will often cause estimation problems and even if the models fit OK, you will likely have larger standard errors than if you didn't have the identifiability problem.\n\n\n\n\n\n\n\n\n\nYou will have to explain what you are trying or aiming to do rather than show what you did and ask if it is OK; it is not clear what the aim of the analysis, what model you are trying to fit, or how the data are structured, etc. (what is To Fa for example?).\n\n\n\n\n\n\n\n\nUnless you think the mean of Asfc for individual taxa changes over time smoothly, then there is no reason to use the taxon specific fs smooths. The random effect structure you propose seems reasonable, except I'm unclear from your description if you have multiple observations of Asfc per Facet? Or is facet informative in some way (inside vs top surface for example). If you don't have multiple observations per facet, you don't need the lowermost level in your ranef structure I believe. If individual taxa have different mean values of complexity (which I understand to be true broadly, but perhaps not in your specific group of taxa) then I think you do need Taxon at the highest level of the random effect structure.\n\n\n\n\nFinally, your model assume that the response Acsf values are conditional distributed Gaussian, meaning any value, negative or positive, is possible. If it is measuring complexity, that implies to me that negative values of the response are not observable, which would suggest the Gaussian is not appropriate. But perhaps this is not the case; the partial residuals don't look too bad, but proper model diagnostics would be need to confirm this. You also might need to consider the problem of temporal autocorrelation, although the Age smooth will help with that to some extent.\n\n\n\n\n\n\n\nAs an aside, how do I only plot the first plot?\n\n\n\n\n\n\n\nUse the select argument to gratia' draw() function. This is a generic function so you need to look at the help for the gam method (https://gavinsimpson.github.io/gratia/reference/draw.gam.html).", "answer_url": "https://stats.stackexchange.com/a/676895", "author": "Gavin Simpson", "author_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-17T09:31:11+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676893, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Gavin Simpson", "profile_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "user_type": "registered"}, "created_at": "2026-08-17T09:31:11+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "344FFDF7-D995-42B0-B0C3-7BDBCFF41311", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/344FFDF7-D995-42B0-B0C3-7BDBCFF41311/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Gavin Simpson", "profile_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "user_type": "registered"}, "created_at": "2026-08-18T07:38:43+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "7758802C-386E-40D4-A5C5-B896DDCE2569", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/7758802C-386E-40D4-A5C5-B896DDCE2569/view-source"}], "score": 5, "updated_at": "2026-08-18T07:38:43+00:00"}], "domain": "statistics", "external_links": ["https://gavinsimpson.github.io/gratia/reference/draw.gam.html", "https://i.sstatic.net/H3mCUZgO.jpg", "https://i.sstatic.net/IXmEOkWk.jpg", "https://i.sstatic.net/KnHUkWbG.jpg", "https://i.sstatic.net/M6wP2hpB.jpg", "https://i.sstatic.net/UmccNppE.jpg", "https://i.sstatic.net/gYiJQdTI.jpg", "https://i.sstatic.net/iV7wvyRj.jpg"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "MrSwaggins", "question_author_url": "https://stats.stackexchange.com/users/331950/mrswaggins", "question_author_user_type": "registered", "question_created_at": "2026-08-17T05:08:58+00:00", "question_html": "

I have ~1400 measurements of teeth from ~40 species (taxon) that go back in time ~35mya (Age).\nThe data is noisy, so there is repetition in measurements from specimens that requires nesting as a random effect.

\n

I wish to see if there are trends in this data through time. I can see the trends as individual taxon boxplots if I roughly order them by time, but I would highly prefer Age as a continuous variable and the repetition accounted for.

\n

The problem is that taxa (i.e. species) generally exist for 1my or less, and there are large gaps, so if I understand gamms properly (not a given here lol) then the smoothing splines will be (in my simple terms) trying to extrapolate/estimate the curves for a species across the entire dataset where they don't really exist. I have tried to compensate for this using factor smoothing for taxon.

\n

To cut to the point after much testing and fiddling, I came up with this:

\n
temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs = "tp") + s(Age, taxon, bs = "fs", k = 3), data = df, random = ~(1|taxon/Specimen/To/Fa))\ntemp4 <- gamm4(Asfc ~ s(Age, k = 8, bs = "tp") + s(Age, taxon, bs = "fs", k = 3), data = df, random = ~(1|Specimen/To/Fa))\ndraw(temp3$gam, residuals = TRUE)\n
\n

And I get something like this:\n\"gamm4

\n

For this data am I "gamm-ing" correctly? The second plot suggests errr no, or is that just the intercept and slope for taxon influence?

\n

Should taxon be in the random effect structure? There are many specimens of each taxon.

\n

As an aside, how do I only plot the first plot?

\n

------ Edit for clarification from questions (and comments) below ------

\n

Each measurement is in this example a "complexity" value of a single facet (Fa has four levels), from a tooth (To has 8 levels). There are 1 to 8 measurements per Specimen requiring it to be a random effect. Each Specimen does belong to a species, though Species may or may not require nesting, or inclusion in the model per se, since most species have a single value for age, or are spread over 0.5 million years at most, it is highly correlated to Age and may be superfluous. Asfc is continuous, well normalised, and is considered gaussian.

\n

This is an updated model with model check based on comments : gamm4(Asfc ~ s(sqrtAge, k = 8, bs ="tp"), data = df, random = ~(1|Specimen/ToothNoLR/Facet))\n\"newGamm\"

\n

\"checkgamm\"

\n

RE check_model() I'm doing this to look for verifiable trends, not for prediction. I realise the large gaps would make the latter difficult, so this is more exploratory to see if a signal is present.

\n
$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3606.394\nRandom effects:\n Groups                   Name         Std.Dev.\n Facet:ToothNoLR:Specimen (Intercept)  0.4767  \n ToothNoLR:Specimen       (Intercept)  0.3814  \n Specimen                 (Intercept)  0.6024  \n Xr                       s(sqrt(Age)) 7.7972  \n Residual                              0.4563  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen, 1430; ToothNoLR:Specimen, 542; Specimen, 421; Xr, 6\nFixed Effects:\n    X(Intercept)  Xs(sqrt(Age))Fx1  \n        0.008243         -0.872465  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n5.56  total = 6.56 \n\nlmer.REML score: 3606.394     \n\nattr(,"class")\n[1] "gamm4" "list" \n
\n

------ 2nd edit updating random effect structure ------\nHere is the model with taxon added. The CI's are worse, but I suspect it is a "truer" model. gamm4(Asfc ~ s(sqrt(Age), k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))

\n

\"REtaxonadded\"

\n

The check shows a more even spread of residuals.

\n

\"retaxoncheck\"

\n

These are the new results.

\n
> temp3 <- gamm4(Asfc ~ s(sqrt(Age), k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.052\nRandom effects:\n Groups                         Name         Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept)  0.4786  \n ToothNoLR:Specimen:taxon       (Intercept)  0.3614  \n Specimen:taxon                 (Intercept)  0.5246  \n taxon                          (Intercept)  0.4379  \n Xr                             s(sqrt(Age)) 4.5753  \n Residual                                    0.4561  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\n    X(Intercept)  Xs(sqrt(Age))Fx1  \n        -0.04013          -0.01014  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n4.3  total = 5.3 \n\nlmer.REML score: 3566.053\n
\n

Compare them to the results where Age is not sqrt()'ed

\n
> temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.762\nRandom effects:\n Groups                         Name        Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4651  \n ToothNoLR:Specimen:taxon       (Intercept) 0.3611  \n Specimen:taxon                 (Intercept) 0.5317  \n taxon                          (Intercept) 0.3790  \n Xr                             s(Age)      7.4438  \n Residual                                   0.4692  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\nX(Intercept)    Xs(Age)Fx1  \n    -0.04286      -0.98535  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(Age, k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n4.77  total = 5.77 \n\nlmer.REML score: 3566.762 \n
\n

I would appreciate any help in interpreting all this.

\n

------ Edit ------\nIn reply to the posterior predictive check. Removal of Facet.\n\"enter\ntemp3 without Facet in nesting, temp4 with Facet in nesting.

\n
> compare_performance(temp3, temp4)\n# Comparison of Model Performance Indices\n\nName  | Model |  AIC (weights) |  BIC (weights) |    R2 |  RMSE | Sigma\n-----------------------------------------------------------------------\ntemp3 | gamm4 | 4031.8 (0.475) | 4065.0 (0.484) | 0.049 | 0.572 | 0.573\ntemp4 | gamm4 | 4031.6 (0.525) | 4064.8 (0.516) | 0.049 | 0.274 | 0.275\n
\n

------ quick edit ------\nSo, yes, when I check $mer I get these results, and it appears to be(?), the missing "components" to complete the response?:

\n
> model_performance(temp3$mer)\n# Indices of model performance\n\nAIC    |   AICc |    BIC | R2 (cond.) | R2 (marg.) |   ICC |  RMSE | Sigma\n--------------------------------------------------------------------------\n3581.9 | 3582.0 | 3618.9 |      0.579 |  1.298e-04 | 0.579 | 0.572 | 0.660\n\n> icc(temp3$mer, by_group = TRUE)\n\nGroup                    |   ICC\n--------------------------------\nToothNoLR:Specimen:taxon | 0.127\nSpecimen:taxon           | 0.267\ntaxon                    | 0.185\n> check_model(temp3$mer)\n
\n

Just the lmer component predictive curve.\n\"enter

\n

> check_model(temp3) Throws an error, so it seems it is incapable of incorporating both $mer and $gam into the check.

\n", "question_id": 676893, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "I have ~1400 measurements of teeth from ~40 species (taxon) that go back in time ~35mya (Age).\nThe data is noisy, so there is repetition in measurements from specimens that requires nesting as a random effect.\n\n\n\n\nI wish to see if there are trends in this data through time. I can see the trends as individual taxon boxplots if I roughly order them by time, but I would highly prefer Age as a continuous variable and the repetition accounted for.\n\n\n\n\nThe problem is that taxa (i.e. species) generally exist for 1my or less, and there are large gaps, so if I understand gamms properly (not a given here lol) then the smoothing splines will be (in my simple terms) trying to extrapolate/estimate the curves for a species across the entire dataset where they don't really exist. I have tried to compensate for this using factor smoothing for taxon.\n\n\n\n\nTo cut to the point after much testing and fiddling, I came up with this:\n\n\n\n\ntemp3 <- gamm4(Asfc ~ s(Age, k = 8, bs = \"tp\") + s(Age, taxon, bs = \"fs\", k = 3), data = df, random = ~(1|taxon/Specimen/To/Fa))\ntemp4 <- gamm4(Asfc ~ s(Age, k = 8, bs = \"tp\") + s(Age, taxon, bs = \"fs\", k = 3), data = df, random = ~(1|Specimen/To/Fa))\ndraw(temp3$gam, residuals = TRUE)\n\n\n\n\n\nAnd I get something like this:\n[image: gamm4 plot; source: https://i.sstatic.net/M6wP2hpB.jpg] (https://i.sstatic.net/M6wP2hpB.jpg)\n\n\n\n\nFor this data am I \"gamm-ing\" correctly? The second plot suggests errr no, or is that just the intercept and slope for taxon influence?\n\n\n\n\nShould taxon be in the random effect structure? There are many specimens of each taxon.\n\n\n\n\nAs an aside, how do I only plot the first plot?\n\n\n\n\n------ Edit for clarification from questions (and comments) below ------\n\n\n\n\nEach measurement is in this example a \"complexity\" value of a single facet (Fa has four levels), from a tooth (To has 8 levels). There are 1 to 8 measurements per Specimen requiring it to be a random effect. Each Specimen does belong to a species, though Species may or may not require nesting, or inclusion in the model per se, since most species have a single value for age, or are spread over 0.5 million years at most, it is highly correlated to Age and may be superfluous. Asfc is continuous, well normalised, and is considered gaussian.\n\n\n\n\nThis is an updated model with model check based on comments : gamm4(Asfc ~ s(sqrtAge, k = 8, bs =\"tp\"), data = df, random = ~(1|Specimen/ToothNoLR/Facet))\n[image: newGamm; source: https://i.sstatic.net/UmccNppE.jpg] (https://i.sstatic.net/UmccNppE.jpg)\n\n\n\n\n[image: checkgamm; source: https://i.sstatic.net/gYiJQdTI.jpg] (https://i.sstatic.net/gYiJQdTI.jpg)\n\n\n\n\nRE check_model() I'm doing this to look for verifiable trends, not for prediction. I realise the large gaps would make the latter difficult, so this is more exploratory to see if a signal is present.\n\n\n\n\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3606.394\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen (Intercept) 0.4767 \n ToothNoLR:Specimen (Intercept) 0.3814 \n Specimen (Intercept) 0.6024 \n Xr s(sqrt(Age)) 7.7972 \n Residual 0.4563 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen, 1430; ToothNoLR:Specimen, 542; Specimen, 421; Xr, 6\nFixed Effects:\n X(Intercept) Xs(sqrt(Age))Fx1 \n 0.008243 -0.872465 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n5.56 total = 6.56 \n\nlmer.REML score: 3606.394 \n\nattr(,\"class\")\n[1] \"gamm4\" \"list\" \n\n\n\n\n\n------ 2nd edit updating random effect structure ------\nHere is the model with taxon added. The CI's are worse, but I suspect it is a \"truer\" model. gamm4(Asfc ~ s(sqrt(Age), k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n\n\n\n\n[image: REtaxonadded; source: https://i.sstatic.net/KnHUkWbG.jpg] (https://i.sstatic.net/KnHUkWbG.jpg)\n\n\n\n\nThe check shows a more even spread of residuals.\n\n\n\n\n[image: retaxoncheck; source: https://i.sstatic.net/IXmEOkWk.jpg] (https://i.sstatic.net/IXmEOkWk.jpg)\n\n\n\n\nThese are the new results.\n\n\n\n\n> temp3 <- gamm4(Asfc ~ s(sqrt(Age), k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.052\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4786 \n ToothNoLR:Specimen:taxon (Intercept) 0.3614 \n Specimen:taxon (Intercept) 0.5246 \n taxon (Intercept) 0.4379 \n Xr s(sqrt(Age)) 4.5753 \n Residual 0.4561 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\n X(Intercept) Xs(sqrt(Age))Fx1 \n -0.04013 -0.01014 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n4.3 total = 5.3 \n\nlmer.REML score: 3566.053\n\n\n\n\n\nCompare them to the results where Age is not sqrt()'ed\n\n\n\n\n> temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.762\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4651 \n ToothNoLR:Specimen:taxon (Intercept) 0.3611 \n Specimen:taxon (Intercept) 0.5317 \n taxon (Intercept) 0.3790 \n Xr s(Age) 7.4438 \n Residual 0.4692 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\nX(Intercept) Xs(Age)Fx1 \n -0.04286 -0.98535 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(Age, k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n4.77 total = 5.77 \n\nlmer.REML score: 3566.762 \n\n\n\n\n\nI would appreciate any help in interpreting all this.\n\n\n\n\n------ Edit ------\nIn reply to the posterior predictive check. Removal of Facet.\n[image: enter image description here; source: https://i.sstatic.net/iV7wvyRj.jpg] (https://i.sstatic.net/iV7wvyRj.jpg)\ntemp3 without Facet in nesting, temp4 with Facet in nesting.\n\n\n\n\n> compare_performance(temp3, temp4)\n# Comparison of Model Performance Indices\n\nName | Model | AIC (weights) | BIC (weights) | R2 | RMSE | Sigma\n-----------------------------------------------------------------------\ntemp3 | gamm4 | 4031.8 (0.475) | 4065.0 (0.484) | 0.049 | 0.572 | 0.573\ntemp4 | gamm4 | 4031.6 (0.525) | 4064.8 (0.516) | 0.049 | 0.274 | 0.275\n\n\n\n\n\n------ quick edit ------\nSo, yes, when I check $mer I get these results, and it appears to be(?), the missing \"components\" to complete the response?:\n\n\n\n\n> model_performance(temp3$mer)\n# Indices of model performance\n\nAIC | AICc | BIC | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma\n--------------------------------------------------------------------------\n3581.9 | 3582.0 | 3618.9 | 0.579 | 1.298e-04 | 0.579 | 0.572 | 0.660\n\n> icc(temp3$mer, by_group = TRUE)\n\nGroup | ICC\n--------------------------------\nToothNoLR:Specimen:taxon | 0.127\nSpecimen:taxon | 0.267\ntaxon | 0.185\n> check_model(temp3$mer)\n\n\n\n\n\nJust the lmer component predictive curve.\n[image: enter image description here; source: https://i.sstatic.net/H3mCUZgO.jpg] (https://i.sstatic.net/H3mCUZgO.jpg)\n\n\n\n\n> check_model(temp3) Throws an error, so it seems it is incapable of incorporating both $mer and $gam into the check.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MrSwaggins", "profile_url": "https://stats.stackexchange.com/users/331950/mrswaggins", "user_type": "registered"}, "created_at": "2026-08-17T05:08:58+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": 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I would suggest you look at a changing a couple of things:

\n
    \n

  1. The distribution of Age is quite skewed, with some data squished up around 0 age. I would suggest trying to spread these values by out transforming Age, say via a square root transformation.

    \n

    If you look at the smooth of Age, most of the smooth is supported by by a few unique time points - the whole right hand side of the plot. Those unique ages are having a potentially bigger influence on the shape of the function than the ages that are all squished up at the left of the x axis. Spreading out the ages allows all the data to influence the smooth more evenly. You can still present the results on the Age scale, What we want to avoid is unnecessary wiggles because the smooth adapted to widely spaced values on the original scale.

    \n
    2. \n

  2. The fs smooths by Taxon aren't really doing much because they are very restricted in terms of basis functions.

    \n
    3. \n

  3. There is potential for an identifiability issue as you include a Taxon random intercept through the fs smooths, and then again through the ranef structure.

    \n

    Identifiability refers to the model's ability to unique identify (estimate a value for) each parameter in the model. You are including a random intercept for taxon through the random argument and the fs basis also includes a random intercept term for taxon. As you have included the same variable in the model twice, the model has no way of knowing how to apportion variance in the response between these terms. This will often cause estimation problems and even if the models fit OK, you will likely have larger standard errors than if you didn't have the identifiability problem.

    \n
    4. \n

  4. You will have to explain what you are trying or aiming to do rather than show what you did and ask if it is OK; it is not clear what the aim of the analysis, what model you are trying to fit, or how the data are structured, etc. (what is To Fa for example?).

    \n
    5. \n
\n

Unless you think the mean of Asfc for individual taxa changes over time smoothly, then there is no reason to use the taxon specific fs smooths. The random effect structure you propose seems reasonable, except I'm unclear from your description if you have multiple observations of Asfc per Facet? Or is facet informative in some way (inside vs top surface for example). If you don't have multiple observations per facet, you don't need the lowermost level in your ranef structure I believe. If individual taxa have different mean values of complexity (which I understand to be true broadly, but perhaps not in your specific group of taxa) then I think you do need Taxon at the highest level of the random effect structure.

\n

Finally, your model assume that the response Acsf values are conditional distributed Gaussian, meaning any value, negative or positive, is possible. If it is measuring complexity, that implies to me that negative values of the response are not observable, which would suggest the Gaussian is not appropriate. But perhaps this is not the case; the partial residuals don't look too bad, but proper model diagnostics would be need to confirm this. You also might need to consider the problem of temporal autocorrelation, although the Age smooth will help with that to some extent.

\n
\n

As an aside, how do I only plot the first plot?

\n
\n

Use the select argument to gratia' draw() function. This is a generic function so you need to look at the help for the gam method.

\n", "answer_id": 676895, "answer_text": "I would suggest you look at a changing a couple of things:\n\n\n\n\n\n\n\nThe distribution of Age is quite skewed, with some data squished up around 0 age. I would suggest trying to spread these values by out transforming Age, say via a square root transformation.\n\n\n\n\nIf you look at the smooth of Age, most of the smooth is supported by by a few unique time points - the whole right hand side of the plot. Those unique ages are having a potentially bigger influence on the shape of the function than the ages that are all squished up at the left of the x axis. Spreading out the ages allows all the data to influence the smooth more evenly. You can still present the results on the Age scale, What we want to avoid is unnecessary wiggles because the smooth adapted to widely spaced values on the original scale.\n\n\n\n\n\n\n\n\n\nThe fs smooths by Taxon aren't really doing much because they are very restricted in terms of basis functions.\n\n\n\n\n\n\n\n\n\nThere is potential for an identifiability issue as you include a Taxon random intercept through the fs smooths, and then again through the ranef structure.\n\n\n\n\nIdentifiability refers to the model's ability to unique identify (estimate a value for) each parameter in the model. You are including a random intercept for taxon through the random argument and the fs basis also includes a random intercept term for taxon. As you have included the same variable in the model twice, the model has no way of knowing how to apportion variance in the response between these terms. This will often cause estimation problems and even if the models fit OK, you will likely have larger standard errors than if you didn't have the identifiability problem.\n\n\n\n\n\n\n\n\n\nYou will have to explain what you are trying or aiming to do rather than show what you did and ask if it is OK; it is not clear what the aim of the analysis, what model you are trying to fit, or how the data are structured, etc. (what is To Fa for example?).\n\n\n\n\n\n\n\n\nUnless you think the mean of Asfc for individual taxa changes over time smoothly, then there is no reason to use the taxon specific fs smooths. The random effect structure you propose seems reasonable, except I'm unclear from your description if you have multiple observations of Asfc per Facet? Or is facet informative in some way (inside vs top surface for example). If you don't have multiple observations per facet, you don't need the lowermost level in your ranef structure I believe. If individual taxa have different mean values of complexity (which I understand to be true broadly, but perhaps not in your specific group of taxa) then I think you do need Taxon at the highest level of the random effect structure.\n\n\n\n\nFinally, your model assume that the response Acsf values are conditional distributed Gaussian, meaning any value, negative or positive, is possible. If it is measuring complexity, that implies to me that negative values of the response are not observable, which would suggest the Gaussian is not appropriate. But perhaps this is not the case; the partial residuals don't look too bad, but proper model diagnostics would be need to confirm this. You also might need to consider the problem of temporal autocorrelation, although the Age smooth will help with that to some extent.\n\n\n\n\n\n\n\nAs an aside, how do I only plot the first plot?\n\n\n\n\n\n\n\nUse the select argument to gratia' draw() function. This is a generic function so you need to look at the help for the gam method (https://gavinsimpson.github.io/gratia/reference/draw.gam.html).", "answer_url": "https://stats.stackexchange.com/a/676895", "author": "Gavin Simpson", "author_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-17T09:31:11+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676893, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Gavin Simpson", "profile_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "user_type": "registered"}, "created_at": "2026-08-17T09:31:11+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "344FFDF7-D995-42B0-B0C3-7BDBCFF41311", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/344FFDF7-D995-42B0-B0C3-7BDBCFF41311/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Gavin Simpson", "profile_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "user_type": "registered"}, "created_at": "2026-08-18T07:38:43+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "7758802C-386E-40D4-A5C5-B896DDCE2569", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/7758802C-386E-40D4-A5C5-B896DDCE2569/view-source"}], "score": 5, "updated_at": "2026-08-18T07:38:43+00:00"}], "domain": "statistics", "external_links": ["https://gavinsimpson.github.io/gratia/reference/draw.gam.html", "https://i.sstatic.net/H3mCUZgO.jpg", "https://i.sstatic.net/IXmEOkWk.jpg", "https://i.sstatic.net/KnHUkWbG.jpg", "https://i.sstatic.net/M6wP2hpB.jpg", "https://i.sstatic.net/UmccNppE.jpg", "https://i.sstatic.net/gYiJQdTI.jpg", "https://i.sstatic.net/iV7wvyRj.jpg"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "MrSwaggins", "question_author_url": "https://stats.stackexchange.com/users/331950/mrswaggins", "question_author_user_type": "registered", "question_created_at": "2026-08-17T05:08:58+00:00", "question_html": "

I have ~1400 measurements of teeth from ~40 species (taxon) that go back in time ~35mya (Age).\nThe data is noisy, so there is repetition in measurements from specimens that requires nesting as a random effect.

\n

I wish to see if there are trends in this data through time. I can see the trends as individual taxon boxplots if I roughly order them by time, but I would highly prefer Age as a continuous variable and the repetition accounted for.

\n

The problem is that taxa (i.e. species) generally exist for 1my or less, and there are large gaps, so if I understand gamms properly (not a given here lol) then the smoothing splines will be (in my simple terms) trying to extrapolate/estimate the curves for a species across the entire dataset where they don't really exist. I have tried to compensate for this using factor smoothing for taxon.

\n

To cut to the point after much testing and fiddling, I came up with this:

\n
temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs = "tp") + s(Age, taxon, bs = "fs", k = 3), data = df, random = ~(1|taxon/Specimen/To/Fa))\ntemp4 <- gamm4(Asfc ~ s(Age, k = 8, bs = "tp") + s(Age, taxon, bs = "fs", k = 3), data = df, random = ~(1|Specimen/To/Fa))\ndraw(temp3$gam, residuals = TRUE)\n
\n

And I get something like this:\n\"gamm4

\n

For this data am I "gamm-ing" correctly? The second plot suggests errr no, or is that just the intercept and slope for taxon influence?

\n

Should taxon be in the random effect structure? There are many specimens of each taxon.

\n

As an aside, how do I only plot the first plot?

\n

------ Edit for clarification from questions (and comments) below ------

\n

Each measurement is in this example a "complexity" value of a single facet (Fa has four levels), from a tooth (To has 8 levels). There are 1 to 8 measurements per Specimen requiring it to be a random effect. Each Specimen does belong to a species, though Species may or may not require nesting, or inclusion in the model per se, since most species have a single value for age, or are spread over 0.5 million years at most, it is highly correlated to Age and may be superfluous. Asfc is continuous, well normalised, and is considered gaussian.

\n

This is an updated model with model check based on comments : gamm4(Asfc ~ s(sqrtAge, k = 8, bs ="tp"), data = df, random = ~(1|Specimen/ToothNoLR/Facet))\n\"newGamm\"

\n

\"checkgamm\"

\n

RE check_model() I'm doing this to look for verifiable trends, not for prediction. I realise the large gaps would make the latter difficult, so this is more exploratory to see if a signal is present.

\n
$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3606.394\nRandom effects:\n Groups                   Name         Std.Dev.\n Facet:ToothNoLR:Specimen (Intercept)  0.4767  \n ToothNoLR:Specimen       (Intercept)  0.3814  \n Specimen                 (Intercept)  0.6024  \n Xr                       s(sqrt(Age)) 7.7972  \n Residual                              0.4563  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen, 1430; ToothNoLR:Specimen, 542; Specimen, 421; Xr, 6\nFixed Effects:\n    X(Intercept)  Xs(sqrt(Age))Fx1  \n        0.008243         -0.872465  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n5.56  total = 6.56 \n\nlmer.REML score: 3606.394     \n\nattr(,"class")\n[1] "gamm4" "list" \n
\n

------ 2nd edit updating random effect structure ------\nHere is the model with taxon added. The CI's are worse, but I suspect it is a "truer" model. gamm4(Asfc ~ s(sqrt(Age), k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))

\n

\"REtaxonadded\"

\n

The check shows a more even spread of residuals.

\n

\"retaxoncheck\"

\n

These are the new results.

\n
> temp3 <- gamm4(Asfc ~ s(sqrt(Age), k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.052\nRandom effects:\n Groups                         Name         Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept)  0.4786  \n ToothNoLR:Specimen:taxon       (Intercept)  0.3614  \n Specimen:taxon                 (Intercept)  0.5246  \n taxon                          (Intercept)  0.4379  \n Xr                             s(sqrt(Age)) 4.5753  \n Residual                                    0.4561  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\n    X(Intercept)  Xs(sqrt(Age))Fx1  \n        -0.04013          -0.01014  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n4.3  total = 5.3 \n\nlmer.REML score: 3566.053\n
\n

Compare them to the results where Age is not sqrt()'ed

\n
> temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.762\nRandom effects:\n Groups                         Name        Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4651  \n ToothNoLR:Specimen:taxon       (Intercept) 0.3611  \n Specimen:taxon                 (Intercept) 0.5317  \n taxon                          (Intercept) 0.3790  \n Xr                             s(Age)      7.4438  \n Residual                                   0.4692  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\nX(Intercept)    Xs(Age)Fx1  \n    -0.04286      -0.98535  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(Age, k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n4.77  total = 5.77 \n\nlmer.REML score: 3566.762 \n
\n

I would appreciate any help in interpreting all this.

\n

------ Edit ------\nIn reply to the posterior predictive check. Removal of Facet.\n\"enter\ntemp3 without Facet in nesting, temp4 with Facet in nesting.

\n
> compare_performance(temp3, temp4)\n# Comparison of Model Performance Indices\n\nName  | Model |  AIC (weights) |  BIC (weights) |    R2 |  RMSE | Sigma\n-----------------------------------------------------------------------\ntemp3 | gamm4 | 4031.8 (0.475) | 4065.0 (0.484) | 0.049 | 0.572 | 0.573\ntemp4 | gamm4 | 4031.6 (0.525) | 4064.8 (0.516) | 0.049 | 0.274 | 0.275\n
\n

------ quick edit ------\nSo, yes, when I check $mer I get these results, and it appears to be(?), the missing "components" to complete the response?:

\n
> model_performance(temp3$mer)\n# Indices of model performance\n\nAIC    |   AICc |    BIC | R2 (cond.) | R2 (marg.) |   ICC |  RMSE | Sigma\n--------------------------------------------------------------------------\n3581.9 | 3582.0 | 3618.9 |      0.579 |  1.298e-04 | 0.579 | 0.572 | 0.660\n\n> icc(temp3$mer, by_group = TRUE)\n\nGroup                    |   ICC\n--------------------------------\nToothNoLR:Specimen:taxon | 0.127\nSpecimen:taxon           | 0.267\ntaxon                    | 0.185\n> check_model(temp3$mer)\n
\n

Just the lmer component predictive curve.\n\"enter

\n

> check_model(temp3) Throws an error, so it seems it is incapable of incorporating both $mer and $gam into the check.

\n", "question_id": 676893, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "I have ~1400 measurements of teeth from ~40 species (taxon) that go back in time ~35mya (Age).\nThe data is noisy, so there is repetition in measurements from specimens that requires nesting as a random effect.\n\n\n\n\nI wish to see if there are trends in this data through time. I can see the trends as individual taxon boxplots if I roughly order them by time, but I would highly prefer Age as a continuous variable and the repetition accounted for.\n\n\n\n\nThe problem is that taxa (i.e. species) generally exist for 1my or less, and there are large gaps, so if I understand gamms properly (not a given here lol) then the smoothing splines will be (in my simple terms) trying to extrapolate/estimate the curves for a species across the entire dataset where they don't really exist. I have tried to compensate for this using factor smoothing for taxon.\n\n\n\n\nTo cut to the point after much testing and fiddling, I came up with this:\n\n\n\n\ntemp3 <- gamm4(Asfc ~ s(Age, k = 8, bs = \"tp\") + s(Age, taxon, bs = \"fs\", k = 3), data = df, random = ~(1|taxon/Specimen/To/Fa))\ntemp4 <- gamm4(Asfc ~ s(Age, k = 8, bs = \"tp\") + s(Age, taxon, bs = \"fs\", k = 3), data = df, random = ~(1|Specimen/To/Fa))\ndraw(temp3$gam, residuals = TRUE)\n\n\n\n\n\nAnd I get something like this:\n[image: gamm4 plot; source: https://i.sstatic.net/M6wP2hpB.jpg] (https://i.sstatic.net/M6wP2hpB.jpg)\n\n\n\n\nFor this data am I \"gamm-ing\" correctly? The second plot suggests errr no, or is that just the intercept and slope for taxon influence?\n\n\n\n\nShould taxon be in the random effect structure? There are many specimens of each taxon.\n\n\n\n\nAs an aside, how do I only plot the first plot?\n\n\n\n\n------ Edit for clarification from questions (and comments) below ------\n\n\n\n\nEach measurement is in this example a \"complexity\" value of a single facet (Fa has four levels), from a tooth (To has 8 levels). There are 1 to 8 measurements per Specimen requiring it to be a random effect. Each Specimen does belong to a species, though Species may or may not require nesting, or inclusion in the model per se, since most species have a single value for age, or are spread over 0.5 million years at most, it is highly correlated to Age and may be superfluous. Asfc is continuous, well normalised, and is considered gaussian.\n\n\n\n\nThis is an updated model with model check based on comments : gamm4(Asfc ~ s(sqrtAge, k = 8, bs =\"tp\"), data = df, random = ~(1|Specimen/ToothNoLR/Facet))\n[image: newGamm; source: https://i.sstatic.net/UmccNppE.jpg] (https://i.sstatic.net/UmccNppE.jpg)\n\n\n\n\n[image: checkgamm; source: https://i.sstatic.net/gYiJQdTI.jpg] (https://i.sstatic.net/gYiJQdTI.jpg)\n\n\n\n\nRE check_model() I'm doing this to look for verifiable trends, not for prediction. I realise the large gaps would make the latter difficult, so this is more exploratory to see if a signal is present.\n\n\n\n\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3606.394\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen (Intercept) 0.4767 \n ToothNoLR:Specimen (Intercept) 0.3814 \n Specimen (Intercept) 0.6024 \n Xr s(sqrt(Age)) 7.7972 \n Residual 0.4563 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen, 1430; ToothNoLR:Specimen, 542; Specimen, 421; Xr, 6\nFixed Effects:\n X(Intercept) Xs(sqrt(Age))Fx1 \n 0.008243 -0.872465 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n5.56 total = 6.56 \n\nlmer.REML score: 3606.394 \n\nattr(,\"class\")\n[1] \"gamm4\" \"list\" \n\n\n\n\n\n------ 2nd edit updating random effect structure ------\nHere is the model with taxon added. The CI's are worse, but I suspect it is a \"truer\" model. gamm4(Asfc ~ s(sqrt(Age), k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n\n\n\n\n[image: REtaxonadded; source: https://i.sstatic.net/KnHUkWbG.jpg] (https://i.sstatic.net/KnHUkWbG.jpg)\n\n\n\n\nThe check shows a more even spread of residuals.\n\n\n\n\n[image: retaxoncheck; source: https://i.sstatic.net/IXmEOkWk.jpg] (https://i.sstatic.net/IXmEOkWk.jpg)\n\n\n\n\nThese are the new results.\n\n\n\n\n> temp3 <- gamm4(Asfc ~ s(sqrt(Age), k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.052\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4786 \n ToothNoLR:Specimen:taxon (Intercept) 0.3614 \n Specimen:taxon (Intercept) 0.5246 \n taxon (Intercept) 0.4379 \n Xr s(sqrt(Age)) 4.5753 \n Residual 0.4561 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\n X(Intercept) Xs(sqrt(Age))Fx1 \n -0.04013 -0.01014 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n4.3 total = 5.3 \n\nlmer.REML score: 3566.053\n\n\n\n\n\nCompare them to the results where Age is not sqrt()'ed\n\n\n\n\n> temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.762\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4651 \n ToothNoLR:Specimen:taxon (Intercept) 0.3611 \n Specimen:taxon (Intercept) 0.5317 \n taxon (Intercept) 0.3790 \n Xr s(Age) 7.4438 \n Residual 0.4692 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\nX(Intercept) Xs(Age)Fx1 \n -0.04286 -0.98535 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(Age, k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n4.77 total = 5.77 \n\nlmer.REML score: 3566.762 \n\n\n\n\n\nI would appreciate any help in interpreting all this.\n\n\n\n\n------ Edit ------\nIn reply to the posterior predictive check. Removal of Facet.\n[image: enter image description here; source: https://i.sstatic.net/iV7wvyRj.jpg] (https://i.sstatic.net/iV7wvyRj.jpg)\ntemp3 without Facet in nesting, temp4 with Facet in nesting.\n\n\n\n\n> compare_performance(temp3, temp4)\n# Comparison of Model Performance Indices\n\nName | Model | AIC (weights) | BIC (weights) | R2 | RMSE | Sigma\n-----------------------------------------------------------------------\ntemp3 | gamm4 | 4031.8 (0.475) | 4065.0 (0.484) | 0.049 | 0.572 | 0.573\ntemp4 | gamm4 | 4031.6 (0.525) | 4064.8 (0.516) | 0.049 | 0.274 | 0.275\n\n\n\n\n\n------ quick edit ------\nSo, yes, when I check $mer I get these results, and it appears to be(?), the missing \"components\" to complete the response?:\n\n\n\n\n> model_performance(temp3$mer)\n# Indices of model performance\n\nAIC | AICc | BIC | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma\n--------------------------------------------------------------------------\n3581.9 | 3582.0 | 3618.9 | 0.579 | 1.298e-04 | 0.579 | 0.572 | 0.660\n\n> icc(temp3$mer, by_group = TRUE)\n\nGroup | ICC\n--------------------------------\nToothNoLR:Specimen:taxon | 0.127\nSpecimen:taxon | 0.267\ntaxon | 0.185\n> check_model(temp3$mer)\n\n\n\n\n\nJust the lmer component predictive curve.\n[image: enter image description here; source: https://i.sstatic.net/H3mCUZgO.jpg] (https://i.sstatic.net/H3mCUZgO.jpg)\n\n\n\n\n> check_model(temp3) Throws an error, so it seems it is incapable of incorporating both $mer and $gam into the check.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MrSwaggins", "profile_url": "https://stats.stackexchange.com/users/331950/mrswaggins", "user_type": "registered"}, "created_at": "2026-08-17T05:08:58+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": 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Removal of Facet.\n[image: enter image description here; source: https://i.sstatic.net/iV7wvyRj.jpg] (https://i.sstatic.net/iV7wvyRj.jpg)\ntemp3 without Facet in nesting, temp4 with Facet in nesting.\n", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://i.sstatic.net/iV7wvyRj.jpg", "kind": "external_url", "post_id": 676893, "post_url": "https://stats.stackexchange.com/questions/676893/is-this-the-correct-specification-for-gamm4-splines-where-species-are-short-te", "product": "citations", "record_id": "Scientific-Citation-Graph:033da72e7eff38c1cfdeae30", "split": "test", "thread": {"accepted_answer_id": 676895, "answers": [{"answer_html": "

I would suggest you look at a changing a couple of things:

\n
    \n

  1. The distribution of Age is quite skewed, with some data squished up around 0 age. I would suggest trying to spread these values by out transforming Age, say via a square root transformation.

    \n

    If you look at the smooth of Age, most of the smooth is supported by by a few unique time points - the whole right hand side of the plot. Those unique ages are having a potentially bigger influence on the shape of the function than the ages that are all squished up at the left of the x axis. Spreading out the ages allows all the data to influence the smooth more evenly. You can still present the results on the Age scale, What we want to avoid is unnecessary wiggles because the smooth adapted to widely spaced values on the original scale.

    \n
    2. \n

  2. The fs smooths by Taxon aren't really doing much because they are very restricted in terms of basis functions.

    \n
    3. \n

  3. There is potential for an identifiability issue as you include a Taxon random intercept through the fs smooths, and then again through the ranef structure.

    \n

    Identifiability refers to the model's ability to unique identify (estimate a value for) each parameter in the model. You are including a random intercept for taxon through the random argument and the fs basis also includes a random intercept term for taxon. As you have included the same variable in the model twice, the model has no way of knowing how to apportion variance in the response between these terms. This will often cause estimation problems and even if the models fit OK, you will likely have larger standard errors than if you didn't have the identifiability problem.

    \n
    4. \n

  4. You will have to explain what you are trying or aiming to do rather than show what you did and ask if it is OK; it is not clear what the aim of the analysis, what model you are trying to fit, or how the data are structured, etc. (what is To Fa for example?).

    \n
    5. \n
\n

Unless you think the mean of Asfc for individual taxa changes over time smoothly, then there is no reason to use the taxon specific fs smooths. The random effect structure you propose seems reasonable, except I'm unclear from your description if you have multiple observations of Asfc per Facet? Or is facet informative in some way (inside vs top surface for example). If you don't have multiple observations per facet, you don't need the lowermost level in your ranef structure I believe. If individual taxa have different mean values of complexity (which I understand to be true broadly, but perhaps not in your specific group of taxa) then I think you do need Taxon at the highest level of the random effect structure.

\n

Finally, your model assume that the response Acsf values are conditional distributed Gaussian, meaning any value, negative or positive, is possible. If it is measuring complexity, that implies to me that negative values of the response are not observable, which would suggest the Gaussian is not appropriate. But perhaps this is not the case; the partial residuals don't look too bad, but proper model diagnostics would be need to confirm this. You also might need to consider the problem of temporal autocorrelation, although the Age smooth will help with that to some extent.

\n
\n

As an aside, how do I only plot the first plot?

\n
\n

Use the select argument to gratia' draw() function. This is a generic function so you need to look at the help for the gam method.

\n", "answer_id": 676895, "answer_text": "I would suggest you look at a changing a couple of things:\n\n\n\n\n\n\n\nThe distribution of Age is quite skewed, with some data squished up around 0 age. I would suggest trying to spread these values by out transforming Age, say via a square root transformation.\n\n\n\n\nIf you look at the smooth of Age, most of the smooth is supported by by a few unique time points - the whole right hand side of the plot. Those unique ages are having a potentially bigger influence on the shape of the function than the ages that are all squished up at the left of the x axis. Spreading out the ages allows all the data to influence the smooth more evenly. You can still present the results on the Age scale, What we want to avoid is unnecessary wiggles because the smooth adapted to widely spaced values on the original scale.\n\n\n\n\n\n\n\n\n\nThe fs smooths by Taxon aren't really doing much because they are very restricted in terms of basis functions.\n\n\n\n\n\n\n\n\n\nThere is potential for an identifiability issue as you include a Taxon random intercept through the fs smooths, and then again through the ranef structure.\n\n\n\n\nIdentifiability refers to the model's ability to unique identify (estimate a value for) each parameter in the model. You are including a random intercept for taxon through the random argument and the fs basis also includes a random intercept term for taxon. As you have included the same variable in the model twice, the model has no way of knowing how to apportion variance in the response between these terms. This will often cause estimation problems and even if the models fit OK, you will likely have larger standard errors than if you didn't have the identifiability problem.\n\n\n\n\n\n\n\n\n\nYou will have to explain what you are trying or aiming to do rather than show what you did and ask if it is OK; it is not clear what the aim of the analysis, what model you are trying to fit, or how the data are structured, etc. (what is To Fa for example?).\n\n\n\n\n\n\n\n\nUnless you think the mean of Asfc for individual taxa changes over time smoothly, then there is no reason to use the taxon specific fs smooths. The random effect structure you propose seems reasonable, except I'm unclear from your description if you have multiple observations of Asfc per Facet? Or is facet informative in some way (inside vs top surface for example). If you don't have multiple observations per facet, you don't need the lowermost level in your ranef structure I believe. If individual taxa have different mean values of complexity (which I understand to be true broadly, but perhaps not in your specific group of taxa) then I think you do need Taxon at the highest level of the random effect structure.\n\n\n\n\nFinally, your model assume that the response Acsf values are conditional distributed Gaussian, meaning any value, negative or positive, is possible. If it is measuring complexity, that implies to me that negative values of the response are not observable, which would suggest the Gaussian is not appropriate. But perhaps this is not the case; the partial residuals don't look too bad, but proper model diagnostics would be need to confirm this. You also might need to consider the problem of temporal autocorrelation, although the Age smooth will help with that to some extent.\n\n\n\n\n\n\n\nAs an aside, how do I only plot the first plot?\n\n\n\n\n\n\n\nUse the select argument to gratia' draw() function. This is a generic function so you need to look at the help for the gam method (https://gavinsimpson.github.io/gratia/reference/draw.gam.html).", "answer_url": "https://stats.stackexchange.com/a/676895", "author": "Gavin Simpson", "author_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-17T09:31:11+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676893, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Gavin Simpson", "profile_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "user_type": "registered"}, "created_at": "2026-08-17T09:31:11+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "344FFDF7-D995-42B0-B0C3-7BDBCFF41311", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/344FFDF7-D995-42B0-B0C3-7BDBCFF41311/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Gavin Simpson", "profile_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "user_type": "registered"}, "created_at": "2026-08-18T07:38:43+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "7758802C-386E-40D4-A5C5-B896DDCE2569", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/7758802C-386E-40D4-A5C5-B896DDCE2569/view-source"}], "score": 5, "updated_at": "2026-08-18T07:38:43+00:00"}], "domain": "statistics", "external_links": ["https://gavinsimpson.github.io/gratia/reference/draw.gam.html", "https://i.sstatic.net/H3mCUZgO.jpg", "https://i.sstatic.net/IXmEOkWk.jpg", "https://i.sstatic.net/KnHUkWbG.jpg", "https://i.sstatic.net/M6wP2hpB.jpg", "https://i.sstatic.net/UmccNppE.jpg", "https://i.sstatic.net/gYiJQdTI.jpg", "https://i.sstatic.net/iV7wvyRj.jpg"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "MrSwaggins", "question_author_url": "https://stats.stackexchange.com/users/331950/mrswaggins", "question_author_user_type": "registered", "question_created_at": "2026-08-17T05:08:58+00:00", "question_html": "

I have ~1400 measurements of teeth from ~40 species (taxon) that go back in time ~35mya (Age).\nThe data is noisy, so there is repetition in measurements from specimens that requires nesting as a random effect.

\n

I wish to see if there are trends in this data through time. I can see the trends as individual taxon boxplots if I roughly order them by time, but I would highly prefer Age as a continuous variable and the repetition accounted for.

\n

The problem is that taxa (i.e. species) generally exist for 1my or less, and there are large gaps, so if I understand gamms properly (not a given here lol) then the smoothing splines will be (in my simple terms) trying to extrapolate/estimate the curves for a species across the entire dataset where they don't really exist. I have tried to compensate for this using factor smoothing for taxon.

\n

To cut to the point after much testing and fiddling, I came up with this:

\n
temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs = "tp") + s(Age, taxon, bs = "fs", k = 3), data = df, random = ~(1|taxon/Specimen/To/Fa))\ntemp4 <- gamm4(Asfc ~ s(Age, k = 8, bs = "tp") + s(Age, taxon, bs = "fs", k = 3), data = df, random = ~(1|Specimen/To/Fa))\ndraw(temp3$gam, residuals = TRUE)\n
\n

And I get something like this:\n\"gamm4

\n

For this data am I "gamm-ing" correctly? The second plot suggests errr no, or is that just the intercept and slope for taxon influence?

\n

Should taxon be in the random effect structure? There are many specimens of each taxon.

\n

As an aside, how do I only plot the first plot?

\n

------ Edit for clarification from questions (and comments) below ------

\n

Each measurement is in this example a "complexity" value of a single facet (Fa has four levels), from a tooth (To has 8 levels). There are 1 to 8 measurements per Specimen requiring it to be a random effect. Each Specimen does belong to a species, though Species may or may not require nesting, or inclusion in the model per se, since most species have a single value for age, or are spread over 0.5 million years at most, it is highly correlated to Age and may be superfluous. Asfc is continuous, well normalised, and is considered gaussian.

\n

This is an updated model with model check based on comments : gamm4(Asfc ~ s(sqrtAge, k = 8, bs ="tp"), data = df, random = ~(1|Specimen/ToothNoLR/Facet))\n\"newGamm\"

\n

\"checkgamm\"

\n

RE check_model() I'm doing this to look for verifiable trends, not for prediction. I realise the large gaps would make the latter difficult, so this is more exploratory to see if a signal is present.

\n
$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3606.394\nRandom effects:\n Groups                   Name         Std.Dev.\n Facet:ToothNoLR:Specimen (Intercept)  0.4767  \n ToothNoLR:Specimen       (Intercept)  0.3814  \n Specimen                 (Intercept)  0.6024  \n Xr                       s(sqrt(Age)) 7.7972  \n Residual                              0.4563  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen, 1430; ToothNoLR:Specimen, 542; Specimen, 421; Xr, 6\nFixed Effects:\n    X(Intercept)  Xs(sqrt(Age))Fx1  \n        0.008243         -0.872465  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n5.56  total = 6.56 \n\nlmer.REML score: 3606.394     \n\nattr(,"class")\n[1] "gamm4" "list" \n
\n

------ 2nd edit updating random effect structure ------\nHere is the model with taxon added. The CI's are worse, but I suspect it is a "truer" model. gamm4(Asfc ~ s(sqrt(Age), k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))

\n

\"REtaxonadded\"

\n

The check shows a more even spread of residuals.

\n

\"retaxoncheck\"

\n

These are the new results.

\n
> temp3 <- gamm4(Asfc ~ s(sqrt(Age), k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.052\nRandom effects:\n Groups                         Name         Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept)  0.4786  \n ToothNoLR:Specimen:taxon       (Intercept)  0.3614  \n Specimen:taxon                 (Intercept)  0.5246  \n taxon                          (Intercept)  0.4379  \n Xr                             s(sqrt(Age)) 4.5753  \n Residual                                    0.4561  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\n    X(Intercept)  Xs(sqrt(Age))Fx1  \n        -0.04013          -0.01014  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n4.3  total = 5.3 \n\nlmer.REML score: 3566.053\n
\n

Compare them to the results where Age is not sqrt()'ed

\n
> temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.762\nRandom effects:\n Groups                         Name        Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4651  \n ToothNoLR:Specimen:taxon       (Intercept) 0.3611  \n Specimen:taxon                 (Intercept) 0.5317  \n taxon                          (Intercept) 0.3790  \n Xr                             s(Age)      7.4438  \n Residual                                   0.4692  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\nX(Intercept)    Xs(Age)Fx1  \n    -0.04286      -0.98535  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(Age, k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n4.77  total = 5.77 \n\nlmer.REML score: 3566.762 \n
\n

I would appreciate any help in interpreting all this.

\n

------ Edit ------\nIn reply to the posterior predictive check. Removal of Facet.\n\"enter\ntemp3 without Facet in nesting, temp4 with Facet in nesting.

\n
> compare_performance(temp3, temp4)\n# Comparison of Model Performance Indices\n\nName  | Model |  AIC (weights) |  BIC (weights) |    R2 |  RMSE | Sigma\n-----------------------------------------------------------------------\ntemp3 | gamm4 | 4031.8 (0.475) | 4065.0 (0.484) | 0.049 | 0.572 | 0.573\ntemp4 | gamm4 | 4031.6 (0.525) | 4064.8 (0.516) | 0.049 | 0.274 | 0.275\n
\n

------ quick edit ------\nSo, yes, when I check $mer I get these results, and it appears to be(?), the missing "components" to complete the response?:

\n
> model_performance(temp3$mer)\n# Indices of model performance\n\nAIC    |   AICc |    BIC | R2 (cond.) | R2 (marg.) |   ICC |  RMSE | Sigma\n--------------------------------------------------------------------------\n3581.9 | 3582.0 | 3618.9 |      0.579 |  1.298e-04 | 0.579 | 0.572 | 0.660\n\n> icc(temp3$mer, by_group = TRUE)\n\nGroup                    |   ICC\n--------------------------------\nToothNoLR:Specimen:taxon | 0.127\nSpecimen:taxon           | 0.267\ntaxon                    | 0.185\n> check_model(temp3$mer)\n
\n

Just the lmer component predictive curve.\n\"enter

\n

> check_model(temp3) Throws an error, so it seems it is incapable of incorporating both $mer and $gam into the check.

\n", "question_id": 676893, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "I have ~1400 measurements of teeth from ~40 species (taxon) that go back in time ~35mya (Age).\nThe data is noisy, so there is repetition in measurements from specimens that requires nesting as a random effect.\n\n\n\n\nI wish to see if there are trends in this data through time. I can see the trends as individual taxon boxplots if I roughly order them by time, but I would highly prefer Age as a continuous variable and the repetition accounted for.\n\n\n\n\nThe problem is that taxa (i.e. species) generally exist for 1my or less, and there are large gaps, so if I understand gamms properly (not a given here lol) then the smoothing splines will be (in my simple terms) trying to extrapolate/estimate the curves for a species across the entire dataset where they don't really exist. I have tried to compensate for this using factor smoothing for taxon.\n\n\n\n\nTo cut to the point after much testing and fiddling, I came up with this:\n\n\n\n\ntemp3 <- gamm4(Asfc ~ s(Age, k = 8, bs = \"tp\") + s(Age, taxon, bs = \"fs\", k = 3), data = df, random = ~(1|taxon/Specimen/To/Fa))\ntemp4 <- gamm4(Asfc ~ s(Age, k = 8, bs = \"tp\") + s(Age, taxon, bs = \"fs\", k = 3), data = df, random = ~(1|Specimen/To/Fa))\ndraw(temp3$gam, residuals = TRUE)\n\n\n\n\n\nAnd I get something like this:\n[image: gamm4 plot; source: https://i.sstatic.net/M6wP2hpB.jpg] (https://i.sstatic.net/M6wP2hpB.jpg)\n\n\n\n\nFor this data am I \"gamm-ing\" correctly? The second plot suggests errr no, or is that just the intercept and slope for taxon influence?\n\n\n\n\nShould taxon be in the random effect structure? There are many specimens of each taxon.\n\n\n\n\nAs an aside, how do I only plot the first plot?\n\n\n\n\n------ Edit for clarification from questions (and comments) below ------\n\n\n\n\nEach measurement is in this example a \"complexity\" value of a single facet (Fa has four levels), from a tooth (To has 8 levels). There are 1 to 8 measurements per Specimen requiring it to be a random effect. Each Specimen does belong to a species, though Species may or may not require nesting, or inclusion in the model per se, since most species have a single value for age, or are spread over 0.5 million years at most, it is highly correlated to Age and may be superfluous. Asfc is continuous, well normalised, and is considered gaussian.\n\n\n\n\nThis is an updated model with model check based on comments : gamm4(Asfc ~ s(sqrtAge, k = 8, bs =\"tp\"), data = df, random = ~(1|Specimen/ToothNoLR/Facet))\n[image: newGamm; source: https://i.sstatic.net/UmccNppE.jpg] (https://i.sstatic.net/UmccNppE.jpg)\n\n\n\n\n[image: checkgamm; source: https://i.sstatic.net/gYiJQdTI.jpg] (https://i.sstatic.net/gYiJQdTI.jpg)\n\n\n\n\nRE check_model() I'm doing this to look for verifiable trends, not for prediction. I realise the large gaps would make the latter difficult, so this is more exploratory to see if a signal is present.\n\n\n\n\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3606.394\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen (Intercept) 0.4767 \n ToothNoLR:Specimen (Intercept) 0.3814 \n Specimen (Intercept) 0.6024 \n Xr s(sqrt(Age)) 7.7972 \n Residual 0.4563 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen, 1430; ToothNoLR:Specimen, 542; Specimen, 421; Xr, 6\nFixed Effects:\n X(Intercept) Xs(sqrt(Age))Fx1 \n 0.008243 -0.872465 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n5.56 total = 6.56 \n\nlmer.REML score: 3606.394 \n\nattr(,\"class\")\n[1] \"gamm4\" \"list\" \n\n\n\n\n\n------ 2nd edit updating random effect structure ------\nHere is the model with taxon added. The CI's are worse, but I suspect it is a \"truer\" model. gamm4(Asfc ~ s(sqrt(Age), k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n\n\n\n\n[image: REtaxonadded; source: https://i.sstatic.net/KnHUkWbG.jpg] (https://i.sstatic.net/KnHUkWbG.jpg)\n\n\n\n\nThe check shows a more even spread of residuals.\n\n\n\n\n[image: retaxoncheck; source: https://i.sstatic.net/IXmEOkWk.jpg] (https://i.sstatic.net/IXmEOkWk.jpg)\n\n\n\n\nThese are the new results.\n\n\n\n\n> temp3 <- gamm4(Asfc ~ s(sqrt(Age), k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.052\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4786 \n ToothNoLR:Specimen:taxon (Intercept) 0.3614 \n Specimen:taxon (Intercept) 0.5246 \n taxon (Intercept) 0.4379 \n Xr s(sqrt(Age)) 4.5753 \n Residual 0.4561 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\n X(Intercept) Xs(sqrt(Age))Fx1 \n -0.04013 -0.01014 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n4.3 total = 5.3 \n\nlmer.REML score: 3566.053\n\n\n\n\n\nCompare them to the results where Age is not sqrt()'ed\n\n\n\n\n> temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.762\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4651 \n ToothNoLR:Specimen:taxon (Intercept) 0.3611 \n Specimen:taxon (Intercept) 0.5317 \n taxon (Intercept) 0.3790 \n Xr s(Age) 7.4438 \n Residual 0.4692 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\nX(Intercept) Xs(Age)Fx1 \n -0.04286 -0.98535 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(Age, k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n4.77 total = 5.77 \n\nlmer.REML score: 3566.762 \n\n\n\n\n\nI would appreciate any help in interpreting all this.\n\n\n\n\n------ Edit ------\nIn reply to the posterior predictive check. Removal of Facet.\n[image: enter image description here; source: https://i.sstatic.net/iV7wvyRj.jpg] (https://i.sstatic.net/iV7wvyRj.jpg)\ntemp3 without Facet in nesting, temp4 with Facet in nesting.\n\n\n\n\n> compare_performance(temp3, temp4)\n# Comparison of Model Performance Indices\n\nName | Model | AIC (weights) | BIC (weights) | R2 | RMSE | Sigma\n-----------------------------------------------------------------------\ntemp3 | gamm4 | 4031.8 (0.475) | 4065.0 (0.484) | 0.049 | 0.572 | 0.573\ntemp4 | gamm4 | 4031.6 (0.525) | 4064.8 (0.516) | 0.049 | 0.274 | 0.275\n\n\n\n\n\n------ quick edit ------\nSo, yes, when I check $mer I get these results, and it appears to be(?), the missing \"components\" to complete the response?:\n\n\n\n\n> model_performance(temp3$mer)\n# Indices of model performance\n\nAIC | AICc | BIC | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma\n--------------------------------------------------------------------------\n3581.9 | 3582.0 | 3618.9 | 0.579 | 1.298e-04 | 0.579 | 0.572 | 0.660\n\n> icc(temp3$mer, by_group = TRUE)\n\nGroup | ICC\n--------------------------------\nToothNoLR:Specimen:taxon | 0.127\nSpecimen:taxon | 0.267\ntaxon | 0.185\n> check_model(temp3$mer)\n\n\n\n\n\nJust the lmer component predictive curve.\n[image: enter image description here; source: https://i.sstatic.net/H3mCUZgO.jpg] (https://i.sstatic.net/H3mCUZgO.jpg)\n\n\n\n\n> check_model(temp3) Throws an error, so it seems it is incapable of incorporating both $mer and $gam into the check.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MrSwaggins", "profile_url": "https://stats.stackexchange.com/users/331950/mrswaggins", "user_type": "registered"}, "created_at": "2026-08-17T05:08:58+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": 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This is a generic function so you need to look at the help for the gam method (https://gavinsimpson.github.io/gratia/reference/draw.gam.html).", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://gavinsimpson.github.io/gratia/reference/draw.gam.html", "kind": "external_url", "post_id": 676895, "post_url": "https://stats.stackexchange.com/a/676895", "product": "citations", "record_id": "Scientific-Citation-Graph:c19664f64abbee8e94eb9e56", "split": "test", "thread": {"accepted_answer_id": 676895, "answers": [{"answer_html": "

I would suggest you look at a changing a couple of things:

\n
    \n

  1. The distribution of Age is quite skewed, with some data squished up around 0 age. I would suggest trying to spread these values by out transforming Age, say via a square root transformation.

    \n

    If you look at the smooth of Age, most of the smooth is supported by by a few unique time points - the whole right hand side of the plot. Those unique ages are having a potentially bigger influence on the shape of the function than the ages that are all squished up at the left of the x axis. Spreading out the ages allows all the data to influence the smooth more evenly. You can still present the results on the Age scale, What we want to avoid is unnecessary wiggles because the smooth adapted to widely spaced values on the original scale.

    \n
    2. \n

  2. The fs smooths by Taxon aren't really doing much because they are very restricted in terms of basis functions.

    \n
    3. \n

  3. There is potential for an identifiability issue as you include a Taxon random intercept through the fs smooths, and then again through the ranef structure.

    \n

    Identifiability refers to the model's ability to unique identify (estimate a value for) each parameter in the model. You are including a random intercept for taxon through the random argument and the fs basis also includes a random intercept term for taxon. As you have included the same variable in the model twice, the model has no way of knowing how to apportion variance in the response between these terms. This will often cause estimation problems and even if the models fit OK, you will likely have larger standard errors than if you didn't have the identifiability problem.

    \n
    4. \n

  4. You will have to explain what you are trying or aiming to do rather than show what you did and ask if it is OK; it is not clear what the aim of the analysis, what model you are trying to fit, or how the data are structured, etc. (what is To Fa for example?).

    \n
    5. \n
\n

Unless you think the mean of Asfc for individual taxa changes over time smoothly, then there is no reason to use the taxon specific fs smooths. The random effect structure you propose seems reasonable, except I'm unclear from your description if you have multiple observations of Asfc per Facet? Or is facet informative in some way (inside vs top surface for example). If you don't have multiple observations per facet, you don't need the lowermost level in your ranef structure I believe. If individual taxa have different mean values of complexity (which I understand to be true broadly, but perhaps not in your specific group of taxa) then I think you do need Taxon at the highest level of the random effect structure.

\n

Finally, your model assume that the response Acsf values are conditional distributed Gaussian, meaning any value, negative or positive, is possible. If it is measuring complexity, that implies to me that negative values of the response are not observable, which would suggest the Gaussian is not appropriate. But perhaps this is not the case; the partial residuals don't look too bad, but proper model diagnostics would be need to confirm this. You also might need to consider the problem of temporal autocorrelation, although the Age smooth will help with that to some extent.

\n
\n

As an aside, how do I only plot the first plot?

\n
\n

Use the select argument to gratia' draw() function. This is a generic function so you need to look at the help for the gam method.

\n", "answer_id": 676895, "answer_text": "I would suggest you look at a changing a couple of things:\n\n\n\n\n\n\n\nThe distribution of Age is quite skewed, with some data squished up around 0 age. I would suggest trying to spread these values by out transforming Age, say via a square root transformation.\n\n\n\n\nIf you look at the smooth of Age, most of the smooth is supported by by a few unique time points - the whole right hand side of the plot. Those unique ages are having a potentially bigger influence on the shape of the function than the ages that are all squished up at the left of the x axis. Spreading out the ages allows all the data to influence the smooth more evenly. You can still present the results on the Age scale, What we want to avoid is unnecessary wiggles because the smooth adapted to widely spaced values on the original scale.\n\n\n\n\n\n\n\n\n\nThe fs smooths by Taxon aren't really doing much because they are very restricted in terms of basis functions.\n\n\n\n\n\n\n\n\n\nThere is potential for an identifiability issue as you include a Taxon random intercept through the fs smooths, and then again through the ranef structure.\n\n\n\n\nIdentifiability refers to the model's ability to unique identify (estimate a value for) each parameter in the model. You are including a random intercept for taxon through the random argument and the fs basis also includes a random intercept term for taxon. As you have included the same variable in the model twice, the model has no way of knowing how to apportion variance in the response between these terms. This will often cause estimation problems and even if the models fit OK, you will likely have larger standard errors than if you didn't have the identifiability problem.\n\n\n\n\n\n\n\n\n\nYou will have to explain what you are trying or aiming to do rather than show what you did and ask if it is OK; it is not clear what the aim of the analysis, what model you are trying to fit, or how the data are structured, etc. (what is To Fa for example?).\n\n\n\n\n\n\n\n\nUnless you think the mean of Asfc for individual taxa changes over time smoothly, then there is no reason to use the taxon specific fs smooths. The random effect structure you propose seems reasonable, except I'm unclear from your description if you have multiple observations of Asfc per Facet? Or is facet informative in some way (inside vs top surface for example). If you don't have multiple observations per facet, you don't need the lowermost level in your ranef structure I believe. If individual taxa have different mean values of complexity (which I understand to be true broadly, but perhaps not in your specific group of taxa) then I think you do need Taxon at the highest level of the random effect structure.\n\n\n\n\nFinally, your model assume that the response Acsf values are conditional distributed Gaussian, meaning any value, negative or positive, is possible. If it is measuring complexity, that implies to me that negative values of the response are not observable, which would suggest the Gaussian is not appropriate. But perhaps this is not the case; the partial residuals don't look too bad, but proper model diagnostics would be need to confirm this. You also might need to consider the problem of temporal autocorrelation, although the Age smooth will help with that to some extent.\n\n\n\n\n\n\n\nAs an aside, how do I only plot the first plot?\n\n\n\n\n\n\n\nUse the select argument to gratia' draw() function. This is a generic function so you need to look at the help for the gam method (https://gavinsimpson.github.io/gratia/reference/draw.gam.html).", "answer_url": "https://stats.stackexchange.com/a/676895", "author": "Gavin Simpson", "author_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-17T09:31:11+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676893, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Gavin Simpson", "profile_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "user_type": "registered"}, "created_at": "2026-08-17T09:31:11+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "344FFDF7-D995-42B0-B0C3-7BDBCFF41311", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/344FFDF7-D995-42B0-B0C3-7BDBCFF41311/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Gavin Simpson", "profile_url": "https://stats.stackexchange.com/users/1390/gavin-simpson", "user_type": "registered"}, "created_at": "2026-08-18T07:38:43+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "7758802C-386E-40D4-A5C5-B896DDCE2569", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/7758802C-386E-40D4-A5C5-B896DDCE2569/view-source"}], "score": 5, "updated_at": "2026-08-18T07:38:43+00:00"}], "domain": "statistics", "external_links": ["https://gavinsimpson.github.io/gratia/reference/draw.gam.html", "https://i.sstatic.net/H3mCUZgO.jpg", "https://i.sstatic.net/IXmEOkWk.jpg", "https://i.sstatic.net/KnHUkWbG.jpg", "https://i.sstatic.net/M6wP2hpB.jpg", "https://i.sstatic.net/UmccNppE.jpg", "https://i.sstatic.net/gYiJQdTI.jpg", "https://i.sstatic.net/iV7wvyRj.jpg"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "MrSwaggins", "question_author_url": "https://stats.stackexchange.com/users/331950/mrswaggins", "question_author_user_type": "registered", "question_created_at": "2026-08-17T05:08:58+00:00", "question_html": "

I have ~1400 measurements of teeth from ~40 species (taxon) that go back in time ~35mya (Age).\nThe data is noisy, so there is repetition in measurements from specimens that requires nesting as a random effect.

\n

I wish to see if there are trends in this data through time. I can see the trends as individual taxon boxplots if I roughly order them by time, but I would highly prefer Age as a continuous variable and the repetition accounted for.

\n

The problem is that taxa (i.e. species) generally exist for 1my or less, and there are large gaps, so if I understand gamms properly (not a given here lol) then the smoothing splines will be (in my simple terms) trying to extrapolate/estimate the curves for a species across the entire dataset where they don't really exist. I have tried to compensate for this using factor smoothing for taxon.

\n

To cut to the point after much testing and fiddling, I came up with this:

\n
temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs = "tp") + s(Age, taxon, bs = "fs", k = 3), data = df, random = ~(1|taxon/Specimen/To/Fa))\ntemp4 <- gamm4(Asfc ~ s(Age, k = 8, bs = "tp") + s(Age, taxon, bs = "fs", k = 3), data = df, random = ~(1|Specimen/To/Fa))\ndraw(temp3$gam, residuals = TRUE)\n
\n

And I get something like this:\n\"gamm4

\n

For this data am I "gamm-ing" correctly? The second plot suggests errr no, or is that just the intercept and slope for taxon influence?

\n

Should taxon be in the random effect structure? There are many specimens of each taxon.

\n

As an aside, how do I only plot the first plot?

\n

------ Edit for clarification from questions (and comments) below ------

\n

Each measurement is in this example a "complexity" value of a single facet (Fa has four levels), from a tooth (To has 8 levels). There are 1 to 8 measurements per Specimen requiring it to be a random effect. Each Specimen does belong to a species, though Species may or may not require nesting, or inclusion in the model per se, since most species have a single value for age, or are spread over 0.5 million years at most, it is highly correlated to Age and may be superfluous. Asfc is continuous, well normalised, and is considered gaussian.

\n

This is an updated model with model check based on comments : gamm4(Asfc ~ s(sqrtAge, k = 8, bs ="tp"), data = df, random = ~(1|Specimen/ToothNoLR/Facet))\n\"newGamm\"

\n

\"checkgamm\"

\n

RE check_model() I'm doing this to look for verifiable trends, not for prediction. I realise the large gaps would make the latter difficult, so this is more exploratory to see if a signal is present.

\n
$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3606.394\nRandom effects:\n Groups                   Name         Std.Dev.\n Facet:ToothNoLR:Specimen (Intercept)  0.4767  \n ToothNoLR:Specimen       (Intercept)  0.3814  \n Specimen                 (Intercept)  0.6024  \n Xr                       s(sqrt(Age)) 7.7972  \n Residual                              0.4563  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen, 1430; ToothNoLR:Specimen, 542; Specimen, 421; Xr, 6\nFixed Effects:\n    X(Intercept)  Xs(sqrt(Age))Fx1  \n        0.008243         -0.872465  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n5.56  total = 6.56 \n\nlmer.REML score: 3606.394     \n\nattr(,"class")\n[1] "gamm4" "list" \n
\n

------ 2nd edit updating random effect structure ------\nHere is the model with taxon added. The CI's are worse, but I suspect it is a "truer" model. gamm4(Asfc ~ s(sqrt(Age), k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))

\n

\"REtaxonadded\"

\n

The check shows a more even spread of residuals.

\n

\"retaxoncheck\"

\n

These are the new results.

\n
> temp3 <- gamm4(Asfc ~ s(sqrt(Age), k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.052\nRandom effects:\n Groups                         Name         Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept)  0.4786  \n ToothNoLR:Specimen:taxon       (Intercept)  0.3614  \n Specimen:taxon                 (Intercept)  0.5246  \n taxon                          (Intercept)  0.4379  \n Xr                             s(sqrt(Age)) 4.5753  \n Residual                                    0.4561  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\n    X(Intercept)  Xs(sqrt(Age))Fx1  \n        -0.04013          -0.01014  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n4.3  total = 5.3 \n\nlmer.REML score: 3566.053\n
\n

Compare them to the results where Age is not sqrt()'ed

\n
> temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs ="tp"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.762\nRandom effects:\n Groups                         Name        Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4651  \n ToothNoLR:Specimen:taxon       (Intercept) 0.3611  \n Specimen:taxon                 (Intercept) 0.5317  \n taxon                          (Intercept) 0.3790  \n Xr                             s(Age)      7.4438  \n Residual                                   0.4692  \nNumber of obs: 1442, groups:  Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\nX(Intercept)    Xs(Age)Fx1  \n    -0.04286      -0.98535  \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(Age, k = 8, bs = "tp")\n\nEstimated degrees of freedom:\n4.77  total = 5.77 \n\nlmer.REML score: 3566.762 \n
\n

I would appreciate any help in interpreting all this.

\n

------ Edit ------\nIn reply to the posterior predictive check. Removal of Facet.\n\"enter\ntemp3 without Facet in nesting, temp4 with Facet in nesting.

\n
> compare_performance(temp3, temp4)\n# Comparison of Model Performance Indices\n\nName  | Model |  AIC (weights) |  BIC (weights) |    R2 |  RMSE | Sigma\n-----------------------------------------------------------------------\ntemp3 | gamm4 | 4031.8 (0.475) | 4065.0 (0.484) | 0.049 | 0.572 | 0.573\ntemp4 | gamm4 | 4031.6 (0.525) | 4064.8 (0.516) | 0.049 | 0.274 | 0.275\n
\n

------ quick edit ------\nSo, yes, when I check $mer I get these results, and it appears to be(?), the missing "components" to complete the response?:

\n
> model_performance(temp3$mer)\n# Indices of model performance\n\nAIC    |   AICc |    BIC | R2 (cond.) | R2 (marg.) |   ICC |  RMSE | Sigma\n--------------------------------------------------------------------------\n3581.9 | 3582.0 | 3618.9 |      0.579 |  1.298e-04 | 0.579 | 0.572 | 0.660\n\n> icc(temp3$mer, by_group = TRUE)\n\nGroup                    |   ICC\n--------------------------------\nToothNoLR:Specimen:taxon | 0.127\nSpecimen:taxon           | 0.267\ntaxon                    | 0.185\n> check_model(temp3$mer)\n
\n

Just the lmer component predictive curve.\n\"enter

\n

> check_model(temp3) Throws an error, so it seems it is incapable of incorporating both $mer and $gam into the check.

\n", "question_id": 676893, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "I have ~1400 measurements of teeth from ~40 species (taxon) that go back in time ~35mya (Age).\nThe data is noisy, so there is repetition in measurements from specimens that requires nesting as a random effect.\n\n\n\n\nI wish to see if there are trends in this data through time. I can see the trends as individual taxon boxplots if I roughly order them by time, but I would highly prefer Age as a continuous variable and the repetition accounted for.\n\n\n\n\nThe problem is that taxa (i.e. species) generally exist for 1my or less, and there are large gaps, so if I understand gamms properly (not a given here lol) then the smoothing splines will be (in my simple terms) trying to extrapolate/estimate the curves for a species across the entire dataset where they don't really exist. I have tried to compensate for this using factor smoothing for taxon.\n\n\n\n\nTo cut to the point after much testing and fiddling, I came up with this:\n\n\n\n\ntemp3 <- gamm4(Asfc ~ s(Age, k = 8, bs = \"tp\") + s(Age, taxon, bs = \"fs\", k = 3), data = df, random = ~(1|taxon/Specimen/To/Fa))\ntemp4 <- gamm4(Asfc ~ s(Age, k = 8, bs = \"tp\") + s(Age, taxon, bs = \"fs\", k = 3), data = df, random = ~(1|Specimen/To/Fa))\ndraw(temp3$gam, residuals = TRUE)\n\n\n\n\n\nAnd I get something like this:\n[image: gamm4 plot; source: https://i.sstatic.net/M6wP2hpB.jpg] (https://i.sstatic.net/M6wP2hpB.jpg)\n\n\n\n\nFor this data am I \"gamm-ing\" correctly? The second plot suggests errr no, or is that just the intercept and slope for taxon influence?\n\n\n\n\nShould taxon be in the random effect structure? There are many specimens of each taxon.\n\n\n\n\nAs an aside, how do I only plot the first plot?\n\n\n\n\n------ Edit for clarification from questions (and comments) below ------\n\n\n\n\nEach measurement is in this example a \"complexity\" value of a single facet (Fa has four levels), from a tooth (To has 8 levels). There are 1 to 8 measurements per Specimen requiring it to be a random effect. Each Specimen does belong to a species, though Species may or may not require nesting, or inclusion in the model per se, since most species have a single value for age, or are spread over 0.5 million years at most, it is highly correlated to Age and may be superfluous. Asfc is continuous, well normalised, and is considered gaussian.\n\n\n\n\nThis is an updated model with model check based on comments : gamm4(Asfc ~ s(sqrtAge, k = 8, bs =\"tp\"), data = df, random = ~(1|Specimen/ToothNoLR/Facet))\n[image: newGamm; source: https://i.sstatic.net/UmccNppE.jpg] (https://i.sstatic.net/UmccNppE.jpg)\n\n\n\n\n[image: checkgamm; source: https://i.sstatic.net/gYiJQdTI.jpg] (https://i.sstatic.net/gYiJQdTI.jpg)\n\n\n\n\nRE check_model() I'm doing this to look for verifiable trends, not for prediction. I realise the large gaps would make the latter difficult, so this is more exploratory to see if a signal is present.\n\n\n\n\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3606.394\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen (Intercept) 0.4767 \n ToothNoLR:Specimen (Intercept) 0.3814 \n Specimen (Intercept) 0.6024 \n Xr s(sqrt(Age)) 7.7972 \n Residual 0.4563 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen, 1430; ToothNoLR:Specimen, 542; Specimen, 421; Xr, 6\nFixed Effects:\n X(Intercept) Xs(sqrt(Age))Fx1 \n 0.008243 -0.872465 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n5.56 total = 6.56 \n\nlmer.REML score: 3606.394 \n\nattr(,\"class\")\n[1] \"gamm4\" \"list\" \n\n\n\n\n\n------ 2nd edit updating random effect structure ------\nHere is the model with taxon added. The CI's are worse, but I suspect it is a \"truer\" model. gamm4(Asfc ~ s(sqrt(Age), k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n\n\n\n\n[image: REtaxonadded; source: https://i.sstatic.net/KnHUkWbG.jpg] (https://i.sstatic.net/KnHUkWbG.jpg)\n\n\n\n\nThe check shows a more even spread of residuals.\n\n\n\n\n[image: retaxoncheck; source: https://i.sstatic.net/IXmEOkWk.jpg] (https://i.sstatic.net/IXmEOkWk.jpg)\n\n\n\n\nThese are the new results.\n\n\n\n\n> temp3 <- gamm4(Asfc ~ s(sqrt(Age), k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.052\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4786 \n ToothNoLR:Specimen:taxon (Intercept) 0.3614 \n Specimen:taxon (Intercept) 0.5246 \n taxon (Intercept) 0.4379 \n Xr s(sqrt(Age)) 4.5753 \n Residual 0.4561 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\n X(Intercept) Xs(sqrt(Age))Fx1 \n -0.04013 -0.01014 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(sqrt(Age), k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n4.3 total = 5.3 \n\nlmer.REML score: 3566.053\n\n\n\n\n\nCompare them to the results where Age is not sqrt()'ed\n\n\n\n\n> temp3 <- gamm4(Asfc ~ s(Age, k = 8, bs =\"tp\"), data = df, random = ~(1|taxon/Specimen/ToothNoLR/Facet))\n> temp3\n$mer\nLinear mixed model fit by REML ['lmerMod']\nREML criterion at convergence: 3566.762\nRandom effects:\n Groups Name Std.Dev.\n Facet:ToothNoLR:Specimen:taxon (Intercept) 0.4651 \n ToothNoLR:Specimen:taxon (Intercept) 0.3611 \n Specimen:taxon (Intercept) 0.5317 \n taxon (Intercept) 0.3790 \n Xr s(Age) 7.4438 \n Residual 0.4692 \nNumber of obs: 1442, groups: Facet:ToothNoLR:Specimen:taxon, 1430; ToothNoLR:Specimen:taxon, 542; Specimen:taxon, 423; taxon, 46; Xr, 6\nFixed Effects:\nX(Intercept) Xs(Age)Fx1 \n -0.04286 -0.98535 \n\n$gam\n\nFamily: gaussian \nLink function: identity \n\nFormula:\nAsfc ~ s(Age, k = 8, bs = \"tp\")\n\nEstimated degrees of freedom:\n4.77 total = 5.77 \n\nlmer.REML score: 3566.762 \n\n\n\n\n\nI would appreciate any help in interpreting all this.\n\n\n\n\n------ Edit ------\nIn reply to the posterior predictive check. Removal of Facet.\n[image: enter image description here; source: https://i.sstatic.net/iV7wvyRj.jpg] (https://i.sstatic.net/iV7wvyRj.jpg)\ntemp3 without Facet in nesting, temp4 with Facet in nesting.\n\n\n\n\n> compare_performance(temp3, temp4)\n# Comparison of Model Performance Indices\n\nName | Model | AIC (weights) | BIC (weights) | R2 | RMSE | Sigma\n-----------------------------------------------------------------------\ntemp3 | gamm4 | 4031.8 (0.475) | 4065.0 (0.484) | 0.049 | 0.572 | 0.573\ntemp4 | gamm4 | 4031.6 (0.525) | 4064.8 (0.516) | 0.049 | 0.274 | 0.275\n\n\n\n\n\n------ quick edit ------\nSo, yes, when I check $mer I get these results, and it appears to be(?), the missing \"components\" to complete the response?:\n\n\n\n\n> model_performance(temp3$mer)\n# Indices of model performance\n\nAIC | AICc | BIC | R2 (cond.) | R2 (marg.) | ICC | RMSE | Sigma\n--------------------------------------------------------------------------\n3581.9 | 3582.0 | 3618.9 | 0.579 | 1.298e-04 | 0.579 | 0.572 | 0.660\n\n> icc(temp3$mer, by_group = TRUE)\n\nGroup | ICC\n--------------------------------\nToothNoLR:Specimen:taxon | 0.127\nSpecimen:taxon | 0.267\ntaxon | 0.185\n> check_model(temp3$mer)\n\n\n\n\n\nJust the lmer component predictive curve.\n[image: enter image description here; source: https://i.sstatic.net/H3mCUZgO.jpg] (https://i.sstatic.net/H3mCUZgO.jpg)\n\n\n\n\n> check_model(temp3) Throws an error, so it seems it is incapable of incorporating both $mer and $gam into the check.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MrSwaggins", "profile_url": "https://stats.stackexchange.com/users/331950/mrswaggins", "user_type": "registered"}, "created_at": "2026-08-17T05:08:58+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": 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One of my coauthors is strongly advocating to use ICC thresholds from this paper (https://pmc.ncbi.nlm.nih.gov/articles/PMC4913118/#bb0090) to interpret those metrics (<0.5 is poor, 0.5 to 0.75 is moderate, 0.75 to 0.9 is good, >0.9 is ex", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC4913118/#bb0090", "kind": "external_url", "post_id": 676924, "post_url": "https://stats.stackexchange.com/questions/676924/interpretation-of-interrater-reliability-metrics", "product": "citations", "record_id": "Scientific-Citation-Graph:13fadfc3dff411d2d964d3b0", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

A few thoughts:

\n
\n

My coauthor ... does want a specific cutoff that we call good, excellent etc.

\n
\n

This probably isn't a useful goal. What presumably matters is whether the differences in annotation will matter in clinical practice. For example, minor disagreements about which individual pixels belong in a region of interest (ROI) wouldn't be expected to have much practical effect. Differences in overall annotations of ROI (e.g., tumor versus normal) would matter a lot. It's not clear that any choice of arbitrary "cutoffs" would capture the practical importance of the differences. The practical difference is what presumably will matter most to your audience.

\n
\n

... I calculated the Jaccard index...

\n
\n

Think carefully about whether that's the appropriate measure for inter-rater reliability. That won't take into account the agreement that would be expected just by chance. The Wikipedia entry explains:

\n
\n

When the number of categories being used is small (e.g. 2 or 3), the likelihood for 2 raters to agree by pure chance increases dramatically.

\n
\n

You only have 2 categories. The Wikipedia entry describes several measures that adjust for chance agreement. Kappa statistics would probably be better choices.

\n
\n

The "ground truth" is the human annotations...

\n
\n

As the 2 humans don't always agree, you don't really have a "ground truth." You might get closer to a "ground truth" if you had 3 human raters and used the majority vote for each assessment.

\n", "answer_id": 676929, "answer_text": "A few thoughts:\n\n\n\n\n\n\n\nMy coauthor ... does want a specific cutoff that we call good, excellent etc.\n\n\n\n\n\n\n\nThis probably isn't a useful goal. What presumably matters is whether the differences in annotation will matter in clinical practice. For example, minor disagreements about which individual pixels belong in a region of interest (ROI) wouldn't be expected to have much practical effect. Differences in overall annotations of ROI (e.g., tumor versus normal) would matter a lot. It's not clear that any choice of arbitrary \"cutoffs\" would capture the practical importance of the differences. The practical difference is what presumably will matter most to your audience.\n\n\n\n\n\n\n\n... I calculated the Jaccard index...\n\n\n\n\n\n\n\nThink carefully about whether that's the appropriate measure for inter-rater reliability. That won't take into account the agreement that would be expected just by chance. The Wikipedia entry (https://en.wikipedia.org/wiki/Inter-rater_reliability) explains:\n\n\n\n\n\n\n\nWhen the number of categories being used is small (e.g. 2 or 3), the likelihood for 2 raters to agree by pure chance increases dramatically.\n\n\n\n\n\n\n\nYou only have 2 categories. The Wikipedia entry describes several measures that adjust for chance agreement. Kappa statistics (https://en.wikipedia.org/wiki/Inter-rater_reliability#Kappa_statistics) would probably be better choices.\n\n\n\n\n\n\n\nThe \"ground truth\" is the human annotations...\n\n\n\n\n\n\n\nAs the 2 humans don't always agree, you don't really have a \"ground truth.\" You might get closer to a \"ground truth\" if you had 3 human raters and used the majority vote for each assessment.", "answer_url": "https://stats.stackexchange.com/a/676929", "author": "EdM", "author_url": "https://stats.stackexchange.com/users/28500/edm", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-21T16:56:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676924, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-08-21T16:56:04+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "00FF675D-4690-4BD3-BC52-6349CAAC7745", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/00FF675D-4690-4BD3-BC52-6349CAAC7745/view-source"}], "score": 2, "updated_at": "2026-08-21T16:56:04+00:00"}], "domain": "statistics", "external_links": ["https://en.wikipedia.org/wiki/Inter-rater_reliability", "https://en.wikipedia.org/wiki/Inter-rater_reliability#Kappa_statistics", "https://pmc.ncbi.nlm.nih.gov/articles/PMC4913118/#bb0090"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "deee", "question_author_url": "https://stats.stackexchange.com/users/492702/deee", "question_author_user_type": "registered", "question_created_at": "2026-08-20T15:23:03+00:00", "question_html": "

I'm working on a medical image segmentation problem. I have the source images, automated annotations, and manual annotations from two human raters. The annotations have two formats: predefined regions, and per-pixel annotation.

\n

For the predefined regions, each rater overlaid a map of 44 semantically meaningful regions onto the source image and annotated each region as True/False. For a given example, there are therefore 44 binary variables that each rater can agree or disagree on.

\n

For the per-pixel annotation, each rater created a pixel mask to identify the region of interest. For a given example, each rater could therefore agree or disagree on each individual pixel in the image.

\n

The "ground truth" is the human annotations. The humans don't perfectly agree on their annotations. The nature of the task means that for the per-pixel annotation there's a fair amount of possible disagreement without one rater being "wrong".

\n

I want to assess the reliability of my automated annotations. I have calculated some metrics between each pair of raters (rater a to automated, rater b to automated, rater a to rater b). For the predefined regions I calculated the Jaccard index on a per-region basis, and for the per-pixel annotations I calculated the Jaccard index on a per-pixel basis, plus the Normalised Surface Distance.

\n

As far as I know, there aren't established conventions on what is "good" for these metrics on this task. One of my coauthors is strongly advocating to use ICC thresholds from this paper to interpret those metrics (<0.5 is poor, 0.5 to 0.75 is moderate, 0.75 to 0.9 is good, >0.9 is excellent). I'm unhappy about this because I think ICC is fundamentally different from the metrics we've used.

\n

My coauthor is happy to use different thresholds if I can find more relevant ones, but does want a specific cutoff that we call good, excellent etc. I can't find any resources for more relevant thresholds.

\n

Is it reasonable to use these thresholds to interpret Jaccard index and Normalised Surface Distance on an image segmentation task? Is there an established way to decide what "good" agreement is for these metrics?

\n", "question_id": 676924, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "I'm working on a medical image segmentation problem. I have the source images, automated annotations, and manual annotations from two human raters. The annotations have two formats: predefined regions, and per-pixel annotation.\n\n\n\n\nFor the predefined regions, each rater overlaid a map of 44 semantically meaningful regions onto the source image and annotated each region as True/False. For a given example, there are therefore 44 binary variables that each rater can agree or disagree on.\n\n\n\n\nFor the per-pixel annotation, each rater created a pixel mask to identify the region of interest. For a given example, each rater could therefore agree or disagree on each individual pixel in the image.\n\n\n\n\nThe \"ground truth\" is the human annotations. The humans don't perfectly agree on their annotations. The nature of the task means that for the per-pixel annotation there's a fair amount of possible disagreement without one rater being \"wrong\".\n\n\n\n\nI want to assess the reliability of my automated annotations. I have calculated some metrics between each pair of raters (rater a to automated, rater b to automated, rater a to rater b). For the predefined regions I calculated the Jaccard index on a per-region basis, and for the per-pixel annotations I calculated the Jaccard index on a per-pixel basis, plus the Normalised Surface Distance.\n\n\n\n\nAs far as I know, there aren't established conventions on what is \"good\" for these metrics on this task. One of my coauthors is strongly advocating to use ICC thresholds from this paper (https://pmc.ncbi.nlm.nih.gov/articles/PMC4913118/#bb0090) to interpret those metrics (<0.5 is poor, 0.5 to 0.75 is moderate, 0.75 to 0.9 is good, >0.9 is excellent). I'm unhappy about this because I think ICC is fundamentally different from the metrics we've used.\n\n\n\n\nMy coauthor is happy to use different thresholds if I can find more relevant ones, but does want a specific cutoff that we call good, excellent etc. I can't find any resources for more relevant thresholds.\n\n\n\n\nIs it reasonable to use these thresholds to interpret Jaccard index and Normalised Surface Distance on an image segmentation task? Is there an established way to decide what \"good\" agreement is for these metrics?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "deee", "profile_url": "https://stats.stackexchange.com/users/492702/deee", "user_type": "registered"}, "created_at": "2026-08-20T15:23:03+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "F3431DE0-82AE-4630-A45E-E672DDBF5F5A", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/F3431DE0-82AE-4630-A45E-E672DDBF5F5A/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-08-21T22:30:56+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "62C64EA4-AD43-4820-A545-BC23853CCAD6", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/62C64EA4-AD43-4820-A545-BC23853CCAD6/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676924/interpretation-of-interrater-reliability-metrics", "split": "test", "split_group": "3a527218b1c4490fdc463d61353fb9bbbeaa42d0e07302db9e210419fe3df06d", "tags": ["interpretation", "intraclass-correlation", "jaccard-similarity"], "thread_id": "stats:676924", "title": "Interpretation of interrater reliability metrics"}} {"citation_context": "t won't take into account the agreement that would be expected just by chance. The Wikipedia entry (https://en.wikipedia.org/wiki/Inter-rater_reliability) explains:\n\n\n\n\n\n\n\nWhen the number of categories being used is small (e.g. 2 or 3), the likelihood f", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Inter-rater_reliability", "kind": "external_url", "post_id": 676929, "post_url": "https://stats.stackexchange.com/a/676929", "product": "citations", "record_id": "Scientific-Citation-Graph:dd35ba7e9280323b5e5ab76f", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

A few thoughts:

\n
\n

My coauthor ... does want a specific cutoff that we call good, excellent etc.

\n
\n

This probably isn't a useful goal. What presumably matters is whether the differences in annotation will matter in clinical practice. For example, minor disagreements about which individual pixels belong in a region of interest (ROI) wouldn't be expected to have much practical effect. Differences in overall annotations of ROI (e.g., tumor versus normal) would matter a lot. It's not clear that any choice of arbitrary "cutoffs" would capture the practical importance of the differences. The practical difference is what presumably will matter most to your audience.

\n
\n

... I calculated the Jaccard index...

\n
\n

Think carefully about whether that's the appropriate measure for inter-rater reliability. That won't take into account the agreement that would be expected just by chance. The Wikipedia entry explains:

\n
\n

When the number of categories being used is small (e.g. 2 or 3), the likelihood for 2 raters to agree by pure chance increases dramatically.

\n
\n

You only have 2 categories. The Wikipedia entry describes several measures that adjust for chance agreement. Kappa statistics would probably be better choices.

\n
\n

The "ground truth" is the human annotations...

\n
\n

As the 2 humans don't always agree, you don't really have a "ground truth." You might get closer to a "ground truth" if you had 3 human raters and used the majority vote for each assessment.

\n", "answer_id": 676929, "answer_text": "A few thoughts:\n\n\n\n\n\n\n\nMy coauthor ... does want a specific cutoff that we call good, excellent etc.\n\n\n\n\n\n\n\nThis probably isn't a useful goal. What presumably matters is whether the differences in annotation will matter in clinical practice. For example, minor disagreements about which individual pixels belong in a region of interest (ROI) wouldn't be expected to have much practical effect. Differences in overall annotations of ROI (e.g., tumor versus normal) would matter a lot. It's not clear that any choice of arbitrary \"cutoffs\" would capture the practical importance of the differences. The practical difference is what presumably will matter most to your audience.\n\n\n\n\n\n\n\n... I calculated the Jaccard index...\n\n\n\n\n\n\n\nThink carefully about whether that's the appropriate measure for inter-rater reliability. That won't take into account the agreement that would be expected just by chance. The Wikipedia entry (https://en.wikipedia.org/wiki/Inter-rater_reliability) explains:\n\n\n\n\n\n\n\nWhen the number of categories being used is small (e.g. 2 or 3), the likelihood for 2 raters to agree by pure chance increases dramatically.\n\n\n\n\n\n\n\nYou only have 2 categories. The Wikipedia entry describes several measures that adjust for chance agreement. Kappa statistics (https://en.wikipedia.org/wiki/Inter-rater_reliability#Kappa_statistics) would probably be better choices.\n\n\n\n\n\n\n\nThe \"ground truth\" is the human annotations...\n\n\n\n\n\n\n\nAs the 2 humans don't always agree, you don't really have a \"ground truth.\" You might get closer to a \"ground truth\" if you had 3 human raters and used the majority vote for each assessment.", "answer_url": "https://stats.stackexchange.com/a/676929", "author": "EdM", "author_url": "https://stats.stackexchange.com/users/28500/edm", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-21T16:56:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676924, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-08-21T16:56:04+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "00FF675D-4690-4BD3-BC52-6349CAAC7745", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/00FF675D-4690-4BD3-BC52-6349CAAC7745/view-source"}], "score": 2, "updated_at": "2026-08-21T16:56:04+00:00"}], "domain": "statistics", "external_links": ["https://en.wikipedia.org/wiki/Inter-rater_reliability", "https://en.wikipedia.org/wiki/Inter-rater_reliability#Kappa_statistics", "https://pmc.ncbi.nlm.nih.gov/articles/PMC4913118/#bb0090"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "deee", "question_author_url": "https://stats.stackexchange.com/users/492702/deee", "question_author_user_type": "registered", "question_created_at": "2026-08-20T15:23:03+00:00", "question_html": "

I'm working on a medical image segmentation problem. I have the source images, automated annotations, and manual annotations from two human raters. The annotations have two formats: predefined regions, and per-pixel annotation.

\n

For the predefined regions, each rater overlaid a map of 44 semantically meaningful regions onto the source image and annotated each region as True/False. For a given example, there are therefore 44 binary variables that each rater can agree or disagree on.

\n

For the per-pixel annotation, each rater created a pixel mask to identify the region of interest. For a given example, each rater could therefore agree or disagree on each individual pixel in the image.

\n

The "ground truth" is the human annotations. The humans don't perfectly agree on their annotations. The nature of the task means that for the per-pixel annotation there's a fair amount of possible disagreement without one rater being "wrong".

\n

I want to assess the reliability of my automated annotations. I have calculated some metrics between each pair of raters (rater a to automated, rater b to automated, rater a to rater b). For the predefined regions I calculated the Jaccard index on a per-region basis, and for the per-pixel annotations I calculated the Jaccard index on a per-pixel basis, plus the Normalised Surface Distance.

\n

As far as I know, there aren't established conventions on what is "good" for these metrics on this task. One of my coauthors is strongly advocating to use ICC thresholds from this paper to interpret those metrics (<0.5 is poor, 0.5 to 0.75 is moderate, 0.75 to 0.9 is good, >0.9 is excellent). I'm unhappy about this because I think ICC is fundamentally different from the metrics we've used.

\n

My coauthor is happy to use different thresholds if I can find more relevant ones, but does want a specific cutoff that we call good, excellent etc. I can't find any resources for more relevant thresholds.

\n

Is it reasonable to use these thresholds to interpret Jaccard index and Normalised Surface Distance on an image segmentation task? Is there an established way to decide what "good" agreement is for these metrics?

\n", "question_id": 676924, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "I'm working on a medical image segmentation problem. I have the source images, automated annotations, and manual annotations from two human raters. The annotations have two formats: predefined regions, and per-pixel annotation.\n\n\n\n\nFor the predefined regions, each rater overlaid a map of 44 semantically meaningful regions onto the source image and annotated each region as True/False. For a given example, there are therefore 44 binary variables that each rater can agree or disagree on.\n\n\n\n\nFor the per-pixel annotation, each rater created a pixel mask to identify the region of interest. For a given example, each rater could therefore agree or disagree on each individual pixel in the image.\n\n\n\n\nThe \"ground truth\" is the human annotations. The humans don't perfectly agree on their annotations. The nature of the task means that for the per-pixel annotation there's a fair amount of possible disagreement without one rater being \"wrong\".\n\n\n\n\nI want to assess the reliability of my automated annotations. I have calculated some metrics between each pair of raters (rater a to automated, rater b to automated, rater a to rater b). For the predefined regions I calculated the Jaccard index on a per-region basis, and for the per-pixel annotations I calculated the Jaccard index on a per-pixel basis, plus the Normalised Surface Distance.\n\n\n\n\nAs far as I know, there aren't established conventions on what is \"good\" for these metrics on this task. One of my coauthors is strongly advocating to use ICC thresholds from this paper (https://pmc.ncbi.nlm.nih.gov/articles/PMC4913118/#bb0090) to interpret those metrics (<0.5 is poor, 0.5 to 0.75 is moderate, 0.75 to 0.9 is good, >0.9 is excellent). I'm unhappy about this because I think ICC is fundamentally different from the metrics we've used.\n\n\n\n\nMy coauthor is happy to use different thresholds if I can find more relevant ones, but does want a specific cutoff that we call good, excellent etc. I can't find any resources for more relevant thresholds.\n\n\n\n\nIs it reasonable to use these thresholds to interpret Jaccard index and Normalised Surface Distance on an image segmentation task? Is there an established way to decide what \"good\" agreement is for these metrics?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "deee", "profile_url": "https://stats.stackexchange.com/users/492702/deee", "user_type": "registered"}, "created_at": "2026-08-20T15:23:03+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "F3431DE0-82AE-4630-A45E-E672DDBF5F5A", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/F3431DE0-82AE-4630-A45E-E672DDBF5F5A/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-08-21T22:30:56+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "62C64EA4-AD43-4820-A545-BC23853CCAD6", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/62C64EA4-AD43-4820-A545-BC23853CCAD6/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676924/interpretation-of-interrater-reliability-metrics", "split": "test", "split_group": "3a527218b1c4490fdc463d61353fb9bbbeaa42d0e07302db9e210419fe3df06d", "tags": ["interpretation", "intraclass-correlation", "jaccard-similarity"], "thread_id": "stats:676924", "title": "Interpretation of interrater reliability metrics"}} {"citation_context": " The Wikipedia entry describes several measures that adjust for chance agreement. Kappa statistics (https://en.wikipedia.org/wiki/Inter-rater_reliability#Kappa_statistics) would probably be better choices.\n\n\n\n\n\n\n\nThe \"ground truth\" is the human annotations...\n\n\n\n\n\n\n\nAs ", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Inter-rater_reliability#Kappa_statistics", "kind": "external_url", "post_id": 676929, "post_url": "https://stats.stackexchange.com/a/676929", "product": "citations", "record_id": "Scientific-Citation-Graph:e7fb834f03e0f8806acdc5f9", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

A few thoughts:

\n
\n

My coauthor ... does want a specific cutoff that we call good, excellent etc.

\n
\n

This probably isn't a useful goal. What presumably matters is whether the differences in annotation will matter in clinical practice. For example, minor disagreements about which individual pixels belong in a region of interest (ROI) wouldn't be expected to have much practical effect. Differences in overall annotations of ROI (e.g., tumor versus normal) would matter a lot. It's not clear that any choice of arbitrary "cutoffs" would capture the practical importance of the differences. The practical difference is what presumably will matter most to your audience.

\n
\n

... I calculated the Jaccard index...

\n
\n

Think carefully about whether that's the appropriate measure for inter-rater reliability. That won't take into account the agreement that would be expected just by chance. The Wikipedia entry explains:

\n
\n

When the number of categories being used is small (e.g. 2 or 3), the likelihood for 2 raters to agree by pure chance increases dramatically.

\n
\n

You only have 2 categories. The Wikipedia entry describes several measures that adjust for chance agreement. Kappa statistics would probably be better choices.

\n
\n

The "ground truth" is the human annotations...

\n
\n

As the 2 humans don't always agree, you don't really have a "ground truth." You might get closer to a "ground truth" if you had 3 human raters and used the majority vote for each assessment.

\n", "answer_id": 676929, "answer_text": "A few thoughts:\n\n\n\n\n\n\n\nMy coauthor ... does want a specific cutoff that we call good, excellent etc.\n\n\n\n\n\n\n\nThis probably isn't a useful goal. What presumably matters is whether the differences in annotation will matter in clinical practice. For example, minor disagreements about which individual pixels belong in a region of interest (ROI) wouldn't be expected to have much practical effect. Differences in overall annotations of ROI (e.g., tumor versus normal) would matter a lot. It's not clear that any choice of arbitrary \"cutoffs\" would capture the practical importance of the differences. The practical difference is what presumably will matter most to your audience.\n\n\n\n\n\n\n\n... I calculated the Jaccard index...\n\n\n\n\n\n\n\nThink carefully about whether that's the appropriate measure for inter-rater reliability. That won't take into account the agreement that would be expected just by chance. The Wikipedia entry (https://en.wikipedia.org/wiki/Inter-rater_reliability) explains:\n\n\n\n\n\n\n\nWhen the number of categories being used is small (e.g. 2 or 3), the likelihood for 2 raters to agree by pure chance increases dramatically.\n\n\n\n\n\n\n\nYou only have 2 categories. The Wikipedia entry describes several measures that adjust for chance agreement. Kappa statistics (https://en.wikipedia.org/wiki/Inter-rater_reliability#Kappa_statistics) would probably be better choices.\n\n\n\n\n\n\n\nThe \"ground truth\" is the human annotations...\n\n\n\n\n\n\n\nAs the 2 humans don't always agree, you don't really have a \"ground truth.\" You might get closer to a \"ground truth\" if you had 3 human raters and used the majority vote for each assessment.", "answer_url": "https://stats.stackexchange.com/a/676929", "author": "EdM", "author_url": "https://stats.stackexchange.com/users/28500/edm", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-21T16:56:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676924, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-08-21T16:56:04+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "00FF675D-4690-4BD3-BC52-6349CAAC7745", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/00FF675D-4690-4BD3-BC52-6349CAAC7745/view-source"}], "score": 2, "updated_at": "2026-08-21T16:56:04+00:00"}], "domain": "statistics", "external_links": ["https://en.wikipedia.org/wiki/Inter-rater_reliability", "https://en.wikipedia.org/wiki/Inter-rater_reliability#Kappa_statistics", "https://pmc.ncbi.nlm.nih.gov/articles/PMC4913118/#bb0090"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "deee", "question_author_url": "https://stats.stackexchange.com/users/492702/deee", "question_author_user_type": "registered", "question_created_at": "2026-08-20T15:23:03+00:00", "question_html": "

I'm working on a medical image segmentation problem. I have the source images, automated annotations, and manual annotations from two human raters. The annotations have two formats: predefined regions, and per-pixel annotation.

\n

For the predefined regions, each rater overlaid a map of 44 semantically meaningful regions onto the source image and annotated each region as True/False. For a given example, there are therefore 44 binary variables that each rater can agree or disagree on.

\n

For the per-pixel annotation, each rater created a pixel mask to identify the region of interest. For a given example, each rater could therefore agree or disagree on each individual pixel in the image.

\n

The "ground truth" is the human annotations. The humans don't perfectly agree on their annotations. The nature of the task means that for the per-pixel annotation there's a fair amount of possible disagreement without one rater being "wrong".

\n

I want to assess the reliability of my automated annotations. I have calculated some metrics between each pair of raters (rater a to automated, rater b to automated, rater a to rater b). For the predefined regions I calculated the Jaccard index on a per-region basis, and for the per-pixel annotations I calculated the Jaccard index on a per-pixel basis, plus the Normalised Surface Distance.

\n

As far as I know, there aren't established conventions on what is "good" for these metrics on this task. One of my coauthors is strongly advocating to use ICC thresholds from this paper to interpret those metrics (<0.5 is poor, 0.5 to 0.75 is moderate, 0.75 to 0.9 is good, >0.9 is excellent). I'm unhappy about this because I think ICC is fundamentally different from the metrics we've used.

\n

My coauthor is happy to use different thresholds if I can find more relevant ones, but does want a specific cutoff that we call good, excellent etc. I can't find any resources for more relevant thresholds.

\n

Is it reasonable to use these thresholds to interpret Jaccard index and Normalised Surface Distance on an image segmentation task? Is there an established way to decide what "good" agreement is for these metrics?

\n", "question_id": 676924, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "I'm working on a medical image segmentation problem. I have the source images, automated annotations, and manual annotations from two human raters. The annotations have two formats: predefined regions, and per-pixel annotation.\n\n\n\n\nFor the predefined regions, each rater overlaid a map of 44 semantically meaningful regions onto the source image and annotated each region as True/False. For a given example, there are therefore 44 binary variables that each rater can agree or disagree on.\n\n\n\n\nFor the per-pixel annotation, each rater created a pixel mask to identify the region of interest. For a given example, each rater could therefore agree or disagree on each individual pixel in the image.\n\n\n\n\nThe \"ground truth\" is the human annotations. The humans don't perfectly agree on their annotations. The nature of the task means that for the per-pixel annotation there's a fair amount of possible disagreement without one rater being \"wrong\".\n\n\n\n\nI want to assess the reliability of my automated annotations. I have calculated some metrics between each pair of raters (rater a to automated, rater b to automated, rater a to rater b). For the predefined regions I calculated the Jaccard index on a per-region basis, and for the per-pixel annotations I calculated the Jaccard index on a per-pixel basis, plus the Normalised Surface Distance.\n\n\n\n\nAs far as I know, there aren't established conventions on what is \"good\" for these metrics on this task. One of my coauthors is strongly advocating to use ICC thresholds from this paper (https://pmc.ncbi.nlm.nih.gov/articles/PMC4913118/#bb0090) to interpret those metrics (<0.5 is poor, 0.5 to 0.75 is moderate, 0.75 to 0.9 is good, >0.9 is excellent). I'm unhappy about this because I think ICC is fundamentally different from the metrics we've used.\n\n\n\n\nMy coauthor is happy to use different thresholds if I can find more relevant ones, but does want a specific cutoff that we call good, excellent etc. I can't find any resources for more relevant thresholds.\n\n\n\n\nIs it reasonable to use these thresholds to interpret Jaccard index and Normalised Surface Distance on an image segmentation task? Is there an established way to decide what \"good\" agreement is for these metrics?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "deee", "profile_url": "https://stats.stackexchange.com/users/492702/deee", "user_type": "registered"}, "created_at": "2026-08-20T15:23:03+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "F3431DE0-82AE-4630-A45E-E672DDBF5F5A", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/F3431DE0-82AE-4630-A45E-E672DDBF5F5A/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-08-21T22:30:56+00:00", "raw_file": "raw/codex_api_v1/01ff643b5e725b2402c38de261074c3bef3326820f24db4342e17e318353268e_1790825246205492400_0.json", "raw_sha256": "a0521ae83c8630be00a12499e9aaa253069e57a5e0ff902fea3e9b8e7acb810f", "revision_guid": "62C64EA4-AD43-4820-A545-BC23853CCAD6", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/62C64EA4-AD43-4820-A545-BC23853CCAD6/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676924/interpretation-of-interrater-reliability-metrics", "split": "test", "split_group": "3a527218b1c4490fdc463d61353fb9bbbeaa42d0e07302db9e210419fe3df06d", "tags": ["interpretation", "intraclass-correlation", "jaccard-similarity"], "thread_id": "stats:676924", "title": "Interpretation of interrater reliability metrics"}} {"citation_context": "-Gamma mixture that brings about the unconstrained Negative Binomial see e.g., p.745, in this book (https://archive.org/details/econometricanaly0000gree_f4x3/econometricanaly0000gree_f4x3)).\n\n\n\n\nAlso notice that the first summation is just the Hessian of the \"parent\" specification: tha", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://archive.org/details/econometricanaly0000gree_f4x3/econometricanaly0000gree_f4x3", "kind": "external_url", "post_id": 676952, "post_url": "https://stats.stackexchange.com/questions/676952/hessian-with-invariably-positive-elements-for-zero-truncated-negative-binomial-r", "product": "citations", "record_id": "Scientific-Citation-Graph:873a0dee883ea4e50254c923", "split": "test", "thread": {"accepted_answer_id": 676993, "answers": [{"answer_html": "

As it turns out there is a mistake in Grogger and Carson's second derivatives of the zero-truncated negative binomial loglikelihood function wrt the regression parameters: blink and you'll miss it (the sign in one of the exponents should have been outside the parenthesis, probably a typo in the original)

\n

\\begin{align}\n\t\\frac{\\partial^2}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\ell_\\mathrm{ZTNB}{\\left(\\boldsymbol{\\beta},\\alpha\\right)} &= -\\sum_{i=1}^n{\\frac{1+\\alpha^{-1} y_i}{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^2}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T} - \\sum_{i=1}^n\\left\\{\\frac{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\left(1+\\alpha\\right)}-e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(\\alpha^{-1}+1\\right)\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^\\color{blue}{-\\left(2+\\alpha\\right)}}{1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}} +\\right. \\nonumber \\\\ \n\t& \\quad \\left. -\\frac{e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-2(1+\\alpha)}}{\\left[1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}\\right]^2}\\right\\}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T \n\\end{align}

\n

I guess I must have been so eager to verify the original results that I conditioned myself to "see" the original notation as correct - even when going through my own derivations over and over again. Few days away from this problem must have broken this perverse loop.

\n", "answer_id": 676993, "answer_text": "As it turns out there is a mistake in Grogger and Carson's second derivatives of the zero-truncated negative binomial loglikelihood function wrt the regression parameters: blink and you'll miss it (the sign in one of the exponents should have been outside the parenthesis, probably a typo in the original)\n\n\n\n\n\\begin{align}\n\t\\frac{\\partial^2}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\ell_\\mathrm{ZTNB}{\\left(\\boldsymbol{\\beta},\\alpha\\right)} &= -\\sum_{i=1}^n{\\frac{1+\\alpha^{-1} y_i}{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^2}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T} - \\sum_{i=1}^n\\left\\{\\frac{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\left(1+\\alpha\\right)}-e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(\\alpha^{-1}+1\\right)\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^\\color{blue}{-\\left(2+\\alpha\\right)}}{1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}} +\\right. \\nonumber \\\\ \n\t& \\quad \\left. -\\frac{e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-2(1+\\alpha)}}{\\left[1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}\\right]^2}\\right\\}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T \n\\end{align}\n\n\n\n\nI guess I must have been so eager to verify the original results that I conditioned myself to \"see\" the original notation as correct - even when going through my own derivations over and over again. Few days away from this problem must have broken this perverse loop.", "answer_url": "https://stats.stackexchange.com/a/676993", "author": "Ettore S", "author_url": "https://stats.stackexchange.com/users/513606/ettore-s", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-28T23:08:55+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676952, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ettore S", "profile_url": "https://stats.stackexchange.com/users/513606/ettore-s", "user_type": "registered"}, "created_at": "2026-08-28T23:08:55+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "E33B0B4F-D54D-46E9-8E25-81C77E90B942", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/E33B0B4F-D54D-46E9-8E25-81C77E90B942/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ettore S", "profile_url": "https://stats.stackexchange.com/users/513606/ettore-s", "user_type": "registered"}, "created_at": "2026-08-28T23:15:33+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "71D393BD-A8FB-4799-92AF-8FD04BFA27AE", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/71D393BD-A8FB-4799-92AF-8FD04BFA27AE/view-source"}], "score": 0, "updated_at": "2026-08-28T23:15:33+00:00"}], "domain": "statistics", "external_links": ["https://archive.org/details/econometricanaly0000gree_f4x3/econometricanaly0000gree_f4x3", "https://www.jstor.org/stable/2096628", "https://www.stata.com/manuals13/rtnbreg.pdf"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Ettore S", "question_author_url": "https://stats.stackexchange.com/users/513606/ettore-s", "question_author_user_type": "registered", "question_created_at": "2026-08-24T16:36:39+00:00", "question_html": "

In the context of zero-truncated negative binomial regression (see this other post) , twice-differentiating the loglikelihood yields a well-known result (see e.g., footnote 5 in this paper):

\n

$$\n\\begin{aligned}\n\t\\frac{\\partial^2}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\ell_\\mathrm{ZTNB}{\\left(\\boldsymbol{\\beta},\\alpha\\right)} &= -\\sum_{i=1}^n{\\frac{1+\\alpha^{-1} y_i}{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^2}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T} -\\sum_{i=1}^n\\left\\{\\frac{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\left(1+\\alpha\\right)}-e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(\\alpha^{-1}+1\\right)\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{\\left(-2+\\alpha\\right)}}{1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}} +\\right. \\nonumber \\\\ \n\t& \\quad \\left. -\\frac{e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-2(1+\\alpha)}}{\\left[1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}\\right]^2}\\right\\}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T\n\\end{aligned}\n$$

\n

where:

\n\n

The above equation is correct as far as I can tell. Yet when I implement it in practice, it seems to invariably yield an Hessian with positive elements.

\n

Maybe this is a silly question, and it all depends on initialisation strategies etc.: but is it possible to ascertain whether the above-mentioned Hessian is, somehow, "bound to" have positive elements?

\n

I thought this should be a no brainer and I confess I didn't expect struggling on its implementation. Having re-checked the equations and code multiple times now, and tried different numerical examples, I begin to worry about being unable to get an Hessian with negative elements - which is what I need to implement the method of maximum likelihood using, say, textbook Newton-Raphson iterations.

\n

I appreciate any pointer to help me understand what I might be getting wrong - a simple illustrative example below.

\n

Example

\n

For the sake of illustration, consider data(medpar) available from the R package COUNT. The data subset data_medpar <- medpar[,c("los", "died", "hmo", "type2", "type3")] corresponds to the example reported in this STATA documentation for tnbreg.

\n\n

And I get a positive Hessian - as I always do

\n
> Hessian_iter\n          [,1]      [,2]      [,3]      [,4]      [,5]\n[1,] 200849.45 53431.282 24465.222 43243.069 39578.773\n[2,]  53431.28 53431.282  6036.786 12451.468 14079.196\n[3,]  24465.22  6036.786 24465.222  4528.242  1145.349\n[4,]  43243.07 12451.468  4528.242 43243.069     0.000\n[5,]  39578.77 14079.196  1145.349     0.000 39578.773\n
\n

Any thoughts? Am I missing anything trivial here? Thanks in advance.

\n", "question_id": 676952, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "In the context of zero-truncated negative binomial regression (see this other post (https://stats.stackexchange.com/q/676385/513606)) , twice-differentiating the loglikelihood yields a well-known result (see e.g., footnote 5 in this paper (https://www.jstor.org/stable/2096628)):\n\n\n\n\n$$\n\\begin{aligned}\n\t\\frac{\\partial^2}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\ell_\\mathrm{ZTNB}{\\left(\\boldsymbol{\\beta},\\alpha\\right)} &= -\\sum_{i=1}^n{\\frac{1+\\alpha^{-1} y_i}{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^2}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T} -\\sum_{i=1}^n\\left\\{\\frac{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\left(1+\\alpha\\right)}-e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(\\alpha^{-1}+1\\right)\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{\\left(-2+\\alpha\\right)}}{1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}} +\\right. \\nonumber \\\\ \n\t& \\quad \\left. -\\frac{e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-2(1+\\alpha)}}{\\left[1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}\\right]^2}\\right\\}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T\n\\end{aligned}\n$$\n\n\n\n\nwhere:\n\n\n\n\n\n$y_i > 0 \\quad (i=1,2,\\dots,n)$ denotes the observed realisations (observations enter a zero-truncated sample only after the first count occurs);\n\n\n\n\n$\\mathbf{x}^T_i$ is the $i$-th row of the regression data matrix;\n\n\n\n\n$\\boldsymbol{\\beta}$ is the unknown vector of regression coefficients (to be estimated);\n\n\n\n\n$\\alpha$ is another unknown parameter to be estimated, namely the reciprocal of the so-called dispersion parameter ($\\alpha$ is inherited from the Poisson-Gamma mixture that brings about the unconstrained Negative Binomial see e.g., p.745, in this book (https://archive.org/details/econometricanaly0000gree_f4x3/econometricanaly0000gree_f4x3)).\n\n\n\n\nAlso notice that the first summation is just the Hessian of the \"parent\" specification: that one works fine i.e., its elements are negative as expected.\n\n\n\n\n\nThe above equation is correct as far as I can tell. Yet when I implement it in practice, it seems to invariably yield an Hessian with positive elements.\n\n\n\n\nMaybe this is a silly question, and it all depends on initialisation strategies etc.: but is it possible to ascertain whether the above-mentioned Hessian is, somehow, \"bound to\" have positive elements?\n\n\n\n\nI thought this should be a no brainer and I confess I didn't expect struggling on its implementation. Having re-checked the equations and code multiple times now, and tried different numerical examples, I begin to worry about being unable to get an Hessian with negative elements - which is what I need to implement the method of maximum likelihood using, say, textbook Newton-Raphson iterations.\n\n\n\n\nI appreciate any pointer to help me understand what I might be getting wrong - a simple illustrative example below.\n\n\n\n\nExample\n\n\n\n\nFor the sake of illustration, consider data(medpar) available from the R package COUNT. The data subset data_medpar <- medpar[,c(\"los\", \"died\", \"hmo\", \"type2\", \"type3\")] corresponds to the example reported in this STATA documentation for tnbreg (https://www.stata.com/manuals13/rtnbreg.pdf).\n\n\n\n\n\n\n\nInitialising the regression coefficients with a zero-truncated Poisson model gives me (intercept: 2.265; died: -0.248; hmo: -0.075; type2: 0.250; type3: 0.750) -- call this vector beta_iter;\n\n\n\n\n\n\n\n\n\nFollowing the alternating method of glm.nb from package MASS I also obtain an initial guess for $\\alpha$, call this scalar p_alpha <- 1.903 (what STATA calls alpha in the document is the recirpocal $\\theta=\\alpha^{-1}=0.525$ i.e. the so-called dispersion parameter).\n\n\n\n\n\n\n\n\n\nWith X the data matrix (including the intercept) and y the response variable vector corresponding to los I plug p_lambda = exp(X %*% beta_iter) and p_alpha in my R implementation below - which I believe should correspond to the second derivatives in question:\n\n\n\n\n n_regressors <- ncol(X)\n n_observ <- nrow(X)\n phi_sub <- (1 + p_theta*p_lambda)\n H_parent <- ((1 + p_theta*y) / phi_sub^2)*p_lambda\n if(zerotrunc){\n phi_sub_1a <- (1 / (phi_sub)^(1+p_alpha))\n phi <- (1/(1 + p_theta*p_lambda)^p_alpha) \n H_zt_A <- ( p_lambda*phi_sub_1a / (1 - phi) )^2\n H_zt_B <- ( p_lambda*phi_sub_1a - (p_lambda^2 * (p_theta + 1) * phi_sub^(-2+p_alpha)) ) / (1 - phi)\n }\n\n Hessian_iter <- matrix(0L,nrow = n_regressors, ncol = n_regressors)\n for(i in 1:n_observ){\n x <- X[i,]\n x <- as.numeric(x)\n outprod_X <- (x %o% x) \n A <- H_parent[i]\n if(zerotrunc){\n B <- H_zt_A[i]\n C <- H_zt_B[i]\n } else {\n B <- C <- 0\n }\n Hessian_iter <- Hessian_iter - ( A - B + C )*outprod_X \n }\n\n\n\n\n\n\n\n\n\nAnd I get a positive Hessian - as I always do\n\n\n\n\n> Hessian_iter\n [,1] [,2] [,3] [,4] [,5]\n[1,] 200849.45 53431.282 24465.222 43243.069 39578.773\n[2,] 53431.28 53431.282 6036.786 12451.468 14079.196\n[3,] 24465.22 6036.786 24465.222 4528.242 1145.349\n[4,] 43243.07 12451.468 4528.242 43243.069 0.000\n[5,] 39578.77 14079.196 1145.349 0.000 39578.773\n\n\n\n\n\nAny thoughts? Am I missing anything trivial here? Thanks in advance.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ettore S", "profile_url": "https://stats.stackexchange.com/users/513606/ettore-s", "user_type": "registered"}, "created_at": "2026-08-24T16:36:39+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "07E45709-2DC4-449E-9EF1-F194BCC37017", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/07E45709-2DC4-449E-9EF1-F194BCC37017/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ettore S", "profile_url": "https://stats.stackexchange.com/users/513606/ettore-s", "user_type": "registered"}, "created_at": "2026-08-24T16:44:54+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "62966E35-E17B-49AB-8C07-589F8E1C8272", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/62966E35-E17B-49AB-8C07-589F8E1C8272/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676952/hessian-with-invariably-positive-elements-for-zero-truncated-negative-binomial-r", "split": "test", "split_group": "7b59a2f46aa3d8cb6ef7b86f03502a2ea8a90a231427a0a51d2360f8ed2dd472", "tags": ["nonlinear-regression", "count-data", "negative-binomial-distribution", "hessian", "truncated-distributions"], "thread_id": "stats:676952", "title": "Hessian with invariably positive elements for zero-truncated negative binomial regression"}} {"citation_context": "e-differentiating the loglikelihood yields a well-known result (see e.g., footnote 5 in this paper (https://www.jstor.org/stable/2096628)):\n\n\n\n\n$$\n\\begin{aligned}\n\t\\frac{\\partial^2}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.jstor.org/stable/2096628", "kind": "external_url", "post_id": 676952, "post_url": "https://stats.stackexchange.com/questions/676952/hessian-with-invariably-positive-elements-for-zero-truncated-negative-binomial-r", "product": "citations", "record_id": "Scientific-Citation-Graph:d210bf52dfb243e1f112c072", "split": "test", "thread": {"accepted_answer_id": 676993, "answers": [{"answer_html": "

As it turns out there is a mistake in Grogger and Carson's second derivatives of the zero-truncated negative binomial loglikelihood function wrt the regression parameters: blink and you'll miss it (the sign in one of the exponents should have been outside the parenthesis, probably a typo in the original)

\n

\\begin{align}\n\t\\frac{\\partial^2}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\ell_\\mathrm{ZTNB}{\\left(\\boldsymbol{\\beta},\\alpha\\right)} &= -\\sum_{i=1}^n{\\frac{1+\\alpha^{-1} y_i}{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^2}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T} - \\sum_{i=1}^n\\left\\{\\frac{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\left(1+\\alpha\\right)}-e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(\\alpha^{-1}+1\\right)\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^\\color{blue}{-\\left(2+\\alpha\\right)}}{1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}} +\\right. \\nonumber \\\\ \n\t& \\quad \\left. -\\frac{e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-2(1+\\alpha)}}{\\left[1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}\\right]^2}\\right\\}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T \n\\end{align}

\n

I guess I must have been so eager to verify the original results that I conditioned myself to "see" the original notation as correct - even when going through my own derivations over and over again. Few days away from this problem must have broken this perverse loop.

\n", "answer_id": 676993, "answer_text": "As it turns out there is a mistake in Grogger and Carson's second derivatives of the zero-truncated negative binomial loglikelihood function wrt the regression parameters: blink and you'll miss it (the sign in one of the exponents should have been outside the parenthesis, probably a typo in the original)\n\n\n\n\n\\begin{align}\n\t\\frac{\\partial^2}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\ell_\\mathrm{ZTNB}{\\left(\\boldsymbol{\\beta},\\alpha\\right)} &= -\\sum_{i=1}^n{\\frac{1+\\alpha^{-1} y_i}{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^2}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T} - \\sum_{i=1}^n\\left\\{\\frac{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\left(1+\\alpha\\right)}-e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(\\alpha^{-1}+1\\right)\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^\\color{blue}{-\\left(2+\\alpha\\right)}}{1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}} +\\right. \\nonumber \\\\ \n\t& \\quad \\left. -\\frac{e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-2(1+\\alpha)}}{\\left[1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}\\right]^2}\\right\\}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T \n\\end{align}\n\n\n\n\nI guess I must have been so eager to verify the original results that I conditioned myself to \"see\" the original notation as correct - even when going through my own derivations over and over again. Few days away from this problem must have broken this perverse loop.", "answer_url": "https://stats.stackexchange.com/a/676993", "author": "Ettore S", "author_url": "https://stats.stackexchange.com/users/513606/ettore-s", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-28T23:08:55+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676952, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ettore S", "profile_url": "https://stats.stackexchange.com/users/513606/ettore-s", "user_type": "registered"}, "created_at": "2026-08-28T23:08:55+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "E33B0B4F-D54D-46E9-8E25-81C77E90B942", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/E33B0B4F-D54D-46E9-8E25-81C77E90B942/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ettore S", "profile_url": "https://stats.stackexchange.com/users/513606/ettore-s", "user_type": "registered"}, "created_at": "2026-08-28T23:15:33+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "71D393BD-A8FB-4799-92AF-8FD04BFA27AE", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/71D393BD-A8FB-4799-92AF-8FD04BFA27AE/view-source"}], "score": 0, "updated_at": "2026-08-28T23:15:33+00:00"}], "domain": "statistics", "external_links": ["https://archive.org/details/econometricanaly0000gree_f4x3/econometricanaly0000gree_f4x3", "https://www.jstor.org/stable/2096628", "https://www.stata.com/manuals13/rtnbreg.pdf"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Ettore S", "question_author_url": "https://stats.stackexchange.com/users/513606/ettore-s", "question_author_user_type": "registered", "question_created_at": "2026-08-24T16:36:39+00:00", "question_html": "

In the context of zero-truncated negative binomial regression (see this other post) , twice-differentiating the loglikelihood yields a well-known result (see e.g., footnote 5 in this paper):

\n

$$\n\\begin{aligned}\n\t\\frac{\\partial^2}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\ell_\\mathrm{ZTNB}{\\left(\\boldsymbol{\\beta},\\alpha\\right)} &= -\\sum_{i=1}^n{\\frac{1+\\alpha^{-1} y_i}{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^2}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T} -\\sum_{i=1}^n\\left\\{\\frac{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\left(1+\\alpha\\right)}-e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(\\alpha^{-1}+1\\right)\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{\\left(-2+\\alpha\\right)}}{1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}} +\\right. \\nonumber \\\\ \n\t& \\quad \\left. -\\frac{e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-2(1+\\alpha)}}{\\left[1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}\\right]^2}\\right\\}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T\n\\end{aligned}\n$$

\n

where:

\n\n

The above equation is correct as far as I can tell. Yet when I implement it in practice, it seems to invariably yield an Hessian with positive elements.

\n

Maybe this is a silly question, and it all depends on initialisation strategies etc.: but is it possible to ascertain whether the above-mentioned Hessian is, somehow, "bound to" have positive elements?

\n

I thought this should be a no brainer and I confess I didn't expect struggling on its implementation. Having re-checked the equations and code multiple times now, and tried different numerical examples, I begin to worry about being unable to get an Hessian with negative elements - which is what I need to implement the method of maximum likelihood using, say, textbook Newton-Raphson iterations.

\n

I appreciate any pointer to help me understand what I might be getting wrong - a simple illustrative example below.

\n

Example

\n

For the sake of illustration, consider data(medpar) available from the R package COUNT. The data subset data_medpar <- medpar[,c("los", "died", "hmo", "type2", "type3")] corresponds to the example reported in this STATA documentation for tnbreg.

\n\n

And I get a positive Hessian - as I always do

\n
> Hessian_iter\n          [,1]      [,2]      [,3]      [,4]      [,5]\n[1,] 200849.45 53431.282 24465.222 43243.069 39578.773\n[2,]  53431.28 53431.282  6036.786 12451.468 14079.196\n[3,]  24465.22  6036.786 24465.222  4528.242  1145.349\n[4,]  43243.07 12451.468  4528.242 43243.069     0.000\n[5,]  39578.77 14079.196  1145.349     0.000 39578.773\n
\n

Any thoughts? Am I missing anything trivial here? Thanks in advance.

\n", "question_id": 676952, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "In the context of zero-truncated negative binomial regression (see this other post (https://stats.stackexchange.com/q/676385/513606)) , twice-differentiating the loglikelihood yields a well-known result (see e.g., footnote 5 in this paper (https://www.jstor.org/stable/2096628)):\n\n\n\n\n$$\n\\begin{aligned}\n\t\\frac{\\partial^2}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\ell_\\mathrm{ZTNB}{\\left(\\boldsymbol{\\beta},\\alpha\\right)} &= -\\sum_{i=1}^n{\\frac{1+\\alpha^{-1} y_i}{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^2}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T} -\\sum_{i=1}^n\\left\\{\\frac{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\left(1+\\alpha\\right)}-e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(\\alpha^{-1}+1\\right)\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{\\left(-2+\\alpha\\right)}}{1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}} +\\right. \\nonumber \\\\ \n\t& \\quad \\left. -\\frac{e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-2(1+\\alpha)}}{\\left[1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}\\right]^2}\\right\\}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T\n\\end{aligned}\n$$\n\n\n\n\nwhere:\n\n\n\n\n\n$y_i > 0 \\quad (i=1,2,\\dots,n)$ denotes the observed realisations (observations enter a zero-truncated sample only after the first count occurs);\n\n\n\n\n$\\mathbf{x}^T_i$ is the $i$-th row of the regression data matrix;\n\n\n\n\n$\\boldsymbol{\\beta}$ is the unknown vector of regression coefficients (to be estimated);\n\n\n\n\n$\\alpha$ is another unknown parameter to be estimated, namely the reciprocal of the so-called dispersion parameter ($\\alpha$ is inherited from the Poisson-Gamma mixture that brings about the unconstrained Negative Binomial see e.g., p.745, in this book (https://archive.org/details/econometricanaly0000gree_f4x3/econometricanaly0000gree_f4x3)).\n\n\n\n\nAlso notice that the first summation is just the Hessian of the \"parent\" specification: that one works fine i.e., its elements are negative as expected.\n\n\n\n\n\nThe above equation is correct as far as I can tell. Yet when I implement it in practice, it seems to invariably yield an Hessian with positive elements.\n\n\n\n\nMaybe this is a silly question, and it all depends on initialisation strategies etc.: but is it possible to ascertain whether the above-mentioned Hessian is, somehow, \"bound to\" have positive elements?\n\n\n\n\nI thought this should be a no brainer and I confess I didn't expect struggling on its implementation. Having re-checked the equations and code multiple times now, and tried different numerical examples, I begin to worry about being unable to get an Hessian with negative elements - which is what I need to implement the method of maximum likelihood using, say, textbook Newton-Raphson iterations.\n\n\n\n\nI appreciate any pointer to help me understand what I might be getting wrong - a simple illustrative example below.\n\n\n\n\nExample\n\n\n\n\nFor the sake of illustration, consider data(medpar) available from the R package COUNT. The data subset data_medpar <- medpar[,c(\"los\", \"died\", \"hmo\", \"type2\", \"type3\")] corresponds to the example reported in this STATA documentation for tnbreg (https://www.stata.com/manuals13/rtnbreg.pdf).\n\n\n\n\n\n\n\nInitialising the regression coefficients with a zero-truncated Poisson model gives me (intercept: 2.265; died: -0.248; hmo: -0.075; type2: 0.250; type3: 0.750) -- call this vector beta_iter;\n\n\n\n\n\n\n\n\n\nFollowing the alternating method of glm.nb from package MASS I also obtain an initial guess for $\\alpha$, call this scalar p_alpha <- 1.903 (what STATA calls alpha in the document is the recirpocal $\\theta=\\alpha^{-1}=0.525$ i.e. the so-called dispersion parameter).\n\n\n\n\n\n\n\n\n\nWith X the data matrix (including the intercept) and y the response variable vector corresponding to los I plug p_lambda = exp(X %*% beta_iter) and p_alpha in my R implementation below - which I believe should correspond to the second derivatives in question:\n\n\n\n\n n_regressors <- ncol(X)\n n_observ <- nrow(X)\n phi_sub <- (1 + p_theta*p_lambda)\n H_parent <- ((1 + p_theta*y) / phi_sub^2)*p_lambda\n if(zerotrunc){\n phi_sub_1a <- (1 / (phi_sub)^(1+p_alpha))\n phi <- (1/(1 + p_theta*p_lambda)^p_alpha) \n H_zt_A <- ( p_lambda*phi_sub_1a / (1 - phi) )^2\n H_zt_B <- ( p_lambda*phi_sub_1a - (p_lambda^2 * (p_theta + 1) * phi_sub^(-2+p_alpha)) ) / (1 - phi)\n }\n\n Hessian_iter <- matrix(0L,nrow = n_regressors, ncol = n_regressors)\n for(i in 1:n_observ){\n x <- X[i,]\n x <- as.numeric(x)\n outprod_X <- (x %o% x) \n A <- H_parent[i]\n if(zerotrunc){\n B <- H_zt_A[i]\n C <- H_zt_B[i]\n } else {\n B <- C <- 0\n }\n Hessian_iter <- Hessian_iter - ( A - B + C )*outprod_X \n }\n\n\n\n\n\n\n\n\n\nAnd I get a positive Hessian - as I always do\n\n\n\n\n> Hessian_iter\n [,1] [,2] [,3] [,4] [,5]\n[1,] 200849.45 53431.282 24465.222 43243.069 39578.773\n[2,] 53431.28 53431.282 6036.786 12451.468 14079.196\n[3,] 24465.22 6036.786 24465.222 4528.242 1145.349\n[4,] 43243.07 12451.468 4528.242 43243.069 0.000\n[5,] 39578.77 14079.196 1145.349 0.000 39578.773\n\n\n\n\n\nAny thoughts? Am I missing anything trivial here? Thanks in advance.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ettore S", "profile_url": "https://stats.stackexchange.com/users/513606/ettore-s", "user_type": "registered"}, "created_at": "2026-08-24T16:36:39+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "07E45709-2DC4-449E-9EF1-F194BCC37017", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/07E45709-2DC4-449E-9EF1-F194BCC37017/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ettore S", "profile_url": "https://stats.stackexchange.com/users/513606/ettore-s", "user_type": "registered"}, "created_at": "2026-08-24T16:44:54+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "62966E35-E17B-49AB-8C07-589F8E1C8272", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/62966E35-E17B-49AB-8C07-589F8E1C8272/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676952/hessian-with-invariably-positive-elements-for-zero-truncated-negative-binomial-r", "split": "test", "split_group": "7b59a2f46aa3d8cb6ef7b86f03502a2ea8a90a231427a0a51d2360f8ed2dd472", "tags": ["nonlinear-regression", "count-data", "negative-binomial-distribution", "hessian", "truncated-distributions"], "thread_id": "stats:676952", "title": "Hessian with invariably positive elements for zero-truncated negative binomial regression"}} {"citation_context": "mo\", \"type2\", \"type3\")] corresponds to the example reported in this STATA documentation for tnbreg (https://www.stata.com/manuals13/rtnbreg.pdf).\n\n\n\n\n\n\n\nInitialising the regression coefficients with a zero-truncated Poisson model gives me (int", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.stata.com/manuals13/rtnbreg.pdf", "kind": "external_url", "post_id": 676952, "post_url": "https://stats.stackexchange.com/questions/676952/hessian-with-invariably-positive-elements-for-zero-truncated-negative-binomial-r", "product": "citations", "record_id": "Scientific-Citation-Graph:f8063dfa5b388ed1b2b84299", "split": "test", "thread": {"accepted_answer_id": 676993, "answers": [{"answer_html": "

As it turns out there is a mistake in Grogger and Carson's second derivatives of the zero-truncated negative binomial loglikelihood function wrt the regression parameters: blink and you'll miss it (the sign in one of the exponents should have been outside the parenthesis, probably a typo in the original)

\n

\\begin{align}\n\t\\frac{\\partial^2}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\ell_\\mathrm{ZTNB}{\\left(\\boldsymbol{\\beta},\\alpha\\right)} &= -\\sum_{i=1}^n{\\frac{1+\\alpha^{-1} y_i}{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^2}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T} - \\sum_{i=1}^n\\left\\{\\frac{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\left(1+\\alpha\\right)}-e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(\\alpha^{-1}+1\\right)\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^\\color{blue}{-\\left(2+\\alpha\\right)}}{1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}} +\\right. \\nonumber \\\\ \n\t& \\quad \\left. -\\frac{e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-2(1+\\alpha)}}{\\left[1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}\\right]^2}\\right\\}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T \n\\end{align}

\n

I guess I must have been so eager to verify the original results that I conditioned myself to "see" the original notation as correct - even when going through my own derivations over and over again. Few days away from this problem must have broken this perverse loop.

\n", "answer_id": 676993, "answer_text": "As it turns out there is a mistake in Grogger and Carson's second derivatives of the zero-truncated negative binomial loglikelihood function wrt the regression parameters: blink and you'll miss it (the sign in one of the exponents should have been outside the parenthesis, probably a typo in the original)\n\n\n\n\n\\begin{align}\n\t\\frac{\\partial^2}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\ell_\\mathrm{ZTNB}{\\left(\\boldsymbol{\\beta},\\alpha\\right)} &= -\\sum_{i=1}^n{\\frac{1+\\alpha^{-1} y_i}{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^2}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T} - \\sum_{i=1}^n\\left\\{\\frac{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\left(1+\\alpha\\right)}-e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(\\alpha^{-1}+1\\right)\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^\\color{blue}{-\\left(2+\\alpha\\right)}}{1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}} +\\right. \\nonumber \\\\ \n\t& \\quad \\left. -\\frac{e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-2(1+\\alpha)}}{\\left[1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}\\right]^2}\\right\\}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T \n\\end{align}\n\n\n\n\nI guess I must have been so eager to verify the original results that I conditioned myself to \"see\" the original notation as correct - even when going through my own derivations over and over again. Few days away from this problem must have broken this perverse loop.", "answer_url": "https://stats.stackexchange.com/a/676993", "author": "Ettore S", "author_url": "https://stats.stackexchange.com/users/513606/ettore-s", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-28T23:08:55+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676952, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ettore S", "profile_url": "https://stats.stackexchange.com/users/513606/ettore-s", "user_type": "registered"}, "created_at": "2026-08-28T23:08:55+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "E33B0B4F-D54D-46E9-8E25-81C77E90B942", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/E33B0B4F-D54D-46E9-8E25-81C77E90B942/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ettore S", "profile_url": "https://stats.stackexchange.com/users/513606/ettore-s", "user_type": "registered"}, "created_at": "2026-08-28T23:15:33+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "71D393BD-A8FB-4799-92AF-8FD04BFA27AE", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/71D393BD-A8FB-4799-92AF-8FD04BFA27AE/view-source"}], "score": 0, "updated_at": "2026-08-28T23:15:33+00:00"}], "domain": "statistics", "external_links": ["https://archive.org/details/econometricanaly0000gree_f4x3/econometricanaly0000gree_f4x3", "https://www.jstor.org/stable/2096628", "https://www.stata.com/manuals13/rtnbreg.pdf"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Ettore S", "question_author_url": "https://stats.stackexchange.com/users/513606/ettore-s", "question_author_user_type": "registered", "question_created_at": "2026-08-24T16:36:39+00:00", "question_html": "

In the context of zero-truncated negative binomial regression (see this other post) , twice-differentiating the loglikelihood yields a well-known result (see e.g., footnote 5 in this paper):

\n

$$\n\\begin{aligned}\n\t\\frac{\\partial^2}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\ell_\\mathrm{ZTNB}{\\left(\\boldsymbol{\\beta},\\alpha\\right)} &= -\\sum_{i=1}^n{\\frac{1+\\alpha^{-1} y_i}{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^2}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T} -\\sum_{i=1}^n\\left\\{\\frac{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\left(1+\\alpha\\right)}-e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(\\alpha^{-1}+1\\right)\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{\\left(-2+\\alpha\\right)}}{1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}} +\\right. \\nonumber \\\\ \n\t& \\quad \\left. -\\frac{e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-2(1+\\alpha)}}{\\left[1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}\\right]^2}\\right\\}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T\n\\end{aligned}\n$$

\n

where:

\n\n

The above equation is correct as far as I can tell. Yet when I implement it in practice, it seems to invariably yield an Hessian with positive elements.

\n

Maybe this is a silly question, and it all depends on initialisation strategies etc.: but is it possible to ascertain whether the above-mentioned Hessian is, somehow, "bound to" have positive elements?

\n

I thought this should be a no brainer and I confess I didn't expect struggling on its implementation. Having re-checked the equations and code multiple times now, and tried different numerical examples, I begin to worry about being unable to get an Hessian with negative elements - which is what I need to implement the method of maximum likelihood using, say, textbook Newton-Raphson iterations.

\n

I appreciate any pointer to help me understand what I might be getting wrong - a simple illustrative example below.

\n

Example

\n

For the sake of illustration, consider data(medpar) available from the R package COUNT. The data subset data_medpar <- medpar[,c("los", "died", "hmo", "type2", "type3")] corresponds to the example reported in this STATA documentation for tnbreg.

\n\n

And I get a positive Hessian - as I always do

\n
> Hessian_iter\n          [,1]      [,2]      [,3]      [,4]      [,5]\n[1,] 200849.45 53431.282 24465.222 43243.069 39578.773\n[2,]  53431.28 53431.282  6036.786 12451.468 14079.196\n[3,]  24465.22  6036.786 24465.222  4528.242  1145.349\n[4,]  43243.07 12451.468  4528.242 43243.069     0.000\n[5,]  39578.77 14079.196  1145.349     0.000 39578.773\n
\n

Any thoughts? Am I missing anything trivial here? Thanks in advance.

\n", "question_id": 676952, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "In the context of zero-truncated negative binomial regression (see this other post (https://stats.stackexchange.com/q/676385/513606)) , twice-differentiating the loglikelihood yields a well-known result (see e.g., footnote 5 in this paper (https://www.jstor.org/stable/2096628)):\n\n\n\n\n$$\n\\begin{aligned}\n\t\\frac{\\partial^2}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\ell_\\mathrm{ZTNB}{\\left(\\boldsymbol{\\beta},\\alpha\\right)} &= -\\sum_{i=1}^n{\\frac{1+\\alpha^{-1} y_i}{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^2}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T} -\\sum_{i=1}^n\\left\\{\\frac{\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\left(1+\\alpha\\right)}-e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(\\alpha^{-1}+1\\right)\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{\\left(-2+\\alpha\\right)}}{1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}} +\\right. \\nonumber \\\\ \n\t& \\quad \\left. -\\frac{e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-2(1+\\alpha)}}{\\left[1-\\left(1+\\alpha^{-1} e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\right)^{-\\alpha}\\right]^2}\\right\\}e^{\\mathbf{x}_i^T\\boldsymbol{\\beta}}\\mathbf{x}_i\\mathbf{x}_i^T\n\\end{aligned}\n$$\n\n\n\n\nwhere:\n\n\n\n\n\n$y_i > 0 \\quad (i=1,2,\\dots,n)$ denotes the observed realisations (observations enter a zero-truncated sample only after the first count occurs);\n\n\n\n\n$\\mathbf{x}^T_i$ is the $i$-th row of the regression data matrix;\n\n\n\n\n$\\boldsymbol{\\beta}$ is the unknown vector of regression coefficients (to be estimated);\n\n\n\n\n$\\alpha$ is another unknown parameter to be estimated, namely the reciprocal of the so-called dispersion parameter ($\\alpha$ is inherited from the Poisson-Gamma mixture that brings about the unconstrained Negative Binomial see e.g., p.745, in this book (https://archive.org/details/econometricanaly0000gree_f4x3/econometricanaly0000gree_f4x3)).\n\n\n\n\nAlso notice that the first summation is just the Hessian of the \"parent\" specification: that one works fine i.e., its elements are negative as expected.\n\n\n\n\n\nThe above equation is correct as far as I can tell. Yet when I implement it in practice, it seems to invariably yield an Hessian with positive elements.\n\n\n\n\nMaybe this is a silly question, and it all depends on initialisation strategies etc.: but is it possible to ascertain whether the above-mentioned Hessian is, somehow, \"bound to\" have positive elements?\n\n\n\n\nI thought this should be a no brainer and I confess I didn't expect struggling on its implementation. Having re-checked the equations and code multiple times now, and tried different numerical examples, I begin to worry about being unable to get an Hessian with negative elements - which is what I need to implement the method of maximum likelihood using, say, textbook Newton-Raphson iterations.\n\n\n\n\nI appreciate any pointer to help me understand what I might be getting wrong - a simple illustrative example below.\n\n\n\n\nExample\n\n\n\n\nFor the sake of illustration, consider data(medpar) available from the R package COUNT. The data subset data_medpar <- medpar[,c(\"los\", \"died\", \"hmo\", \"type2\", \"type3\")] corresponds to the example reported in this STATA documentation for tnbreg (https://www.stata.com/manuals13/rtnbreg.pdf).\n\n\n\n\n\n\n\nInitialising the regression coefficients with a zero-truncated Poisson model gives me (intercept: 2.265; died: -0.248; hmo: -0.075; type2: 0.250; type3: 0.750) -- call this vector beta_iter;\n\n\n\n\n\n\n\n\n\nFollowing the alternating method of glm.nb from package MASS I also obtain an initial guess for $\\alpha$, call this scalar p_alpha <- 1.903 (what STATA calls alpha in the document is the recirpocal $\\theta=\\alpha^{-1}=0.525$ i.e. the so-called dispersion parameter).\n\n\n\n\n\n\n\n\n\nWith X the data matrix (including the intercept) and y the response variable vector corresponding to los I plug p_lambda = exp(X %*% beta_iter) and p_alpha in my R implementation below - which I believe should correspond to the second derivatives in question:\n\n\n\n\n n_regressors <- ncol(X)\n n_observ <- nrow(X)\n phi_sub <- (1 + p_theta*p_lambda)\n H_parent <- ((1 + p_theta*y) / phi_sub^2)*p_lambda\n if(zerotrunc){\n phi_sub_1a <- (1 / (phi_sub)^(1+p_alpha))\n phi <- (1/(1 + p_theta*p_lambda)^p_alpha) \n H_zt_A <- ( p_lambda*phi_sub_1a / (1 - phi) )^2\n H_zt_B <- ( p_lambda*phi_sub_1a - (p_lambda^2 * (p_theta + 1) * phi_sub^(-2+p_alpha)) ) / (1 - phi)\n }\n\n Hessian_iter <- matrix(0L,nrow = n_regressors, ncol = n_regressors)\n for(i in 1:n_observ){\n x <- X[i,]\n x <- as.numeric(x)\n outprod_X <- (x %o% x) \n A <- H_parent[i]\n if(zerotrunc){\n B <- H_zt_A[i]\n C <- H_zt_B[i]\n } else {\n B <- C <- 0\n }\n Hessian_iter <- Hessian_iter - ( A - B + C )*outprod_X \n }\n\n\n\n\n\n\n\n\n\nAnd I get a positive Hessian - as I always do\n\n\n\n\n> Hessian_iter\n [,1] [,2] [,3] [,4] [,5]\n[1,] 200849.45 53431.282 24465.222 43243.069 39578.773\n[2,] 53431.28 53431.282 6036.786 12451.468 14079.196\n[3,] 24465.22 6036.786 24465.222 4528.242 1145.349\n[4,] 43243.07 12451.468 4528.242 43243.069 0.000\n[5,] 39578.77 14079.196 1145.349 0.000 39578.773\n\n\n\n\n\nAny thoughts? Am I missing anything trivial here? Thanks in advance.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ettore S", "profile_url": "https://stats.stackexchange.com/users/513606/ettore-s", "user_type": "registered"}, "created_at": "2026-08-24T16:36:39+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "07E45709-2DC4-449E-9EF1-F194BCC37017", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/07E45709-2DC4-449E-9EF1-F194BCC37017/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Ettore S", "profile_url": "https://stats.stackexchange.com/users/513606/ettore-s", "user_type": "registered"}, "created_at": "2026-08-24T16:44:54+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "62966E35-E17B-49AB-8C07-589F8E1C8272", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/62966E35-E17B-49AB-8C07-589F8E1C8272/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676952/hessian-with-invariably-positive-elements-for-zero-truncated-negative-binomial-r", "split": "test", "split_group": "7b59a2f46aa3d8cb6ef7b86f03502a2ea8a90a231427a0a51d2360f8ed2dd472", "tags": ["nonlinear-regression", "count-data", "negative-binomial-distribution", "hessian", "truncated-distributions"], "thread_id": "stats:676952", "title": "Hessian with invariably positive elements for zero-truncated negative binomial regression"}} {"citation_context": "by Lillelund et al., \"Stop Chasing the C-index: This Is How We Should Evaluate Our Survival Models (https://arxiv.org/html/2506.02075v1),\" goes into more detail and explains better evaluation methods. The \"Review of Statistical Methods", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://arxiv.org/html/2506.02075v1", "kind": "external_url", "post_id": 677008, "post_url": "https://stats.stackexchange.com/a/677008", "product": "citations", "record_id": "Scientific-Citation-Graph:dbab4563a6899514245c84a6", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "
\n

I .. wish to evaluate a survival forest using all but one special variable on this same data, and compare the results with those of the model using all variables.

\n
\n

Frank Harrell has a superb summary of how to evaluate the value of additional predictors in modeling. That's straightforward with nested regression models, which can be compared in a likelihood-ratio test. If you need to use random survival forests, some measure of explained variation in outcomes would be appropriate.

\n
\n

I can compute the concordance index...

\n
\n

Frank Harrell introduced the concordance/c-index to survival analysis. Although it is a useful measure of a single model's discriminative ability, he doesn't think that it's a good way to compare models; see the link above. It only evaluates how well the model gets the order of events correct, not how well the model matches the event probability over time as a function of covariates. Furthermore, the usual c-index can have bias depending on censoring patterns. There are ways to deal with that, but you are still left with a measure of discrimination only.

\n

A recent arXiv paper by Lillelund et al., "Stop Chasing the C-index: This Is How We Should Evaluate Our Survival Models," goes into more detail and explains better evaluation methods. The "Review of Statistical Methods for Evaluating the Performance of Survival or Other Time-to-Event Prediction Models (from Conventional to Deep Learning Approaches)" by Park et al., Korean J Radiol. 22:1697-1707 (2021) is also on-topic.

\n

Your choice of evaluation method might best depend on your intended use of model, which isn't clear from this question.

\n
\n

... at what point (in terms of size of data and censoring/nr of events) would you consider that evaluating through cross-validation is preferable over a simple training/test split?

\n
\n

A problem with a training/test split is that you limit both the amount of information used to train the model and the power to test the model reliably. Frank Harrell estimates that you need on the order of 20,000 subjects before a train/test split is as stable as resampling from the data with cross-validation or bootstrapping. With the power of survival models essentially determined by the number of subjects with events, you are thus unlikely to have clinical survival data with the necessary tens of thousands of events.

\n

As cross-validation involves train/test splits, it also has the problem of a small test sample in each fold. Combining all 10 test sets in 10-fold cross-validation only uses the number of cases in the original data set for testing. Repeated cross-validation helps, both in reducing reliance on a single set of splits and in increasing the effective number of test cases. Bootstrapping uses the number of cases in the original data set in each bootstrap sample, and one might use 50-100 bootstrap samples. Frank Harrell thus estimates that "To be as good as the bootstrap, about 100 repeats of 10-fold cross-validation are required."

\n

With resampling you are validating the modeling process rather than the model itself. Under the bootstrap principle, drawing samples with replacement from the available data represents the process of drawing the available data from the underlying population. Modeling each of repeated bootstrap samples and evaluating performance of each model on the full data set thus represents how well your modeling process captures the properties of the population. Comparing performance of each (possibly overfit) bootstrap-sample model on its own sample against its performance on the entire data set is the "optimism bootstrap" that evaluates overfitting. Once you accept that you are validating the process, objections to including training data in testing become much less compelling.

\n
\n

I get the out of bag [OOB] concordance index calculated on the training data...

\n
\n

This raises an issue for whatever measure of model performance you choose. Using OOB data for testing does mean that, within each tree, the test data don't overlap with the training data. As noted above, however, that isn't necessarily required and it limits you to about 1/3 of the data in each test set. Alternatively, you could use performance within each tree's model on the entire data set as an optimism bootstrap to validate the modeling process. Frank Harrell notes that distinction in this answer.

\n
\n

... assuming I have the concordance index on the unseen data for all imputations computed, what is a reasonable way to join and report them - should I just average the scores?

\n
\n

See this question and its answer on how to use Rubin's rules to combine random forest models on multiply imputed data sets. If your score of model performance is close enough to normally distributed, then you do average scores for the point estimate. Comparisons between models require estimating the variances of the point estimates, again following Rubin's rules that combine within-imputation and between-imputation variances.

\n

A few suggestions

\n

Survival analysis, similarly to binomial regression, can suffer from omitted-variable bias if any outcome-associated variable is omitted from the model. If you are studying clinical survival data, don't fall into the trap of omitting standard clinical outcome-related variables from the model. Models of outcome with predictors like gene-expression levels that don't include standard clinical variables run a serious risk of that bias and might just find proxies for clinical variables in a way that makes clinical application of the models pretty useless.

\n

Consider whether your goals might better be met with standard regression models. Their results are typically much easier to interpret heuristically than those of a random forest. Evaluating the added value of a single predictor is simple with regression models.

\n

Yes, random forests can incorporate unexpected interactions among predictors in ways that regression model's can't, at least with large numbers of predictors. Identifying what those interactions involve isn't so straightforward.

\n", "answer_id": 677008, "answer_text": "I .. wish to evaluate a survival forest using all but one special variable on this same data, and compare the results with those of the model using all variables.\n\n\n\n\n\n\n\nFrank Harrell has a superb summary of how to evaluate the value of additional predictors (https://www.fharrell.com/post/addvalue/) in modeling. That's straightforward with nested regression models, which can be compared in a likelihood-ratio test. If you need to use random survival forests, some measure of explained variation in outcomes would be appropriate.\n\n\n\n\n\n\n\nI can compute the concordance index...\n\n\n\n\n\n\n\nFrank Harrell introduced the concordance/c-index to survival analysis. Although it is a useful measure of a single model's discriminative ability, he doesn't think that it's a good way to compare models; see the link (https://www.fharrell.com/post/addvalue/) above. It only evaluates how well the model gets the order of events correct, not how well the model matches the event probability over time as a function of covariates. Furthermore, the usual c-index can have bias depending on censoring patterns. There are ways to deal with that, but you are still left with a measure of discrimination only.\n\n\n\n\nA recent arXiv paper by Lillelund et al., \"Stop Chasing the C-index: This Is How We Should Evaluate Our Survival Models (https://arxiv.org/html/2506.02075v1),\" goes into more detail and explains better evaluation methods. The \"Review of Statistical Methods for Evaluating the Performance of Survival or Other Time-to-Event Prediction Models (from Conventional to Deep Learning Approaches) (https://doi.org/10.3348/kjr.2021.0223)\" by Park et al., Korean J Radiol. 22:1697-1707 (2021) is also on-topic.\n\n\n\n\nYour choice of evaluation method might best depend on your intended use of model, which isn't clear from this question.\n\n\n\n\n\n\n\n... at what point (in terms of size of data and censoring/nr of events) would you consider that evaluating through cross-validation is preferable over a simple training/test split?\n\n\n\n\n\n\n\nA problem with a training/test split is that you limit both the amount of information used to train the model and the power to test the model reliably. Frank Harrell estimates that you need on the order of 20,000 subjects (https://www.fharrell.com/post/split-val/) before a train/test split is as stable as resampling from the data with cross-validation or bootstrapping. With the power of survival models essentially determined by the number of subjects with events, you are thus unlikely to have clinical survival data with the necessary tens of thousands of events.\n\n\n\n\nAs cross-validation involves train/test splits, it also has the problem of a small test sample in each fold. Combining all 10 test sets in 10-fold cross-validation only uses the number of cases in the original data set for testing. Repeated cross-validation helps, both in reducing reliance on a single set of splits and in increasing the effective number of test cases. Bootstrapping uses the number of cases in the original data set in each bootstrap sample, and one might use 50-100 bootstrap samples. Frank Harrell thus estimates that \"To be as good as the bootstrap, about 100 repeats of 10-fold cross-validation are required (https://www.fharrell.com/post/split-val/).\"\n\n\n\n\nWith resampling you are validating the modeling process rather than the model itself. Under the bootstrap principle, drawing samples with replacement from the available data represents the process of drawing the available data from the underlying population. Modeling each of repeated bootstrap samples and evaluating performance of each model on the full data set thus represents how well your modeling process captures the properties of the population. Comparing performance of each (possibly overfit) bootstrap-sample model on its own sample against its performance on the entire data set is the \"optimism bootstrap\" that evaluates overfitting. Once you accept that you are validating the process, objections to including training data in testing become much less compelling.\n\n\n\n\n\n\n\nI get the out of bag [OOB] concordance index calculated on the training data...\n\n\n\n\n\n\n\nThis raises an issue for whatever measure of model performance you choose. Using OOB data for testing does mean that, within each tree, the test data don't overlap with the training data. As noted above, however, that isn't necessarily required and it limits you to about 1/3 of the data in each test set. Alternatively, you could use performance within each tree's model on the entire data set as an optimism bootstrap to validate the modeling process. Frank Harrell notes that distinction in this answer (https://stats.stackexchange.com/a/656190/28500).\n\n\n\n\n\n\n\n... assuming I have the concordance index on the unseen data for all imputations computed, what is a reasonable way to join and report them - should I just average the scores?\n\n\n\n\n\n\n\nSee this question (https://stats.stackexchange.com/q/476829/28500) and its answer (https://stats.stackexchange.com/a/476849/28500) on how to use Rubin's rules to combine random forest models on multiply imputed data sets. If your score of model performance is close enough to normally distributed, then you do average scores for the point estimate. Comparisons between models require estimating the variances of the point estimates, again following Rubin's rules that combine within-imputation and between-imputation variances.\n\n\n\n\nA few suggestions\n\n\n\n\nSurvival analysis, similarly to binomial regression, can suffer from omitted-variable bias (https://stats.stackexchange.com/q/113766/28500) if any outcome-associated variable is omitted from the model. If you are studying clinical survival data, don't fall into the trap of omitting standard clinical outcome-related variables from the model. Models of outcome with predictors like gene-expression levels that don't include standard clinical variables run a serious risk of that bias and might just find proxies for clinical variables in a way that makes clinical application of the models pretty useless.\n\n\n\n\nConsider whether your goals might better be met with standard regression models. Their results are typically much easier to interpret heuristically than those of a random forest. Evaluating the added value of a single predictor is simple with regression models.\n\n\n\n\nYes, random forests can incorporate unexpected interactions among predictors in ways that regression model's can't, at least with large numbers of predictors. Identifying what those interactions involve isn't so straightforward.", "answer_url": "https://stats.stackexchange.com/a/677008", "author": "EdM", "author_url": "https://stats.stackexchange.com/users/28500/edm", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-30T15:43:41+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676956, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-08-30T15:43:41+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "65108C55-42C2-445B-B21B-0B094DADB7B2", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/65108C55-42C2-445B-B21B-0B094DADB7B2/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-08-30T15:54:06+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "34531043-A9BE-4349-88AF-6D5B08F325DD", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/34531043-A9BE-4349-88AF-6D5B08F325DD/view-source"}], "score": 1, "updated_at": "2026-08-30T15:54:06+00:00"}], "domain": "statistics", "external_links": ["https://arxiv.org/html/2506.02075v1", "https://doi.org/10.3348/kjr.2021.0223", "https://www.fharrell.com/post/addvalue/", "https://www.fharrell.com/post/split-val/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Polhek", "question_author_url": "https://stats.stackexchange.com/users/128159/polhek", "question_author_user_type": "registered", "question_created_at": "2026-08-25T13:00:28+00:00", "question_html": "

I've worked with tree-based models before, but I'm new to survival analysis. I have a very large dataset of highly censored data, and multiple imputations (let's say 5). I wish to train a survival forest on this data and evaluate it. More than this, I also wish to evaluate a survival forest using all but one special variable on this same data, and compare the results with those of the model using all variables.

\n

What I am confused about is the evaluation. The way I was planning to do it is the following:

\n
    \n
  1. First, I split the samples into training/testing (stratified by events, 80-20 split).
    2. \n
  2. Then for every imputation, I train a survival forest using all variables on the imputed training samples.
    3. \n
  3. After training, I get the out of bag concordance index calculated on the training data and I can compute the concordance index on the using test samples also.
    4. \n
\n

At this point I'm wondering, is the training OOB concordance index a better evaluation metrics of a model than the concordance index on the unseen portion of the data?\nAnd, assuming I have the concordance index on the unseen data for all imputations computed, what is a reasonable way to join and report them - should I just average the scores?

\n
    \n
  1. Next I do the same (training a model for every imputation on the training samples) using all but one variable of interest. I get OOB c-index and the c-index on the unseen data for each model/imputation.
    2. \n
\n

And here I wonder, how to compare the two? Do I just test the average concordance indexes of the models being significantly different? Or is there a better way of comparison?

\n

And as a last, more general question - at what point (in terms of size of data and censoring/nr of events) would you consider that evaluating through cross-validation is preferable over a simple training/test split?

\n", "question_id": 676956, "question_license": "CC BY-SA 4.0", "question_score": 0, "question_text": "I've worked with tree-based models before, but I'm new to survival analysis. I have a very large dataset of highly censored data, and multiple imputations (let's say 5). I wish to train a survival forest on this data and evaluate it. More than this, I also wish to evaluate a survival forest using all but one special variable on this same data, and compare the results with those of the model using all variables.\n\n\n\n\nWhat I am confused about is the evaluation. The way I was planning to do it is the following:\n\n\n\n\n\nFirst, I split the samples into training/testing (stratified by events, 80-20 split).\n\n\n\n\nThen for every imputation, I train a survival forest using all variables on the imputed training samples.\n\n\n\n\nAfter training, I get the out of bag concordance index calculated on the training data and I can compute the concordance index on the using test samples also.\n\n\n\n\n\nAt this point I'm wondering, is the training OOB concordance index a better evaluation metrics of a model than the concordance index on the unseen portion of the data?\nAnd, assuming I have the concordance index on the unseen data for all imputations computed, what is a reasonable way to join and report them - should I just average the scores?\n\n\n\n\n\nNext I do the same (training a model for every imputation on the training samples) using all but one variable of interest. I get OOB c-index and the c-index on the unseen data for each model/imputation.\n\n\n\n\n\nAnd here I wonder, how to compare the two? Do I just test the average concordance indexes of the models being significantly different? Or is there a better way of comparison?\n\n\n\n\nAnd as a last, more general question - at what point (in terms of size of data and censoring/nr of events) would you consider that evaluating through cross-validation is preferable over a simple training/test split?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Polhek", "profile_url": "https://stats.stackexchange.com/users/128159/polhek", "user_type": "registered"}, "created_at": "2026-08-25T13:00:28+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "C4B771B4-ADC3-4FD6-AE5D-16BE2127FFCA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/C4B771B4-ADC3-4FD6-AE5D-16BE2127FFCA/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676956/evaluating-survival-forest-models-on-multiple-imputation-data", "split": "test", "split_group": "8636b1b5f40d7aa127b413ad0a54ccb1823c8f472ffcec2eef386149ce3eef6d", "tags": ["survival", "random-forest", "multiple-imputation", "concordance"], "thread_id": "stats:676956", "title": "Evaluating survival forest models on multiple imputation data"}} {"citation_context": " Survival or Other Time-to-Event Prediction Models (from Conventional to Deep Learning Approaches) (https://doi.org/10.3348/kjr.2021.0223)\" by Park et al., Korean J Radiol. 22:1697-1707 (2021) is also on-topic.\n\n\n\n\nYour choice of evaluat", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": "10.3348/kjr.2021.0223", "external_url": "https://doi.org/10.3348/kjr.2021.0223", "kind": "doi_url", "post_id": 677008, "post_url": "https://stats.stackexchange.com/a/677008", "product": "citations", "record_id": "Scientific-Citation-Graph:617b7e26248da03d19f8431b", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "
\n

I .. wish to evaluate a survival forest using all but one special variable on this same data, and compare the results with those of the model using all variables.

\n
\n

Frank Harrell has a superb summary of how to evaluate the value of additional predictors in modeling. That's straightforward with nested regression models, which can be compared in a likelihood-ratio test. If you need to use random survival forests, some measure of explained variation in outcomes would be appropriate.

\n
\n

I can compute the concordance index...

\n
\n

Frank Harrell introduced the concordance/c-index to survival analysis. Although it is a useful measure of a single model's discriminative ability, he doesn't think that it's a good way to compare models; see the link above. It only evaluates how well the model gets the order of events correct, not how well the model matches the event probability over time as a function of covariates. Furthermore, the usual c-index can have bias depending on censoring patterns. There are ways to deal with that, but you are still left with a measure of discrimination only.

\n

A recent arXiv paper by Lillelund et al., "Stop Chasing the C-index: This Is How We Should Evaluate Our Survival Models," goes into more detail and explains better evaluation methods. The "Review of Statistical Methods for Evaluating the Performance of Survival or Other Time-to-Event Prediction Models (from Conventional to Deep Learning Approaches)" by Park et al., Korean J Radiol. 22:1697-1707 (2021) is also on-topic.

\n

Your choice of evaluation method might best depend on your intended use of model, which isn't clear from this question.

\n
\n

... at what point (in terms of size of data and censoring/nr of events) would you consider that evaluating through cross-validation is preferable over a simple training/test split?

\n
\n

A problem with a training/test split is that you limit both the amount of information used to train the model and the power to test the model reliably. Frank Harrell estimates that you need on the order of 20,000 subjects before a train/test split is as stable as resampling from the data with cross-validation or bootstrapping. With the power of survival models essentially determined by the number of subjects with events, you are thus unlikely to have clinical survival data with the necessary tens of thousands of events.

\n

As cross-validation involves train/test splits, it also has the problem of a small test sample in each fold. Combining all 10 test sets in 10-fold cross-validation only uses the number of cases in the original data set for testing. Repeated cross-validation helps, both in reducing reliance on a single set of splits and in increasing the effective number of test cases. Bootstrapping uses the number of cases in the original data set in each bootstrap sample, and one might use 50-100 bootstrap samples. Frank Harrell thus estimates that "To be as good as the bootstrap, about 100 repeats of 10-fold cross-validation are required."

\n

With resampling you are validating the modeling process rather than the model itself. Under the bootstrap principle, drawing samples with replacement from the available data represents the process of drawing the available data from the underlying population. Modeling each of repeated bootstrap samples and evaluating performance of each model on the full data set thus represents how well your modeling process captures the properties of the population. Comparing performance of each (possibly overfit) bootstrap-sample model on its own sample against its performance on the entire data set is the "optimism bootstrap" that evaluates overfitting. Once you accept that you are validating the process, objections to including training data in testing become much less compelling.

\n
\n

I get the out of bag [OOB] concordance index calculated on the training data...

\n
\n

This raises an issue for whatever measure of model performance you choose. Using OOB data for testing does mean that, within each tree, the test data don't overlap with the training data. As noted above, however, that isn't necessarily required and it limits you to about 1/3 of the data in each test set. Alternatively, you could use performance within each tree's model on the entire data set as an optimism bootstrap to validate the modeling process. Frank Harrell notes that distinction in this answer.

\n
\n

... assuming I have the concordance index on the unseen data for all imputations computed, what is a reasonable way to join and report them - should I just average the scores?

\n
\n

See this question and its answer on how to use Rubin's rules to combine random forest models on multiply imputed data sets. If your score of model performance is close enough to normally distributed, then you do average scores for the point estimate. Comparisons between models require estimating the variances of the point estimates, again following Rubin's rules that combine within-imputation and between-imputation variances.

\n

A few suggestions

\n

Survival analysis, similarly to binomial regression, can suffer from omitted-variable bias if any outcome-associated variable is omitted from the model. If you are studying clinical survival data, don't fall into the trap of omitting standard clinical outcome-related variables from the model. Models of outcome with predictors like gene-expression levels that don't include standard clinical variables run a serious risk of that bias and might just find proxies for clinical variables in a way that makes clinical application of the models pretty useless.

\n

Consider whether your goals might better be met with standard regression models. Their results are typically much easier to interpret heuristically than those of a random forest. Evaluating the added value of a single predictor is simple with regression models.

\n

Yes, random forests can incorporate unexpected interactions among predictors in ways that regression model's can't, at least with large numbers of predictors. Identifying what those interactions involve isn't so straightforward.

\n", "answer_id": 677008, "answer_text": "I .. wish to evaluate a survival forest using all but one special variable on this same data, and compare the results with those of the model using all variables.\n\n\n\n\n\n\n\nFrank Harrell has a superb summary of how to evaluate the value of additional predictors (https://www.fharrell.com/post/addvalue/) in modeling. That's straightforward with nested regression models, which can be compared in a likelihood-ratio test. If you need to use random survival forests, some measure of explained variation in outcomes would be appropriate.\n\n\n\n\n\n\n\nI can compute the concordance index...\n\n\n\n\n\n\n\nFrank Harrell introduced the concordance/c-index to survival analysis. Although it is a useful measure of a single model's discriminative ability, he doesn't think that it's a good way to compare models; see the link (https://www.fharrell.com/post/addvalue/) above. It only evaluates how well the model gets the order of events correct, not how well the model matches the event probability over time as a function of covariates. Furthermore, the usual c-index can have bias depending on censoring patterns. There are ways to deal with that, but you are still left with a measure of discrimination only.\n\n\n\n\nA recent arXiv paper by Lillelund et al., \"Stop Chasing the C-index: This Is How We Should Evaluate Our Survival Models (https://arxiv.org/html/2506.02075v1),\" goes into more detail and explains better evaluation methods. The \"Review of Statistical Methods for Evaluating the Performance of Survival or Other Time-to-Event Prediction Models (from Conventional to Deep Learning Approaches) (https://doi.org/10.3348/kjr.2021.0223)\" by Park et al., Korean J Radiol. 22:1697-1707 (2021) is also on-topic.\n\n\n\n\nYour choice of evaluation method might best depend on your intended use of model, which isn't clear from this question.\n\n\n\n\n\n\n\n... at what point (in terms of size of data and censoring/nr of events) would you consider that evaluating through cross-validation is preferable over a simple training/test split?\n\n\n\n\n\n\n\nA problem with a training/test split is that you limit both the amount of information used to train the model and the power to test the model reliably. Frank Harrell estimates that you need on the order of 20,000 subjects (https://www.fharrell.com/post/split-val/) before a train/test split is as stable as resampling from the data with cross-validation or bootstrapping. With the power of survival models essentially determined by the number of subjects with events, you are thus unlikely to have clinical survival data with the necessary tens of thousands of events.\n\n\n\n\nAs cross-validation involves train/test splits, it also has the problem of a small test sample in each fold. Combining all 10 test sets in 10-fold cross-validation only uses the number of cases in the original data set for testing. Repeated cross-validation helps, both in reducing reliance on a single set of splits and in increasing the effective number of test cases. Bootstrapping uses the number of cases in the original data set in each bootstrap sample, and one might use 50-100 bootstrap samples. Frank Harrell thus estimates that \"To be as good as the bootstrap, about 100 repeats of 10-fold cross-validation are required (https://www.fharrell.com/post/split-val/).\"\n\n\n\n\nWith resampling you are validating the modeling process rather than the model itself. Under the bootstrap principle, drawing samples with replacement from the available data represents the process of drawing the available data from the underlying population. Modeling each of repeated bootstrap samples and evaluating performance of each model on the full data set thus represents how well your modeling process captures the properties of the population. Comparing performance of each (possibly overfit) bootstrap-sample model on its own sample against its performance on the entire data set is the \"optimism bootstrap\" that evaluates overfitting. Once you accept that you are validating the process, objections to including training data in testing become much less compelling.\n\n\n\n\n\n\n\nI get the out of bag [OOB] concordance index calculated on the training data...\n\n\n\n\n\n\n\nThis raises an issue for whatever measure of model performance you choose. Using OOB data for testing does mean that, within each tree, the test data don't overlap with the training data. As noted above, however, that isn't necessarily required and it limits you to about 1/3 of the data in each test set. Alternatively, you could use performance within each tree's model on the entire data set as an optimism bootstrap to validate the modeling process. Frank Harrell notes that distinction in this answer (https://stats.stackexchange.com/a/656190/28500).\n\n\n\n\n\n\n\n... assuming I have the concordance index on the unseen data for all imputations computed, what is a reasonable way to join and report them - should I just average the scores?\n\n\n\n\n\n\n\nSee this question (https://stats.stackexchange.com/q/476829/28500) and its answer (https://stats.stackexchange.com/a/476849/28500) on how to use Rubin's rules to combine random forest models on multiply imputed data sets. If your score of model performance is close enough to normally distributed, then you do average scores for the point estimate. Comparisons between models require estimating the variances of the point estimates, again following Rubin's rules that combine within-imputation and between-imputation variances.\n\n\n\n\nA few suggestions\n\n\n\n\nSurvival analysis, similarly to binomial regression, can suffer from omitted-variable bias (https://stats.stackexchange.com/q/113766/28500) if any outcome-associated variable is omitted from the model. If you are studying clinical survival data, don't fall into the trap of omitting standard clinical outcome-related variables from the model. Models of outcome with predictors like gene-expression levels that don't include standard clinical variables run a serious risk of that bias and might just find proxies for clinical variables in a way that makes clinical application of the models pretty useless.\n\n\n\n\nConsider whether your goals might better be met with standard regression models. Their results are typically much easier to interpret heuristically than those of a random forest. Evaluating the added value of a single predictor is simple with regression models.\n\n\n\n\nYes, random forests can incorporate unexpected interactions among predictors in ways that regression model's can't, at least with large numbers of predictors. Identifying what those interactions involve isn't so straightforward.", "answer_url": "https://stats.stackexchange.com/a/677008", "author": "EdM", "author_url": "https://stats.stackexchange.com/users/28500/edm", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-30T15:43:41+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676956, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-08-30T15:43:41+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "65108C55-42C2-445B-B21B-0B094DADB7B2", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/65108C55-42C2-445B-B21B-0B094DADB7B2/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-08-30T15:54:06+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "34531043-A9BE-4349-88AF-6D5B08F325DD", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/34531043-A9BE-4349-88AF-6D5B08F325DD/view-source"}], "score": 1, "updated_at": "2026-08-30T15:54:06+00:00"}], "domain": "statistics", "external_links": ["https://arxiv.org/html/2506.02075v1", "https://doi.org/10.3348/kjr.2021.0223", "https://www.fharrell.com/post/addvalue/", "https://www.fharrell.com/post/split-val/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Polhek", "question_author_url": "https://stats.stackexchange.com/users/128159/polhek", "question_author_user_type": "registered", "question_created_at": "2026-08-25T13:00:28+00:00", "question_html": "

I've worked with tree-based models before, but I'm new to survival analysis. I have a very large dataset of highly censored data, and multiple imputations (let's say 5). I wish to train a survival forest on this data and evaluate it. More than this, I also wish to evaluate a survival forest using all but one special variable on this same data, and compare the results with those of the model using all variables.

\n

What I am confused about is the evaluation. The way I was planning to do it is the following:

\n
    \n
  1. First, I split the samples into training/testing (stratified by events, 80-20 split).
    2. \n
  2. Then for every imputation, I train a survival forest using all variables on the imputed training samples.
    3. \n
  3. After training, I get the out of bag concordance index calculated on the training data and I can compute the concordance index on the using test samples also.
    4. \n
\n

At this point I'm wondering, is the training OOB concordance index a better evaluation metrics of a model than the concordance index on the unseen portion of the data?\nAnd, assuming I have the concordance index on the unseen data for all imputations computed, what is a reasonable way to join and report them - should I just average the scores?

\n
    \n
  1. Next I do the same (training a model for every imputation on the training samples) using all but one variable of interest. I get OOB c-index and the c-index on the unseen data for each model/imputation.
    2. \n
\n

And here I wonder, how to compare the two? Do I just test the average concordance indexes of the models being significantly different? Or is there a better way of comparison?

\n

And as a last, more general question - at what point (in terms of size of data and censoring/nr of events) would you consider that evaluating through cross-validation is preferable over a simple training/test split?

\n", "question_id": 676956, "question_license": "CC BY-SA 4.0", "question_score": 0, "question_text": "I've worked with tree-based models before, but I'm new to survival analysis. I have a very large dataset of highly censored data, and multiple imputations (let's say 5). I wish to train a survival forest on this data and evaluate it. More than this, I also wish to evaluate a survival forest using all but one special variable on this same data, and compare the results with those of the model using all variables.\n\n\n\n\nWhat I am confused about is the evaluation. The way I was planning to do it is the following:\n\n\n\n\n\nFirst, I split the samples into training/testing (stratified by events, 80-20 split).\n\n\n\n\nThen for every imputation, I train a survival forest using all variables on the imputed training samples.\n\n\n\n\nAfter training, I get the out of bag concordance index calculated on the training data and I can compute the concordance index on the using test samples also.\n\n\n\n\n\nAt this point I'm wondering, is the training OOB concordance index a better evaluation metrics of a model than the concordance index on the unseen portion of the data?\nAnd, assuming I have the concordance index on the unseen data for all imputations computed, what is a reasonable way to join and report them - should I just average the scores?\n\n\n\n\n\nNext I do the same (training a model for every imputation on the training samples) using all but one variable of interest. I get OOB c-index and the c-index on the unseen data for each model/imputation.\n\n\n\n\n\nAnd here I wonder, how to compare the two? Do I just test the average concordance indexes of the models being significantly different? Or is there a better way of comparison?\n\n\n\n\nAnd as a last, more general question - at what point (in terms of size of data and censoring/nr of events) would you consider that evaluating through cross-validation is preferable over a simple training/test split?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Polhek", "profile_url": "https://stats.stackexchange.com/users/128159/polhek", "user_type": "registered"}, "created_at": "2026-08-25T13:00:28+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "C4B771B4-ADC3-4FD6-AE5D-16BE2127FFCA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/C4B771B4-ADC3-4FD6-AE5D-16BE2127FFCA/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676956/evaluating-survival-forest-models-on-multiple-imputation-data", "split": "test", "split_group": "8636b1b5f40d7aa127b413ad0a54ccb1823c8f472ffcec2eef386149ce3eef6d", "tags": ["survival", "random-forest", "multiple-imputation", "concordance"], "thread_id": "stats:676956", "title": "Evaluating survival forest models on multiple imputation data"}} {"citation_context": "s.\n\n\n\n\n\n\n\nFrank Harrell has a superb summary of how to evaluate the value of additional predictors (https://www.fharrell.com/post/addvalue/) in modeling. That's straightforward with nested regression models, which can be compared in a like", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.fharrell.com/post/addvalue/", "kind": "external_url", "post_id": 677008, "post_url": "https://stats.stackexchange.com/a/677008", "product": "citations", "record_id": "Scientific-Citation-Graph:2c997ee194b0093adfd040cb", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "
\n

I .. wish to evaluate a survival forest using all but one special variable on this same data, and compare the results with those of the model using all variables.

\n
\n

Frank Harrell has a superb summary of how to evaluate the value of additional predictors in modeling. That's straightforward with nested regression models, which can be compared in a likelihood-ratio test. If you need to use random survival forests, some measure of explained variation in outcomes would be appropriate.

\n
\n

I can compute the concordance index...

\n
\n

Frank Harrell introduced the concordance/c-index to survival analysis. Although it is a useful measure of a single model's discriminative ability, he doesn't think that it's a good way to compare models; see the link above. It only evaluates how well the model gets the order of events correct, not how well the model matches the event probability over time as a function of covariates. Furthermore, the usual c-index can have bias depending on censoring patterns. There are ways to deal with that, but you are still left with a measure of discrimination only.

\n

A recent arXiv paper by Lillelund et al., "Stop Chasing the C-index: This Is How We Should Evaluate Our Survival Models," goes into more detail and explains better evaluation methods. The "Review of Statistical Methods for Evaluating the Performance of Survival or Other Time-to-Event Prediction Models (from Conventional to Deep Learning Approaches)" by Park et al., Korean J Radiol. 22:1697-1707 (2021) is also on-topic.

\n

Your choice of evaluation method might best depend on your intended use of model, which isn't clear from this question.

\n
\n

... at what point (in terms of size of data and censoring/nr of events) would you consider that evaluating through cross-validation is preferable over a simple training/test split?

\n
\n

A problem with a training/test split is that you limit both the amount of information used to train the model and the power to test the model reliably. Frank Harrell estimates that you need on the order of 20,000 subjects before a train/test split is as stable as resampling from the data with cross-validation or bootstrapping. With the power of survival models essentially determined by the number of subjects with events, you are thus unlikely to have clinical survival data with the necessary tens of thousands of events.

\n

As cross-validation involves train/test splits, it also has the problem of a small test sample in each fold. Combining all 10 test sets in 10-fold cross-validation only uses the number of cases in the original data set for testing. Repeated cross-validation helps, both in reducing reliance on a single set of splits and in increasing the effective number of test cases. Bootstrapping uses the number of cases in the original data set in each bootstrap sample, and one might use 50-100 bootstrap samples. Frank Harrell thus estimates that "To be as good as the bootstrap, about 100 repeats of 10-fold cross-validation are required."

\n

With resampling you are validating the modeling process rather than the model itself. Under the bootstrap principle, drawing samples with replacement from the available data represents the process of drawing the available data from the underlying population. Modeling each of repeated bootstrap samples and evaluating performance of each model on the full data set thus represents how well your modeling process captures the properties of the population. Comparing performance of each (possibly overfit) bootstrap-sample model on its own sample against its performance on the entire data set is the "optimism bootstrap" that evaluates overfitting. Once you accept that you are validating the process, objections to including training data in testing become much less compelling.

\n
\n

I get the out of bag [OOB] concordance index calculated on the training data...

\n
\n

This raises an issue for whatever measure of model performance you choose. Using OOB data for testing does mean that, within each tree, the test data don't overlap with the training data. As noted above, however, that isn't necessarily required and it limits you to about 1/3 of the data in each test set. Alternatively, you could use performance within each tree's model on the entire data set as an optimism bootstrap to validate the modeling process. Frank Harrell notes that distinction in this answer.

\n
\n

... assuming I have the concordance index on the unseen data for all imputations computed, what is a reasonable way to join and report them - should I just average the scores?

\n
\n

See this question and its answer on how to use Rubin's rules to combine random forest models on multiply imputed data sets. If your score of model performance is close enough to normally distributed, then you do average scores for the point estimate. Comparisons between models require estimating the variances of the point estimates, again following Rubin's rules that combine within-imputation and between-imputation variances.

\n

A few suggestions

\n

Survival analysis, similarly to binomial regression, can suffer from omitted-variable bias if any outcome-associated variable is omitted from the model. If you are studying clinical survival data, don't fall into the trap of omitting standard clinical outcome-related variables from the model. Models of outcome with predictors like gene-expression levels that don't include standard clinical variables run a serious risk of that bias and might just find proxies for clinical variables in a way that makes clinical application of the models pretty useless.

\n

Consider whether your goals might better be met with standard regression models. Their results are typically much easier to interpret heuristically than those of a random forest. Evaluating the added value of a single predictor is simple with regression models.

\n

Yes, random forests can incorporate unexpected interactions among predictors in ways that regression model's can't, at least with large numbers of predictors. Identifying what those interactions involve isn't so straightforward.

\n", "answer_id": 677008, "answer_text": "I .. wish to evaluate a survival forest using all but one special variable on this same data, and compare the results with those of the model using all variables.\n\n\n\n\n\n\n\nFrank Harrell has a superb summary of how to evaluate the value of additional predictors (https://www.fharrell.com/post/addvalue/) in modeling. That's straightforward with nested regression models, which can be compared in a likelihood-ratio test. If you need to use random survival forests, some measure of explained variation in outcomes would be appropriate.\n\n\n\n\n\n\n\nI can compute the concordance index...\n\n\n\n\n\n\n\nFrank Harrell introduced the concordance/c-index to survival analysis. Although it is a useful measure of a single model's discriminative ability, he doesn't think that it's a good way to compare models; see the link (https://www.fharrell.com/post/addvalue/) above. It only evaluates how well the model gets the order of events correct, not how well the model matches the event probability over time as a function of covariates. Furthermore, the usual c-index can have bias depending on censoring patterns. There are ways to deal with that, but you are still left with a measure of discrimination only.\n\n\n\n\nA recent arXiv paper by Lillelund et al., \"Stop Chasing the C-index: This Is How We Should Evaluate Our Survival Models (https://arxiv.org/html/2506.02075v1),\" goes into more detail and explains better evaluation methods. The \"Review of Statistical Methods for Evaluating the Performance of Survival or Other Time-to-Event Prediction Models (from Conventional to Deep Learning Approaches) (https://doi.org/10.3348/kjr.2021.0223)\" by Park et al., Korean J Radiol. 22:1697-1707 (2021) is also on-topic.\n\n\n\n\nYour choice of evaluation method might best depend on your intended use of model, which isn't clear from this question.\n\n\n\n\n\n\n\n... at what point (in terms of size of data and censoring/nr of events) would you consider that evaluating through cross-validation is preferable over a simple training/test split?\n\n\n\n\n\n\n\nA problem with a training/test split is that you limit both the amount of information used to train the model and the power to test the model reliably. Frank Harrell estimates that you need on the order of 20,000 subjects (https://www.fharrell.com/post/split-val/) before a train/test split is as stable as resampling from the data with cross-validation or bootstrapping. With the power of survival models essentially determined by the number of subjects with events, you are thus unlikely to have clinical survival data with the necessary tens of thousands of events.\n\n\n\n\nAs cross-validation involves train/test splits, it also has the problem of a small test sample in each fold. Combining all 10 test sets in 10-fold cross-validation only uses the number of cases in the original data set for testing. Repeated cross-validation helps, both in reducing reliance on a single set of splits and in increasing the effective number of test cases. Bootstrapping uses the number of cases in the original data set in each bootstrap sample, and one might use 50-100 bootstrap samples. Frank Harrell thus estimates that \"To be as good as the bootstrap, about 100 repeats of 10-fold cross-validation are required (https://www.fharrell.com/post/split-val/).\"\n\n\n\n\nWith resampling you are validating the modeling process rather than the model itself. Under the bootstrap principle, drawing samples with replacement from the available data represents the process of drawing the available data from the underlying population. Modeling each of repeated bootstrap samples and evaluating performance of each model on the full data set thus represents how well your modeling process captures the properties of the population. Comparing performance of each (possibly overfit) bootstrap-sample model on its own sample against its performance on the entire data set is the \"optimism bootstrap\" that evaluates overfitting. Once you accept that you are validating the process, objections to including training data in testing become much less compelling.\n\n\n\n\n\n\n\nI get the out of bag [OOB] concordance index calculated on the training data...\n\n\n\n\n\n\n\nThis raises an issue for whatever measure of model performance you choose. Using OOB data for testing does mean that, within each tree, the test data don't overlap with the training data. As noted above, however, that isn't necessarily required and it limits you to about 1/3 of the data in each test set. Alternatively, you could use performance within each tree's model on the entire data set as an optimism bootstrap to validate the modeling process. Frank Harrell notes that distinction in this answer (https://stats.stackexchange.com/a/656190/28500).\n\n\n\n\n\n\n\n... assuming I have the concordance index on the unseen data for all imputations computed, what is a reasonable way to join and report them - should I just average the scores?\n\n\n\n\n\n\n\nSee this question (https://stats.stackexchange.com/q/476829/28500) and its answer (https://stats.stackexchange.com/a/476849/28500) on how to use Rubin's rules to combine random forest models on multiply imputed data sets. If your score of model performance is close enough to normally distributed, then you do average scores for the point estimate. Comparisons between models require estimating the variances of the point estimates, again following Rubin's rules that combine within-imputation and between-imputation variances.\n\n\n\n\nA few suggestions\n\n\n\n\nSurvival analysis, similarly to binomial regression, can suffer from omitted-variable bias (https://stats.stackexchange.com/q/113766/28500) if any outcome-associated variable is omitted from the model. If you are studying clinical survival data, don't fall into the trap of omitting standard clinical outcome-related variables from the model. Models of outcome with predictors like gene-expression levels that don't include standard clinical variables run a serious risk of that bias and might just find proxies for clinical variables in a way that makes clinical application of the models pretty useless.\n\n\n\n\nConsider whether your goals might better be met with standard regression models. Their results are typically much easier to interpret heuristically than those of a random forest. Evaluating the added value of a single predictor is simple with regression models.\n\n\n\n\nYes, random forests can incorporate unexpected interactions among predictors in ways that regression model's can't, at least with large numbers of predictors. Identifying what those interactions involve isn't so straightforward.", "answer_url": "https://stats.stackexchange.com/a/677008", "author": "EdM", "author_url": "https://stats.stackexchange.com/users/28500/edm", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-30T15:43:41+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676956, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-08-30T15:43:41+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "65108C55-42C2-445B-B21B-0B094DADB7B2", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/65108C55-42C2-445B-B21B-0B094DADB7B2/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-08-30T15:54:06+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "34531043-A9BE-4349-88AF-6D5B08F325DD", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/34531043-A9BE-4349-88AF-6D5B08F325DD/view-source"}], "score": 1, "updated_at": "2026-08-30T15:54:06+00:00"}], "domain": "statistics", "external_links": ["https://arxiv.org/html/2506.02075v1", "https://doi.org/10.3348/kjr.2021.0223", "https://www.fharrell.com/post/addvalue/", "https://www.fharrell.com/post/split-val/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Polhek", "question_author_url": "https://stats.stackexchange.com/users/128159/polhek", "question_author_user_type": "registered", "question_created_at": "2026-08-25T13:00:28+00:00", "question_html": "

I've worked with tree-based models before, but I'm new to survival analysis. I have a very large dataset of highly censored data, and multiple imputations (let's say 5). I wish to train a survival forest on this data and evaluate it. More than this, I also wish to evaluate a survival forest using all but one special variable on this same data, and compare the results with those of the model using all variables.

\n

What I am confused about is the evaluation. The way I was planning to do it is the following:

\n
    \n
  1. First, I split the samples into training/testing (stratified by events, 80-20 split).
    2. \n
  2. Then for every imputation, I train a survival forest using all variables on the imputed training samples.
    3. \n
  3. After training, I get the out of bag concordance index calculated on the training data and I can compute the concordance index on the using test samples also.
    4. \n
\n

At this point I'm wondering, is the training OOB concordance index a better evaluation metrics of a model than the concordance index on the unseen portion of the data?\nAnd, assuming I have the concordance index on the unseen data for all imputations computed, what is a reasonable way to join and report them - should I just average the scores?

\n
    \n
  1. Next I do the same (training a model for every imputation on the training samples) using all but one variable of interest. I get OOB c-index and the c-index on the unseen data for each model/imputation.
    2. \n
\n

And here I wonder, how to compare the two? Do I just test the average concordance indexes of the models being significantly different? Or is there a better way of comparison?

\n

And as a last, more general question - at what point (in terms of size of data and censoring/nr of events) would you consider that evaluating through cross-validation is preferable over a simple training/test split?

\n", "question_id": 676956, "question_license": "CC BY-SA 4.0", "question_score": 0, "question_text": "I've worked with tree-based models before, but I'm new to survival analysis. I have a very large dataset of highly censored data, and multiple imputations (let's say 5). I wish to train a survival forest on this data and evaluate it. More than this, I also wish to evaluate a survival forest using all but one special variable on this same data, and compare the results with those of the model using all variables.\n\n\n\n\nWhat I am confused about is the evaluation. The way I was planning to do it is the following:\n\n\n\n\n\nFirst, I split the samples into training/testing (stratified by events, 80-20 split).\n\n\n\n\nThen for every imputation, I train a survival forest using all variables on the imputed training samples.\n\n\n\n\nAfter training, I get the out of bag concordance index calculated on the training data and I can compute the concordance index on the using test samples also.\n\n\n\n\n\nAt this point I'm wondering, is the training OOB concordance index a better evaluation metrics of a model than the concordance index on the unseen portion of the data?\nAnd, assuming I have the concordance index on the unseen data for all imputations computed, what is a reasonable way to join and report them - should I just average the scores?\n\n\n\n\n\nNext I do the same (training a model for every imputation on the training samples) using all but one variable of interest. I get OOB c-index and the c-index on the unseen data for each model/imputation.\n\n\n\n\n\nAnd here I wonder, how to compare the two? Do I just test the average concordance indexes of the models being significantly different? Or is there a better way of comparison?\n\n\n\n\nAnd as a last, more general question - at what point (in terms of size of data and censoring/nr of events) would you consider that evaluating through cross-validation is preferable over a simple training/test split?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Polhek", "profile_url": "https://stats.stackexchange.com/users/128159/polhek", "user_type": "registered"}, "created_at": "2026-08-25T13:00:28+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "C4B771B4-ADC3-4FD6-AE5D-16BE2127FFCA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/C4B771B4-ADC3-4FD6-AE5D-16BE2127FFCA/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676956/evaluating-survival-forest-models-on-multiple-imputation-data", "split": "test", "split_group": "8636b1b5f40d7aa127b413ad0a54ccb1823c8f472ffcec2eef386149ce3eef6d", "tags": ["survival", "random-forest", "multiple-imputation", "concordance"], "thread_id": "stats:676956", "title": "Evaluating survival forest models on multiple imputation data"}} {"citation_context": " to test the model reliably. Frank Harrell estimates that you need on the order of 20,000 subjects (https://www.fharrell.com/post/split-val/) before a train/test split is as stable as resampling from the data with cross-validation or bootst", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.fharrell.com/post/split-val/", "kind": "external_url", "post_id": 677008, "post_url": "https://stats.stackexchange.com/a/677008", "product": "citations", "record_id": "Scientific-Citation-Graph:ac2cf0267cba39bbd04f7d80", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "
\n

I .. wish to evaluate a survival forest using all but one special variable on this same data, and compare the results with those of the model using all variables.

\n
\n

Frank Harrell has a superb summary of how to evaluate the value of additional predictors in modeling. That's straightforward with nested regression models, which can be compared in a likelihood-ratio test. If you need to use random survival forests, some measure of explained variation in outcomes would be appropriate.

\n
\n

I can compute the concordance index...

\n
\n

Frank Harrell introduced the concordance/c-index to survival analysis. Although it is a useful measure of a single model's discriminative ability, he doesn't think that it's a good way to compare models; see the link above. It only evaluates how well the model gets the order of events correct, not how well the model matches the event probability over time as a function of covariates. Furthermore, the usual c-index can have bias depending on censoring patterns. There are ways to deal with that, but you are still left with a measure of discrimination only.

\n

A recent arXiv paper by Lillelund et al., "Stop Chasing the C-index: This Is How We Should Evaluate Our Survival Models," goes into more detail and explains better evaluation methods. The "Review of Statistical Methods for Evaluating the Performance of Survival or Other Time-to-Event Prediction Models (from Conventional to Deep Learning Approaches)" by Park et al., Korean J Radiol. 22:1697-1707 (2021) is also on-topic.

\n

Your choice of evaluation method might best depend on your intended use of model, which isn't clear from this question.

\n
\n

... at what point (in terms of size of data and censoring/nr of events) would you consider that evaluating through cross-validation is preferable over a simple training/test split?

\n
\n

A problem with a training/test split is that you limit both the amount of information used to train the model and the power to test the model reliably. Frank Harrell estimates that you need on the order of 20,000 subjects before a train/test split is as stable as resampling from the data with cross-validation or bootstrapping. With the power of survival models essentially determined by the number of subjects with events, you are thus unlikely to have clinical survival data with the necessary tens of thousands of events.

\n

As cross-validation involves train/test splits, it also has the problem of a small test sample in each fold. Combining all 10 test sets in 10-fold cross-validation only uses the number of cases in the original data set for testing. Repeated cross-validation helps, both in reducing reliance on a single set of splits and in increasing the effective number of test cases. Bootstrapping uses the number of cases in the original data set in each bootstrap sample, and one might use 50-100 bootstrap samples. Frank Harrell thus estimates that "To be as good as the bootstrap, about 100 repeats of 10-fold cross-validation are required."

\n

With resampling you are validating the modeling process rather than the model itself. Under the bootstrap principle, drawing samples with replacement from the available data represents the process of drawing the available data from the underlying population. Modeling each of repeated bootstrap samples and evaluating performance of each model on the full data set thus represents how well your modeling process captures the properties of the population. Comparing performance of each (possibly overfit) bootstrap-sample model on its own sample against its performance on the entire data set is the "optimism bootstrap" that evaluates overfitting. Once you accept that you are validating the process, objections to including training data in testing become much less compelling.

\n
\n

I get the out of bag [OOB] concordance index calculated on the training data...

\n
\n

This raises an issue for whatever measure of model performance you choose. Using OOB data for testing does mean that, within each tree, the test data don't overlap with the training data. As noted above, however, that isn't necessarily required and it limits you to about 1/3 of the data in each test set. Alternatively, you could use performance within each tree's model on the entire data set as an optimism bootstrap to validate the modeling process. Frank Harrell notes that distinction in this answer.

\n
\n

... assuming I have the concordance index on the unseen data for all imputations computed, what is a reasonable way to join and report them - should I just average the scores?

\n
\n

See this question and its answer on how to use Rubin's rules to combine random forest models on multiply imputed data sets. If your score of model performance is close enough to normally distributed, then you do average scores for the point estimate. Comparisons between models require estimating the variances of the point estimates, again following Rubin's rules that combine within-imputation and between-imputation variances.

\n

A few suggestions

\n

Survival analysis, similarly to binomial regression, can suffer from omitted-variable bias if any outcome-associated variable is omitted from the model. If you are studying clinical survival data, don't fall into the trap of omitting standard clinical outcome-related variables from the model. Models of outcome with predictors like gene-expression levels that don't include standard clinical variables run a serious risk of that bias and might just find proxies for clinical variables in a way that makes clinical application of the models pretty useless.

\n

Consider whether your goals might better be met with standard regression models. Their results are typically much easier to interpret heuristically than those of a random forest. Evaluating the added value of a single predictor is simple with regression models.

\n

Yes, random forests can incorporate unexpected interactions among predictors in ways that regression model's can't, at least with large numbers of predictors. Identifying what those interactions involve isn't so straightforward.

\n", "answer_id": 677008, "answer_text": "I .. wish to evaluate a survival forest using all but one special variable on this same data, and compare the results with those of the model using all variables.\n\n\n\n\n\n\n\nFrank Harrell has a superb summary of how to evaluate the value of additional predictors (https://www.fharrell.com/post/addvalue/) in modeling. That's straightforward with nested regression models, which can be compared in a likelihood-ratio test. If you need to use random survival forests, some measure of explained variation in outcomes would be appropriate.\n\n\n\n\n\n\n\nI can compute the concordance index...\n\n\n\n\n\n\n\nFrank Harrell introduced the concordance/c-index to survival analysis. Although it is a useful measure of a single model's discriminative ability, he doesn't think that it's a good way to compare models; see the link (https://www.fharrell.com/post/addvalue/) above. It only evaluates how well the model gets the order of events correct, not how well the model matches the event probability over time as a function of covariates. Furthermore, the usual c-index can have bias depending on censoring patterns. There are ways to deal with that, but you are still left with a measure of discrimination only.\n\n\n\n\nA recent arXiv paper by Lillelund et al., \"Stop Chasing the C-index: This Is How We Should Evaluate Our Survival Models (https://arxiv.org/html/2506.02075v1),\" goes into more detail and explains better evaluation methods. The \"Review of Statistical Methods for Evaluating the Performance of Survival or Other Time-to-Event Prediction Models (from Conventional to Deep Learning Approaches) (https://doi.org/10.3348/kjr.2021.0223)\" by Park et al., Korean J Radiol. 22:1697-1707 (2021) is also on-topic.\n\n\n\n\nYour choice of evaluation method might best depend on your intended use of model, which isn't clear from this question.\n\n\n\n\n\n\n\n... at what point (in terms of size of data and censoring/nr of events) would you consider that evaluating through cross-validation is preferable over a simple training/test split?\n\n\n\n\n\n\n\nA problem with a training/test split is that you limit both the amount of information used to train the model and the power to test the model reliably. Frank Harrell estimates that you need on the order of 20,000 subjects (https://www.fharrell.com/post/split-val/) before a train/test split is as stable as resampling from the data with cross-validation or bootstrapping. With the power of survival models essentially determined by the number of subjects with events, you are thus unlikely to have clinical survival data with the necessary tens of thousands of events.\n\n\n\n\nAs cross-validation involves train/test splits, it also has the problem of a small test sample in each fold. Combining all 10 test sets in 10-fold cross-validation only uses the number of cases in the original data set for testing. Repeated cross-validation helps, both in reducing reliance on a single set of splits and in increasing the effective number of test cases. Bootstrapping uses the number of cases in the original data set in each bootstrap sample, and one might use 50-100 bootstrap samples. Frank Harrell thus estimates that \"To be as good as the bootstrap, about 100 repeats of 10-fold cross-validation are required (https://www.fharrell.com/post/split-val/).\"\n\n\n\n\nWith resampling you are validating the modeling process rather than the model itself. Under the bootstrap principle, drawing samples with replacement from the available data represents the process of drawing the available data from the underlying population. Modeling each of repeated bootstrap samples and evaluating performance of each model on the full data set thus represents how well your modeling process captures the properties of the population. Comparing performance of each (possibly overfit) bootstrap-sample model on its own sample against its performance on the entire data set is the \"optimism bootstrap\" that evaluates overfitting. Once you accept that you are validating the process, objections to including training data in testing become much less compelling.\n\n\n\n\n\n\n\nI get the out of bag [OOB] concordance index calculated on the training data...\n\n\n\n\n\n\n\nThis raises an issue for whatever measure of model performance you choose. Using OOB data for testing does mean that, within each tree, the test data don't overlap with the training data. As noted above, however, that isn't necessarily required and it limits you to about 1/3 of the data in each test set. Alternatively, you could use performance within each tree's model on the entire data set as an optimism bootstrap to validate the modeling process. Frank Harrell notes that distinction in this answer (https://stats.stackexchange.com/a/656190/28500).\n\n\n\n\n\n\n\n... assuming I have the concordance index on the unseen data for all imputations computed, what is a reasonable way to join and report them - should I just average the scores?\n\n\n\n\n\n\n\nSee this question (https://stats.stackexchange.com/q/476829/28500) and its answer (https://stats.stackexchange.com/a/476849/28500) on how to use Rubin's rules to combine random forest models on multiply imputed data sets. If your score of model performance is close enough to normally distributed, then you do average scores for the point estimate. Comparisons between models require estimating the variances of the point estimates, again following Rubin's rules that combine within-imputation and between-imputation variances.\n\n\n\n\nA few suggestions\n\n\n\n\nSurvival analysis, similarly to binomial regression, can suffer from omitted-variable bias (https://stats.stackexchange.com/q/113766/28500) if any outcome-associated variable is omitted from the model. If you are studying clinical survival data, don't fall into the trap of omitting standard clinical outcome-related variables from the model. Models of outcome with predictors like gene-expression levels that don't include standard clinical variables run a serious risk of that bias and might just find proxies for clinical variables in a way that makes clinical application of the models pretty useless.\n\n\n\n\nConsider whether your goals might better be met with standard regression models. Their results are typically much easier to interpret heuristically than those of a random forest. Evaluating the added value of a single predictor is simple with regression models.\n\n\n\n\nYes, random forests can incorporate unexpected interactions among predictors in ways that regression model's can't, at least with large numbers of predictors. Identifying what those interactions involve isn't so straightforward.", "answer_url": "https://stats.stackexchange.com/a/677008", "author": "EdM", "author_url": "https://stats.stackexchange.com/users/28500/edm", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-30T15:43:41+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676956, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-08-30T15:43:41+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "65108C55-42C2-445B-B21B-0B094DADB7B2", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/65108C55-42C2-445B-B21B-0B094DADB7B2/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-08-30T15:54:06+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "34531043-A9BE-4349-88AF-6D5B08F325DD", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/34531043-A9BE-4349-88AF-6D5B08F325DD/view-source"}], "score": 1, "updated_at": "2026-08-30T15:54:06+00:00"}], "domain": "statistics", "external_links": ["https://arxiv.org/html/2506.02075v1", "https://doi.org/10.3348/kjr.2021.0223", "https://www.fharrell.com/post/addvalue/", "https://www.fharrell.com/post/split-val/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Polhek", "question_author_url": "https://stats.stackexchange.com/users/128159/polhek", "question_author_user_type": "registered", "question_created_at": "2026-08-25T13:00:28+00:00", "question_html": "

I've worked with tree-based models before, but I'm new to survival analysis. I have a very large dataset of highly censored data, and multiple imputations (let's say 5). I wish to train a survival forest on this data and evaluate it. More than this, I also wish to evaluate a survival forest using all but one special variable on this same data, and compare the results with those of the model using all variables.

\n

What I am confused about is the evaluation. The way I was planning to do it is the following:

\n
    \n
  1. First, I split the samples into training/testing (stratified by events, 80-20 split).
    2. \n
  2. Then for every imputation, I train a survival forest using all variables on the imputed training samples.
    3. \n
  3. After training, I get the out of bag concordance index calculated on the training data and I can compute the concordance index on the using test samples also.
    4. \n
\n

At this point I'm wondering, is the training OOB concordance index a better evaluation metrics of a model than the concordance index on the unseen portion of the data?\nAnd, assuming I have the concordance index on the unseen data for all imputations computed, what is a reasonable way to join and report them - should I just average the scores?

\n
    \n
  1. Next I do the same (training a model for every imputation on the training samples) using all but one variable of interest. I get OOB c-index and the c-index on the unseen data for each model/imputation.
    2. \n
\n

And here I wonder, how to compare the two? Do I just test the average concordance indexes of the models being significantly different? Or is there a better way of comparison?

\n

And as a last, more general question - at what point (in terms of size of data and censoring/nr of events) would you consider that evaluating through cross-validation is preferable over a simple training/test split?

\n", "question_id": 676956, "question_license": "CC BY-SA 4.0", "question_score": 0, "question_text": "I've worked with tree-based models before, but I'm new to survival analysis. I have a very large dataset of highly censored data, and multiple imputations (let's say 5). I wish to train a survival forest on this data and evaluate it. More than this, I also wish to evaluate a survival forest using all but one special variable on this same data, and compare the results with those of the model using all variables.\n\n\n\n\nWhat I am confused about is the evaluation. The way I was planning to do it is the following:\n\n\n\n\n\nFirst, I split the samples into training/testing (stratified by events, 80-20 split).\n\n\n\n\nThen for every imputation, I train a survival forest using all variables on the imputed training samples.\n\n\n\n\nAfter training, I get the out of bag concordance index calculated on the training data and I can compute the concordance index on the using test samples also.\n\n\n\n\n\nAt this point I'm wondering, is the training OOB concordance index a better evaluation metrics of a model than the concordance index on the unseen portion of the data?\nAnd, assuming I have the concordance index on the unseen data for all imputations computed, what is a reasonable way to join and report them - should I just average the scores?\n\n\n\n\n\nNext I do the same (training a model for every imputation on the training samples) using all but one variable of interest. I get OOB c-index and the c-index on the unseen data for each model/imputation.\n\n\n\n\n\nAnd here I wonder, how to compare the two? Do I just test the average concordance indexes of the models being significantly different? Or is there a better way of comparison?\n\n\n\n\nAnd as a last, more general question - at what point (in terms of size of data and censoring/nr of events) would you consider that evaluating through cross-validation is preferable over a simple training/test split?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Polhek", "profile_url": "https://stats.stackexchange.com/users/128159/polhek", "user_type": "registered"}, "created_at": "2026-08-25T13:00:28+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "C4B771B4-ADC3-4FD6-AE5D-16BE2127FFCA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/C4B771B4-ADC3-4FD6-AE5D-16BE2127FFCA/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676956/evaluating-survival-forest-models-on-multiple-imputation-data", "split": "test", "split_group": "8636b1b5f40d7aa127b413ad0a54ccb1823c8f472ffcec2eef386149ce3eef6d", "tags": ["survival", "random-forest", "multiple-imputation", "concordance"], "thread_id": "stats:676956", "title": "Evaluating survival forest models on multiple imputation data"}} {"citation_context": "ompare a standard deviation value to an RMSE value.\n\n\n\n\nFor example, lets look at the Bosch BMM150 (https://www.bosch-sensortec.com/media/boschsensortec/downloads/datasheets/bst-bmm150-ds001.pdf) sensor. It's a magnetic field sensor and measures its heading/azimuth. The datasheet claims an acc", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.bosch-sensortec.com/media/boschsensortec/downloads/datasheets/bst-bmm150-ds001.pdf", "kind": "external_url", "post_id": 676975, "post_url": "https://stats.stackexchange.com/questions/676975/how-to-compare-a-standard-deviation-to-a-root-mean-square-error", "product": "citations", "record_id": "Scientific-Citation-Graph:4abee4cf6f87bda757dd2a65", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

It would appear that the Bosch BMM150 sensor is implicitly declared/accepted as an unbiased measuring instrument. This I infer by the summary way that the pamflet informs on what the min-max values are ("$\\pm 3\\sigma$", pointing to a zero-mean Normal distribution), and also by the way the OP builds on this information to obtain the implied standard deviation, invoking silently the Normal.

\n

With zero bias, we have\n$${\\rm RMSE }\\;(BMM150) = \\sigma = 0.833$$

\n

to be compared to the other sensor with RMSE = 2.5.

\n

For some informal intuition, the information on the Bosch sensor says that "$2.5$" is an extreme value of the error (half-length of a Confidence Interval on the error, with very high statistical confidence), while for the RMSE of the other sensor "$2.5$" is its average value. If this is an average, it is logical to expect from the 2nd sensor to have with some frequency even higher error-values, and so that it ends up inferior in RMSE terms.

\n", "answer_id": 677000, "answer_text": "It would appear that the Bosch BMM150 sensor is implicitly declared/accepted as an unbiased measuring instrument. This I infer by the summary way that the pamflet informs on what the min-max values are (\"$\\pm 3\\sigma$\", pointing to a zero-mean Normal distribution), and also by the way the OP builds on this information to obtain the implied standard deviation, invoking silently the Normal.\n\n\n\n\nWith zero bias, we have\n$${\\rm RMSE }\\;(BMM150) = \\sigma = 0.833$$\n\n\n\n\nto be compared to the other sensor with RMSE = 2.5.\n\n\n\n\nFor some informal intuition, the information on the Bosch sensor says that \"$2.5$\" is an extreme value of the error (half-length of a Confidence Interval on the error, with very high statistical confidence), while for the RMSE of the other sensor \"$2.5$\" is its average value. If this is an average, it is logical to expect from the 2nd sensor to have with some frequency even higher error-values, and so that it ends up inferior in RMSE terms.", "answer_url": "https://stats.stackexchange.com/a/677000", "author": "Alecos Papadopoulos", "author_url": "https://stats.stackexchange.com/users/28746/alecos-papadopoulos", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-29T17:24:38+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 676975, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Alecos Papadopoulos", "profile_url": "https://stats.stackexchange.com/users/28746/alecos-papadopoulos", "user_type": "registered"}, "created_at": "2026-08-29T17:24:38+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "08B127CA-03A0-4A61-8D0D-8F3FF0F9CBF1", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/08B127CA-03A0-4A61-8D0D-8F3FF0F9CBF1/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Alecos Papadopoulos", "profile_url": "https://stats.stackexchange.com/users/28746/alecos-papadopoulos", "user_type": "registered"}, "created_at": "2026-08-30T17:48:55+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "79E36E85-896B-4E05-B1B2-D421C8680DF1", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/79E36E85-896B-4E05-B1B2-D421C8680DF1/view-source"}], "score": 2, "updated_at": "2026-08-30T17:48:55+00:00"}], "domain": "statistics", "external_links": ["https://www.bosch-sensortec.com/media/boschsensortec/downloads/datasheets/bst-bmm150-ds001.pdf"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "M.X", "question_author_url": "https://stats.stackexchange.com/users/515989/m-x", "question_author_user_type": "registered", "question_created_at": "2026-08-27T12:58:22+00:00", "question_html": "

I understand their fundamental differences and that they are measuring different things. There are quite a few threads already comparing the two methods to each other.\nHowever, none really answer how to "best" compare a standard deviation value to an RMSE value.

\n

For example, lets look at the Bosch BMM150 sensor. It's a magnetic field sensor and measures its heading/azimuth. The datasheet claims an accuary of $\\pm2.5°$ regarding $\\pm3\\sigma$. That means the standard deviation is $\\sigma=0.83°$ and that $99.7\\%$ of its measured values are within $2.5°$ of the actual heading.

\n

Now lets say I have another sensor that claims to have an RMSE of $2.5°$. Is it more or less accuate than the Bosch sensor?

\n", "question_id": 676975, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "I understand their fundamental differences and that they are measuring different things. There are quite a few threads already comparing the two methods to each other.\nHowever, none really answer how to \"best\" compare a standard deviation value to an RMSE value.\n\n\n\n\nFor example, lets look at the Bosch BMM150 (https://www.bosch-sensortec.com/media/boschsensortec/downloads/datasheets/bst-bmm150-ds001.pdf) sensor. It's a magnetic field sensor and measures its heading/azimuth. The datasheet claims an accuary of $\\pm2.5°$ regarding $\\pm3\\sigma$. That means the standard deviation is $\\sigma=0.83°$ and that $99.7\\%$ of its measured values are within $2.5°$ of the actual heading.\n\n\n\n\nNow lets say I have another sensor that claims to have an RMSE of $2.5°$. Is it more or less accuate than the Bosch sensor?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "M.X", "profile_url": "https://stats.stackexchange.com/users/515989/m-x", "user_type": "registered"}, "created_at": "2026-08-27T12:58:22+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "90A46F66-D397-415D-B481-592C45F29D24", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/90A46F66-D397-415D-B481-592C45F29D24/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/676975/how-to-compare-a-standard-deviation-to-a-root-mean-square-error", "split": "test", "split_group": "cd99f41c0a42d92d6e8aa8fd37dea2f75901b57bc32e8ea30cf079304b90a422", "tags": ["standard-deviation", "mse", "rms"], "thread_id": "stats:676975", "title": "How to compare a standard deviation to a root mean square error?"}} {"citation_context": "tion 5.2 of the 2016 paper \"Why Should I Trust You?\": Explaining the Predictions of Any Classifier (https://dl.acm.org/doi/10.1145/2939672.2939778) tests the Recall of different XAI methods comparing them to interpretable methods.\n\n\n\n\nMy question", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": "10.1145/2939672.2939778", "external_url": "https://dl.acm.org/doi/10.1145/2939672.2939778", "kind": "doi_url", "post_id": 677035, "post_url": "https://stats.stackexchange.com/questions/677035/k-lasso-and-recall-in-lime-simulated-experiments", "product": "citations", "record_id": "Scientific-Citation-Graph:1fed5df595ad7498088cd44d", "split": "test", "thread": {"accepted_answer_id": 677040, "answers": [{"answer_html": "
\n

It seems that the rationale here is to see whether the explanation models recover the same input features than the original...

\n
\n

The idea is instead to come close enough to the same outcome predictions of the model. This isn't just a problem with "machine learning" models. For example, Section 5.5.2 of Frank Harrell's Regression Modeling Strategies outlines approaches to the same problem with potentially complex, difficult-to-interpret, multiple regression models. One approach is to use a (more interpretable) subset of the features to fit an OLS model of the predictor values from the full model.

\n
\n

I think the selection of features (through K-LASSO) is an important yet under-explained part of the paper.

\n
\n

In principle, the above simplification of a multiple regression model is not much different from LIME. For a continuous outcome, LIME similarly uses a subset of the features to fit model predictions near a region of interest. K-LASSO selects which K of the features to use.

\n
\n

So the aim is to test whether LIME selects the same features of all available ones as compared to the original model.

\n
\n

A full machine learning model often involves all of the candidate features in some way, so LIME can't typically "select the same features." LASSO is an exception. In LASSO for linear regression, you start with a loss form similar to what you show.

\n

$$L = \\sum_{i} (y_i - g(z_i))^2 + \\lambda \\sum_k{|\\beta_k|},$$

\n

where the $\\beta_k$ are the coefficient estimates for the predictors. The $\\lambda \\sum_k{|\\beta_k|}$ term is called an L1 penalty, which sets increasing numbers of coefficients exactly to 0 as $\\lambda$ increases. See this page and its links.

\n

LASSO usually involves choosing $\\lambda$ to minimize that loss. The K-LASSO evidently finds instead a value of $\\lambda$ that retains only K non-zero coefficients (perhaps using a different loss function).

\n
\n

I could read LASSO in detail but my bandwidth right now is just about enough for LIME/SP-LIME...

\n
\n

I'd recommend devoting more bandwidth to multiple regression, including LASSO and other penalization methods (e.g., ridge regression and elastic net) that minimize overfitting of the data. An Introduction to Statistical Learning is a useful reference on those and other major modeling methods.

\n", "answer_id": 677040, "answer_text": "It seems that the rationale here is to see whether the explanation models recover the same input features than the original...\n\n\n\n\n\n\n\nThe idea is instead to come close enough to the same outcome predictions of the model. This isn't just a problem with \"machine learning\" models. For example, Section 5.5.2 of Frank Harrell's Regression Modeling Strategies (https://hbiostat.org/rmsc/validate#approximating-the-full-model) outlines approaches to the same problem with potentially complex, difficult-to-interpret, multiple regression models. One approach is to use a (more interpretable) subset of the features to fit an OLS model of the predictor values from the full model.\n\n\n\n\n\n\n\nI think the selection of features (through K-LASSO) is an important yet under-explained part of the paper.\n\n\n\n\n\n\n\nIn principle, the above simplification of a multiple regression model is not much different from LIME. For a continuous outcome, LIME similarly uses a subset of the features to fit model predictions near a region of interest. K-LASSO selects which K of the features to use.\n\n\n\n\n\n\n\nSo the aim is to test whether LIME selects the same features of all available ones as compared to the original model.\n\n\n\n\n\n\n\nA full machine learning model often involves all of the candidate features in some way, so LIME can't typically \"select the same features.\" LASSO is an exception. In LASSO for linear regression, you start with a loss form similar to what you show.\n\n\n\n\n$$L = \\sum_{i} (y_i - g(z_i))^2 + \\lambda \\sum_k{|\\beta_k|},$$\n\n\n\n\nwhere the $\\beta_k$ are the coefficient estimates for the predictors. The $\\lambda \\sum_k{|\\beta_k|}$ term is called an L1 penalty, which sets increasing numbers of coefficients exactly to 0 as $\\lambda$ increases. See this page (https://stats.stackexchange.com/q/74542/28500) and its links.\n\n\n\n\nLASSO usually involves choosing $\\lambda$ to minimize that loss. The K-LASSO evidently finds instead a value of $\\lambda$ that retains only K non-zero coefficients (perhaps using a different loss function).\n\n\n\n\n\n\n\nI could read LASSO in detail but my bandwidth right now is just about enough for LIME/SP-LIME...\n\n\n\n\n\n\n\nI'd recommend devoting more bandwidth to multiple regression, including LASSO and other penalization methods (e.g., ridge regression and elastic net) that minimize overfitting of the data. An Introduction to Statistical Learning (https://www.statlearning.com/) is a useful reference on those and other major modeling methods.", "answer_url": "https://stats.stackexchange.com/a/677040", "author": "EdM", "author_url": "https://stats.stackexchange.com/users/28500/edm", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-01T19:10:48+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677035, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-09-01T19:10:48+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "12B0F5F5-4922-40E3-B683-A890D9DA3239", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/12B0F5F5-4922-40E3-B683-A890D9DA3239/view-source"}], "score": 2, "updated_at": "2026-09-01T19:10:48+00:00"}], "domain": "statistics", "external_links": ["https://dl.acm.org/doi/10.1145/2939672.2939778", "https://hbiostat.org/rmsc/validate#approximating-the-full-model", "https://www.statlearning.com/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "kindleman", "question_author_url": "https://stats.stackexchange.com/users/510622/kindleman", "question_author_user_type": "registered", "question_created_at": "2026-09-01T13:58:20+00:00", "question_html": "

Context

\n

Section 5.2 of the 2016 paper "Why Should I Trust You?": Explaining the Predictions of Any Classifier tests the Recall of different XAI methods comparing them to interpretable methods.

\n

My question is about interpreting this section, and the role played by K-LASSO.

\n

It seems that the rationale here is to see whether the explanation models recover the same input features than the original, since in this case the original model is interpretable (also its input, a bag of words).

\n

Selecting Features

\n

So the aim is to test whether LIME selects the same features of all available ones as compared to the original model.

\n

I think the selection of features (through K-LASSO) is an important yet under-explained part of the paper.

\n

The algorithm that applies here, for their model, is LIME (not SP-LIME), which uses K-LASSO to select $K$ features:

\n
\n

(...) selecting $K$ features with Lasso (using the regularization path [9]) and then learning the weights via least squares (a procedure we call K-LASSO in Algorithm 1).

\n
\n

From talking to a chatbot, my intuition is that $K$-LASSO usually yields a sparse model, given that some coefficients will be 0, and those features will be the ones we retain or discard from all the ones available.

\n

I am aware I could read LASSO in detail but my bandwidth right now is just about enough for LIME/SP-LIME, so I am using my knowledge of Least-Squares to get an intuition of what is happening.

\n

Questions

\n\n

For completeness, the paper uses $g$ explanation model, $f$ original model, $\\pi_x (z)$ is used as a distance-weight multiplying the loss-L-component $L = \\sum_{z,z'} \\pi_x (f(z)-g(z'))^2$ and $\\Omega$ a model-complexity measure.

\n

Comment

\n

The chatbot says LASSO is done to select features (0 coefficients are features we then discard), but the coeffients arent the best to fit the original model (since there is the extra penalty in the Loss).

\n

So then Least Squares to re-fit or just fit the coefficients. I'd appreciate corrections if this is wrong, but it does make sense to me

\n", "question_id": 677035, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "Context\n\n\n\n\nSection 5.2 of the 2016 paper \"Why Should I Trust You?\": Explaining the Predictions of Any Classifier (https://dl.acm.org/doi/10.1145/2939672.2939778) tests the Recall of different XAI methods comparing them to interpretable methods.\n\n\n\n\nMy question is about interpreting this section, and the role played by K-LASSO.\n\n\n\n\nIt seems that the rationale here is to see whether the explanation models recover the same input features than the original, since in this case the original model is interpretable (also its input, a bag of words).\n\n\n\n\nSelecting Features\n\n\n\n\nSo the aim is to test whether LIME selects the same features of all available ones as compared to the original model.\n\n\n\n\nI think the selection of features (through K-LASSO) is an important yet under-explained part of the paper.\n\n\n\n\nThe algorithm that applies here, for their model, is LIME (not SP-LIME), which uses K-LASSO to select $K$ features:\n\n\n\n\n\n\n\n(...) selecting $K$ features with Lasso (using the regularization path [9]) and then learning the weights via least squares (a procedure we call K-LASSO in Algorithm 1).\n\n\n\n\n\n\n\nFrom talking to a chatbot, my intuition is that $K$-LASSO usually yields a sparse model, given that some coefficients will be 0, and those features will be the ones we retain or discard from all the ones available.\n\n\n\n\nI am aware I could read LASSO in detail but my bandwidth right now is just about enough for LIME/SP-LIME, so I am using my knowledge of Least-Squares to get an intuition of what is happening.\n\n\n\n\nQuestions\n\n\n\n\n\nIs the overall idea is correct, or what corrections you'd make?\n\n\n\n\nIn the paper LIME shows a loss $\\xi (x) = \\mathrm{argmin_g} L (f,g,\\pi_x (z)) + \\Omega(g)$, and I am assuming LASSO can be performed with such loss as well, otherwise there are two optimisations and the pieces don't fit well in my head.\n\n\n\n\n\nFor completeness, the paper uses $g$ explanation model, $f$ original model, $\\pi_x (z)$ is used as a distance-weight multiplying the loss-L-component $L = \\sum_{z,z'} \\pi_x (f(z)-g(z'))^2$ and $\\Omega$ a model-complexity measure.\n\n\n\n\nComment\n\n\n\n\nThe chatbot says LASSO is done to select features (0 coefficients are features we then discard), but the coeffients arent the best to fit the original model (since there is the extra penalty in the Loss).\n\n\n\n\nSo then Least Squares to re-fit or just fit the coefficients. I'd appreciate corrections if this is wrong, but it does make sense to me", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "kindleman", "profile_url": "https://stats.stackexchange.com/users/510622/kindleman", "user_type": "registered"}, "created_at": "2026-09-01T13:58:20+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "1ECA98F4-6DB3-4398-B85E-C435796E45DF", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/1ECA98F4-6DB3-4398-B85E-C435796E45DF/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-09-01T14:21:40+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "AAF72B85-DA54-49C6-8BEA-FF155201085C", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/AAF72B85-DA54-49C6-8BEA-FF155201085C/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "kindleman", "profile_url": "https://stats.stackexchange.com/users/510622/kindleman", "user_type": "registered"}, "created_at": "2026-09-01T15:22:05+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "588BA2AD-F204-4473-8EB5-7D8AC4DB30CD", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/588BA2AD-F204-4473-8EB5-7D8AC4DB30CD/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-09-02T02:40:31+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "FD4B782E-B4DA-469C-805C-494937FC4942", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/FD4B782E-B4DA-469C-805C-494937FC4942/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/677035/k-lasso-and-recall-in-lime-simulated-experiments", "split": "test", "split_group": "9f7b02658ea7a661e8290f49805b5687b2ff03f604d83ced4faa2c5d53587ee2", "tags": ["linear-model", "lasso", "lime", "explainable-ai"], "thread_id": "stats:677035", "title": "K-LASSO and Recall in LIME (simulated experiments)"}} {"citation_context": "ine learning\" models. For example, Section 5.5.2 of Frank Harrell's Regression Modeling Strategies (https://hbiostat.org/rmsc/validate#approximating-the-full-model) outlines approaches to the same problem with potentially complex, difficult-to-interpret, multiple", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://hbiostat.org/rmsc/validate#approximating-the-full-model", "kind": "external_url", "post_id": 677040, "post_url": "https://stats.stackexchange.com/a/677040", "product": "citations", "record_id": "Scientific-Citation-Graph:da8d957e5fbd339a2c551efd", "split": "test", "thread": {"accepted_answer_id": 677040, "answers": [{"answer_html": "
\n

It seems that the rationale here is to see whether the explanation models recover the same input features than the original...

\n
\n

The idea is instead to come close enough to the same outcome predictions of the model. This isn't just a problem with "machine learning" models. For example, Section 5.5.2 of Frank Harrell's Regression Modeling Strategies outlines approaches to the same problem with potentially complex, difficult-to-interpret, multiple regression models. One approach is to use a (more interpretable) subset of the features to fit an OLS model of the predictor values from the full model.

\n
\n

I think the selection of features (through K-LASSO) is an important yet under-explained part of the paper.

\n
\n

In principle, the above simplification of a multiple regression model is not much different from LIME. For a continuous outcome, LIME similarly uses a subset of the features to fit model predictions near a region of interest. K-LASSO selects which K of the features to use.

\n
\n

So the aim is to test whether LIME selects the same features of all available ones as compared to the original model.

\n
\n

A full machine learning model often involves all of the candidate features in some way, so LIME can't typically "select the same features." LASSO is an exception. In LASSO for linear regression, you start with a loss form similar to what you show.

\n

$$L = \\sum_{i} (y_i - g(z_i))^2 + \\lambda \\sum_k{|\\beta_k|},$$

\n

where the $\\beta_k$ are the coefficient estimates for the predictors. The $\\lambda \\sum_k{|\\beta_k|}$ term is called an L1 penalty, which sets increasing numbers of coefficients exactly to 0 as $\\lambda$ increases. See this page and its links.

\n

LASSO usually involves choosing $\\lambda$ to minimize that loss. The K-LASSO evidently finds instead a value of $\\lambda$ that retains only K non-zero coefficients (perhaps using a different loss function).

\n
\n

I could read LASSO in detail but my bandwidth right now is just about enough for LIME/SP-LIME...

\n
\n

I'd recommend devoting more bandwidth to multiple regression, including LASSO and other penalization methods (e.g., ridge regression and elastic net) that minimize overfitting of the data. An Introduction to Statistical Learning is a useful reference on those and other major modeling methods.

\n", "answer_id": 677040, "answer_text": "It seems that the rationale here is to see whether the explanation models recover the same input features than the original...\n\n\n\n\n\n\n\nThe idea is instead to come close enough to the same outcome predictions of the model. This isn't just a problem with \"machine learning\" models. For example, Section 5.5.2 of Frank Harrell's Regression Modeling Strategies (https://hbiostat.org/rmsc/validate#approximating-the-full-model) outlines approaches to the same problem with potentially complex, difficult-to-interpret, multiple regression models. One approach is to use a (more interpretable) subset of the features to fit an OLS model of the predictor values from the full model.\n\n\n\n\n\n\n\nI think the selection of features (through K-LASSO) is an important yet under-explained part of the paper.\n\n\n\n\n\n\n\nIn principle, the above simplification of a multiple regression model is not much different from LIME. For a continuous outcome, LIME similarly uses a subset of the features to fit model predictions near a region of interest. K-LASSO selects which K of the features to use.\n\n\n\n\n\n\n\nSo the aim is to test whether LIME selects the same features of all available ones as compared to the original model.\n\n\n\n\n\n\n\nA full machine learning model often involves all of the candidate features in some way, so LIME can't typically \"select the same features.\" LASSO is an exception. In LASSO for linear regression, you start with a loss form similar to what you show.\n\n\n\n\n$$L = \\sum_{i} (y_i - g(z_i))^2 + \\lambda \\sum_k{|\\beta_k|},$$\n\n\n\n\nwhere the $\\beta_k$ are the coefficient estimates for the predictors. The $\\lambda \\sum_k{|\\beta_k|}$ term is called an L1 penalty, which sets increasing numbers of coefficients exactly to 0 as $\\lambda$ increases. See this page (https://stats.stackexchange.com/q/74542/28500) and its links.\n\n\n\n\nLASSO usually involves choosing $\\lambda$ to minimize that loss. The K-LASSO evidently finds instead a value of $\\lambda$ that retains only K non-zero coefficients (perhaps using a different loss function).\n\n\n\n\n\n\n\nI could read LASSO in detail but my bandwidth right now is just about enough for LIME/SP-LIME...\n\n\n\n\n\n\n\nI'd recommend devoting more bandwidth to multiple regression, including LASSO and other penalization methods (e.g., ridge regression and elastic net) that minimize overfitting of the data. An Introduction to Statistical Learning (https://www.statlearning.com/) is a useful reference on those and other major modeling methods.", "answer_url": "https://stats.stackexchange.com/a/677040", "author": "EdM", "author_url": "https://stats.stackexchange.com/users/28500/edm", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-01T19:10:48+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677035, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-09-01T19:10:48+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "12B0F5F5-4922-40E3-B683-A890D9DA3239", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/12B0F5F5-4922-40E3-B683-A890D9DA3239/view-source"}], "score": 2, "updated_at": "2026-09-01T19:10:48+00:00"}], "domain": "statistics", "external_links": ["https://dl.acm.org/doi/10.1145/2939672.2939778", "https://hbiostat.org/rmsc/validate#approximating-the-full-model", "https://www.statlearning.com/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "kindleman", "question_author_url": "https://stats.stackexchange.com/users/510622/kindleman", "question_author_user_type": "registered", "question_created_at": "2026-09-01T13:58:20+00:00", "question_html": "

Context

\n

Section 5.2 of the 2016 paper "Why Should I Trust You?": Explaining the Predictions of Any Classifier tests the Recall of different XAI methods comparing them to interpretable methods.

\n

My question is about interpreting this section, and the role played by K-LASSO.

\n

It seems that the rationale here is to see whether the explanation models recover the same input features than the original, since in this case the original model is interpretable (also its input, a bag of words).

\n

Selecting Features

\n

So the aim is to test whether LIME selects the same features of all available ones as compared to the original model.

\n

I think the selection of features (through K-LASSO) is an important yet under-explained part of the paper.

\n

The algorithm that applies here, for their model, is LIME (not SP-LIME), which uses K-LASSO to select $K$ features:

\n
\n

(...) selecting $K$ features with Lasso (using the regularization path [9]) and then learning the weights via least squares (a procedure we call K-LASSO in Algorithm 1).

\n
\n

From talking to a chatbot, my intuition is that $K$-LASSO usually yields a sparse model, given that some coefficients will be 0, and those features will be the ones we retain or discard from all the ones available.

\n

I am aware I could read LASSO in detail but my bandwidth right now is just about enough for LIME/SP-LIME, so I am using my knowledge of Least-Squares to get an intuition of what is happening.

\n

Questions

\n\n

For completeness, the paper uses $g$ explanation model, $f$ original model, $\\pi_x (z)$ is used as a distance-weight multiplying the loss-L-component $L = \\sum_{z,z'} \\pi_x (f(z)-g(z'))^2$ and $\\Omega$ a model-complexity measure.

\n

Comment

\n

The chatbot says LASSO is done to select features (0 coefficients are features we then discard), but the coeffients arent the best to fit the original model (since there is the extra penalty in the Loss).

\n

So then Least Squares to re-fit or just fit the coefficients. I'd appreciate corrections if this is wrong, but it does make sense to me

\n", "question_id": 677035, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "Context\n\n\n\n\nSection 5.2 of the 2016 paper \"Why Should I Trust You?\": Explaining the Predictions of Any Classifier (https://dl.acm.org/doi/10.1145/2939672.2939778) tests the Recall of different XAI methods comparing them to interpretable methods.\n\n\n\n\nMy question is about interpreting this section, and the role played by K-LASSO.\n\n\n\n\nIt seems that the rationale here is to see whether the explanation models recover the same input features than the original, since in this case the original model is interpretable (also its input, a bag of words).\n\n\n\n\nSelecting Features\n\n\n\n\nSo the aim is to test whether LIME selects the same features of all available ones as compared to the original model.\n\n\n\n\nI think the selection of features (through K-LASSO) is an important yet under-explained part of the paper.\n\n\n\n\nThe algorithm that applies here, for their model, is LIME (not SP-LIME), which uses K-LASSO to select $K$ features:\n\n\n\n\n\n\n\n(...) selecting $K$ features with Lasso (using the regularization path [9]) and then learning the weights via least squares (a procedure we call K-LASSO in Algorithm 1).\n\n\n\n\n\n\n\nFrom talking to a chatbot, my intuition is that $K$-LASSO usually yields a sparse model, given that some coefficients will be 0, and those features will be the ones we retain or discard from all the ones available.\n\n\n\n\nI am aware I could read LASSO in detail but my bandwidth right now is just about enough for LIME/SP-LIME, so I am using my knowledge of Least-Squares to get an intuition of what is happening.\n\n\n\n\nQuestions\n\n\n\n\n\nIs the overall idea is correct, or what corrections you'd make?\n\n\n\n\nIn the paper LIME shows a loss $\\xi (x) = \\mathrm{argmin_g} L (f,g,\\pi_x (z)) + \\Omega(g)$, and I am assuming LASSO can be performed with such loss as well, otherwise there are two optimisations and the pieces don't fit well in my head.\n\n\n\n\n\nFor completeness, the paper uses $g$ explanation model, $f$ original model, $\\pi_x (z)$ is used as a distance-weight multiplying the loss-L-component $L = \\sum_{z,z'} \\pi_x (f(z)-g(z'))^2$ and $\\Omega$ a model-complexity measure.\n\n\n\n\nComment\n\n\n\n\nThe chatbot says LASSO is done to select features (0 coefficients are features we then discard), but the coeffients arent the best to fit the original model (since there is the extra penalty in the Loss).\n\n\n\n\nSo then Least Squares to re-fit or just fit the coefficients. I'd appreciate corrections if this is wrong, but it does make sense to me", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "kindleman", "profile_url": "https://stats.stackexchange.com/users/510622/kindleman", "user_type": "registered"}, "created_at": "2026-09-01T13:58:20+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "1ECA98F4-6DB3-4398-B85E-C435796E45DF", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/1ECA98F4-6DB3-4398-B85E-C435796E45DF/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-09-01T14:21:40+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "AAF72B85-DA54-49C6-8BEA-FF155201085C", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/AAF72B85-DA54-49C6-8BEA-FF155201085C/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "kindleman", "profile_url": "https://stats.stackexchange.com/users/510622/kindleman", "user_type": "registered"}, "created_at": "2026-09-01T15:22:05+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "588BA2AD-F204-4473-8EB5-7D8AC4DB30CD", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/588BA2AD-F204-4473-8EB5-7D8AC4DB30CD/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-09-02T02:40:31+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "FD4B782E-B4DA-469C-805C-494937FC4942", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/FD4B782E-B4DA-469C-805C-494937FC4942/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/677035/k-lasso-and-recall-in-lime-simulated-experiments", "split": "test", "split_group": "9f7b02658ea7a661e8290f49805b5687b2ff03f604d83ced4faa2c5d53587ee2", "tags": ["linear-model", "lasso", "lime", "explainable-ai"], "thread_id": "stats:677035", "title": "K-LASSO and Recall in LIME (simulated experiments)"}} {"citation_context": "on and elastic net) that minimize overfitting of the data. An Introduction to Statistical Learning (https://www.statlearning.com/) is a useful reference on those and other major modeling methods.", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.statlearning.com/", "kind": "external_url", "post_id": 677040, "post_url": "https://stats.stackexchange.com/a/677040", "product": "citations", "record_id": "Scientific-Citation-Graph:9e233f4fdd536daa99ae2e53", "split": "test", "thread": {"accepted_answer_id": 677040, "answers": [{"answer_html": "
\n

It seems that the rationale here is to see whether the explanation models recover the same input features than the original...

\n
\n

The idea is instead to come close enough to the same outcome predictions of the model. This isn't just a problem with "machine learning" models. For example, Section 5.5.2 of Frank Harrell's Regression Modeling Strategies outlines approaches to the same problem with potentially complex, difficult-to-interpret, multiple regression models. One approach is to use a (more interpretable) subset of the features to fit an OLS model of the predictor values from the full model.

\n
\n

I think the selection of features (through K-LASSO) is an important yet under-explained part of the paper.

\n
\n

In principle, the above simplification of a multiple regression model is not much different from LIME. For a continuous outcome, LIME similarly uses a subset of the features to fit model predictions near a region of interest. K-LASSO selects which K of the features to use.

\n
\n

So the aim is to test whether LIME selects the same features of all available ones as compared to the original model.

\n
\n

A full machine learning model often involves all of the candidate features in some way, so LIME can't typically "select the same features." LASSO is an exception. In LASSO for linear regression, you start with a loss form similar to what you show.

\n

$$L = \\sum_{i} (y_i - g(z_i))^2 + \\lambda \\sum_k{|\\beta_k|},$$

\n

where the $\\beta_k$ are the coefficient estimates for the predictors. The $\\lambda \\sum_k{|\\beta_k|}$ term is called an L1 penalty, which sets increasing numbers of coefficients exactly to 0 as $\\lambda$ increases. See this page and its links.

\n

LASSO usually involves choosing $\\lambda$ to minimize that loss. The K-LASSO evidently finds instead a value of $\\lambda$ that retains only K non-zero coefficients (perhaps using a different loss function).

\n
\n

I could read LASSO in detail but my bandwidth right now is just about enough for LIME/SP-LIME...

\n
\n

I'd recommend devoting more bandwidth to multiple regression, including LASSO and other penalization methods (e.g., ridge regression and elastic net) that minimize overfitting of the data. An Introduction to Statistical Learning is a useful reference on those and other major modeling methods.

\n", "answer_id": 677040, "answer_text": "It seems that the rationale here is to see whether the explanation models recover the same input features than the original...\n\n\n\n\n\n\n\nThe idea is instead to come close enough to the same outcome predictions of the model. This isn't just a problem with \"machine learning\" models. For example, Section 5.5.2 of Frank Harrell's Regression Modeling Strategies (https://hbiostat.org/rmsc/validate#approximating-the-full-model) outlines approaches to the same problem with potentially complex, difficult-to-interpret, multiple regression models. One approach is to use a (more interpretable) subset of the features to fit an OLS model of the predictor values from the full model.\n\n\n\n\n\n\n\nI think the selection of features (through K-LASSO) is an important yet under-explained part of the paper.\n\n\n\n\n\n\n\nIn principle, the above simplification of a multiple regression model is not much different from LIME. For a continuous outcome, LIME similarly uses a subset of the features to fit model predictions near a region of interest. K-LASSO selects which K of the features to use.\n\n\n\n\n\n\n\nSo the aim is to test whether LIME selects the same features of all available ones as compared to the original model.\n\n\n\n\n\n\n\nA full machine learning model often involves all of the candidate features in some way, so LIME can't typically \"select the same features.\" LASSO is an exception. In LASSO for linear regression, you start with a loss form similar to what you show.\n\n\n\n\n$$L = \\sum_{i} (y_i - g(z_i))^2 + \\lambda \\sum_k{|\\beta_k|},$$\n\n\n\n\nwhere the $\\beta_k$ are the coefficient estimates for the predictors. The $\\lambda \\sum_k{|\\beta_k|}$ term is called an L1 penalty, which sets increasing numbers of coefficients exactly to 0 as $\\lambda$ increases. See this page (https://stats.stackexchange.com/q/74542/28500) and its links.\n\n\n\n\nLASSO usually involves choosing $\\lambda$ to minimize that loss. The K-LASSO evidently finds instead a value of $\\lambda$ that retains only K non-zero coefficients (perhaps using a different loss function).\n\n\n\n\n\n\n\nI could read LASSO in detail but my bandwidth right now is just about enough for LIME/SP-LIME...\n\n\n\n\n\n\n\nI'd recommend devoting more bandwidth to multiple regression, including LASSO and other penalization methods (e.g., ridge regression and elastic net) that minimize overfitting of the data. An Introduction to Statistical Learning (https://www.statlearning.com/) is a useful reference on those and other major modeling methods.", "answer_url": "https://stats.stackexchange.com/a/677040", "author": "EdM", "author_url": "https://stats.stackexchange.com/users/28500/edm", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-01T19:10:48+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677035, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-09-01T19:10:48+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "12B0F5F5-4922-40E3-B683-A890D9DA3239", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/12B0F5F5-4922-40E3-B683-A890D9DA3239/view-source"}], "score": 2, "updated_at": "2026-09-01T19:10:48+00:00"}], "domain": "statistics", "external_links": ["https://dl.acm.org/doi/10.1145/2939672.2939778", "https://hbiostat.org/rmsc/validate#approximating-the-full-model", "https://www.statlearning.com/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "kindleman", "question_author_url": "https://stats.stackexchange.com/users/510622/kindleman", "question_author_user_type": "registered", "question_created_at": "2026-09-01T13:58:20+00:00", "question_html": "

Context

\n

Section 5.2 of the 2016 paper "Why Should I Trust You?": Explaining the Predictions of Any Classifier tests the Recall of different XAI methods comparing them to interpretable methods.

\n

My question is about interpreting this section, and the role played by K-LASSO.

\n

It seems that the rationale here is to see whether the explanation models recover the same input features than the original, since in this case the original model is interpretable (also its input, a bag of words).

\n

Selecting Features

\n

So the aim is to test whether LIME selects the same features of all available ones as compared to the original model.

\n

I think the selection of features (through K-LASSO) is an important yet under-explained part of the paper.

\n

The algorithm that applies here, for their model, is LIME (not SP-LIME), which uses K-LASSO to select $K$ features:

\n
\n

(...) selecting $K$ features with Lasso (using the regularization path [9]) and then learning the weights via least squares (a procedure we call K-LASSO in Algorithm 1).

\n
\n

From talking to a chatbot, my intuition is that $K$-LASSO usually yields a sparse model, given that some coefficients will be 0, and those features will be the ones we retain or discard from all the ones available.

\n

I am aware I could read LASSO in detail but my bandwidth right now is just about enough for LIME/SP-LIME, so I am using my knowledge of Least-Squares to get an intuition of what is happening.

\n

Questions

\n\n

For completeness, the paper uses $g$ explanation model, $f$ original model, $\\pi_x (z)$ is used as a distance-weight multiplying the loss-L-component $L = \\sum_{z,z'} \\pi_x (f(z)-g(z'))^2$ and $\\Omega$ a model-complexity measure.

\n

Comment

\n

The chatbot says LASSO is done to select features (0 coefficients are features we then discard), but the coeffients arent the best to fit the original model (since there is the extra penalty in the Loss).

\n

So then Least Squares to re-fit or just fit the coefficients. I'd appreciate corrections if this is wrong, but it does make sense to me

\n", "question_id": 677035, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "Context\n\n\n\n\nSection 5.2 of the 2016 paper \"Why Should I Trust You?\": Explaining the Predictions of Any Classifier (https://dl.acm.org/doi/10.1145/2939672.2939778) tests the Recall of different XAI methods comparing them to interpretable methods.\n\n\n\n\nMy question is about interpreting this section, and the role played by K-LASSO.\n\n\n\n\nIt seems that the rationale here is to see whether the explanation models recover the same input features than the original, since in this case the original model is interpretable (also its input, a bag of words).\n\n\n\n\nSelecting Features\n\n\n\n\nSo the aim is to test whether LIME selects the same features of all available ones as compared to the original model.\n\n\n\n\nI think the selection of features (through K-LASSO) is an important yet under-explained part of the paper.\n\n\n\n\nThe algorithm that applies here, for their model, is LIME (not SP-LIME), which uses K-LASSO to select $K$ features:\n\n\n\n\n\n\n\n(...) selecting $K$ features with Lasso (using the regularization path [9]) and then learning the weights via least squares (a procedure we call K-LASSO in Algorithm 1).\n\n\n\n\n\n\n\nFrom talking to a chatbot, my intuition is that $K$-LASSO usually yields a sparse model, given that some coefficients will be 0, and those features will be the ones we retain or discard from all the ones available.\n\n\n\n\nI am aware I could read LASSO in detail but my bandwidth right now is just about enough for LIME/SP-LIME, so I am using my knowledge of Least-Squares to get an intuition of what is happening.\n\n\n\n\nQuestions\n\n\n\n\n\nIs the overall idea is correct, or what corrections you'd make?\n\n\n\n\nIn the paper LIME shows a loss $\\xi (x) = \\mathrm{argmin_g} L (f,g,\\pi_x (z)) + \\Omega(g)$, and I am assuming LASSO can be performed with such loss as well, otherwise there are two optimisations and the pieces don't fit well in my head.\n\n\n\n\n\nFor completeness, the paper uses $g$ explanation model, $f$ original model, $\\pi_x (z)$ is used as a distance-weight multiplying the loss-L-component $L = \\sum_{z,z'} \\pi_x (f(z)-g(z'))^2$ and $\\Omega$ a model-complexity measure.\n\n\n\n\nComment\n\n\n\n\nThe chatbot says LASSO is done to select features (0 coefficients are features we then discard), but the coeffients arent the best to fit the original model (since there is the extra penalty in the Loss).\n\n\n\n\nSo then Least Squares to re-fit or just fit the coefficients. I'd appreciate corrections if this is wrong, but it does make sense to me", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "kindleman", "profile_url": "https://stats.stackexchange.com/users/510622/kindleman", "user_type": "registered"}, "created_at": "2026-09-01T13:58:20+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "1ECA98F4-6DB3-4398-B85E-C435796E45DF", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/1ECA98F4-6DB3-4398-B85E-C435796E45DF/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-09-01T14:21:40+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "AAF72B85-DA54-49C6-8BEA-FF155201085C", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/AAF72B85-DA54-49C6-8BEA-FF155201085C/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "kindleman", "profile_url": "https://stats.stackexchange.com/users/510622/kindleman", "user_type": "registered"}, "created_at": "2026-09-01T15:22:05+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "588BA2AD-F204-4473-8EB5-7D8AC4DB30CD", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/588BA2AD-F204-4473-8EB5-7D8AC4DB30CD/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-09-02T02:40:31+00:00", "raw_file": "raw/codex_api_v1/84bb317e707465a80f008019404ef1f770e152d74ef692d3b81c48903ec855cc_1790825232001984700_0.json", "raw_sha256": "75778d86d5325e15f4b491a748dc70ae6ac6ee98840d584e01ed28416cb71fbe", "revision_guid": "FD4B782E-B4DA-469C-805C-494937FC4942", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/FD4B782E-B4DA-469C-805C-494937FC4942/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/677035/k-lasso-and-recall-in-lime-simulated-experiments", "split": "test", "split_group": "9f7b02658ea7a661e8290f49805b5687b2ff03f604d83ced4faa2c5d53587ee2", "tags": ["linear-model", "lasso", "lime", "explainable-ai"], "thread_id": "stats:677035", "title": "K-LASSO and Recall in LIME (simulated experiments)"}} {"citation_context": "et a pooled variance estimate, which you use for all the time points.* In R, packages like emmeans (https://cran.r-project.org/package=emmeans) can help with that.\n\n\n\n\nThat said, I've seen lots of plots with separate analyses for each time po", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://cran.r-project.org/package=emmeans", "kind": "external_url", "post_id": 677084, "post_url": "https://stats.stackexchange.com/a/677084", "product": "citations", "record_id": "Scientific-Citation-Graph:3ab99dc3a29892fc3090329c", "split": "test", "thread": {"accepted_answer_id": 677084, "answers": [{"answer_html": "

The 2019 Technical Perspective by Daniel, Thomas and Katherine Pollard, "Empowering statistical methods for cellular and molecular biologists" Molecular Biology of the Cell 30: 1359-1368 is a good practical introduction to study design and statistical analysis for studies like yours. I have quibbles with some details of their recommendations, but you should find it very helpful particularly as you design and analyze future experiments.

\n

Subject-matter preliminaries

\n

Subject-matter knowledge is important before you design or analyze experiments. You don't say much about the biological hypothesis per se, but I've run enough Western blots at least to know that quantifying them isn't trivial. The issues are covered, for example, by Pillai-Kastoori et al., "A systematic approach to quantitative Western blot analysis," Analytical Biochemistry 593: article 1136082020 (2020).

\n

This answer points out that differences between gels and blots sometimes overwhelm the differences due to treatments. Your results will be most believable if you run samples that you want to compare on the same gel and blot, even if your quantitation is OK. Current best practice expects you to provide annotated images of the entire blots anyway, at least in supplemental data.

\n

Technical versus biological replicates

\n

With all cells obtained from only 1 organ, the best you can do is test whether the protein level was associated with the treatment for the 1 organ you dissociated. The 3 samples at each combination of time and treatment are technical replicates. Differences among the 3 samples at any such combination represent technical differences in culturing the cells, extracting proteins, running the gels, exposing the Western blots, quantifying the bands, and (perhaps) normalizing against a "housekeeping" protein not expected to be affected by treatment.

\n

You need to have multiple biological replicates to support any more general hypothesis about the results. In your situation, that would at least involve organs from multiple animals from different litters, possibly of different sexes, maybe also of different ages or even different species, depending on how general you want the results to be. The Technical Perspective by the Pollards explains the difference between technical and biological replicates.

\n

Statistical analysis

\n

Although you can only examine differences for this 1 organ, the following general principles also apply to experiments with biological replicates.

\n

You have a continuous outcome (protein level via Western blot) with treatment/control and time-point (4 values) as factors. Following Figure 2 of the Technical Report by the Pollards, you could do ANOVA (analysis of variance) or a linear regression model. (ANOVA is simply a specific form of a linear regression model, so that distinction isn't very important.)

\n

If "the effect of treatment on protein levels changes with incubation time," there isn't a single "effect of treatment on protein levels (regardless of time)" or a single "effect of time on protein levels (regardless of treatment)." A 2-way ANOVA, with treatment/control in one direction and time-point in the other direction, can test whether "the effect of treatment on protein levels changes with incubation time." If it doesn't, then you can estimate the "effect of treatment on protein levels (regardless of time)" and the "effect of time on protein levels (regardless of treatment)." If it does, you can use associated "post-hoc" tests to evaluate the difference between any treatment/time-point combinations.

\n

In response to comment

\n

With treatment/control and 4 time points, you presumably have 3 interaction coefficients. When you say "2 Way ANOVA resulted in (mostly) not significant results for treatment * time interactions," I suspect that means you only found one of those coefficients to be "statistically significantly" different from 0. What that means depends on how the software codes the predictors, which can vary among software implementations and how you call their functios. You can get an overall estimate of the interaction by comparing models with and without the interaction term, for example via a likelihood-ratio test. Some implementations of 2-way ANOVA will do that automatically.

\n

For t-tests between treatment and control at each time point, it's best to start with a 2-way ANOVA. A t-test is based on the estimate of the variance of observed values around the model's predictions. If you perform a t-test at each time point, ignoring all the other time points, each test only uses the number of observations at that time point. You thus get imprecise variance estimates that can differ substantially among time points. A 2-way ANOVA instead uses all the observations/predictions to get a pooled variance estimate, which you use for all the time points.* In R, packages like emmeans can help with that.

\n

That said, I've seen lots of plots with separate analyses for each time point. In cell biology, you typically need visually compelling differences to convince your audience. If the differences are very visually compelling, they are likely to be "statistically significant" even if the statistical tests aren't optimal.

\n

You also should be aware of the multiple comparisons problem. The more tests you run, the more likely you are to find a "significant" result just by chance. There are two things you can control to minimize that problem: the "family-wise error rate" (FWER), the probability that none of the comparisons is falsely positive, or the "false-discovery rate" (FDR), the fraction of apparent positive results likely to be false positives. In large-scale experiments in genomics and proteomics, FDR control is the usual choice.

\n
\n

*Using pooled variance estimates becomes very important in large-scale experiments like gene-expression studies on 20,000 or so genes, in which single-gene variance estimates can vary widely. The Bioconductor limma package uses an "empirical Bayes" variance estimate for each gene, which starts with individual variance estimates but then "squeezes" the estimates toward a common value. The package's author outlines that method here, with references.

\n", "answer_id": 677084, "answer_text": "The 2019 Technical Perspective by Daniel, Thomas and Katherine Pollard, \"Empowering statistical methods for cellular and molecular biologists (https://doi.org/10.1091/mbc.E15-02-0076)\" Molecular Biology of the Cell 30: 1359-1368 is a good practical introduction to study design and statistical analysis for studies like yours. I have quibbles with some details of their recommendations, but you should find it very helpful particularly as you design and analyze future experiments.\n\n\n\n\nSubject-matter preliminaries\n\n\n\n\nSubject-matter knowledge is important before you design or analyze experiments. You don't say much about the biological hypothesis per se, but I've run enough Western blots at least to know that quantifying them isn't trivial. The issues are covered, for example, by Pillai-Kastoori et al., \"A systematic approach to quantitative Western blot analysis (https://doi.org/10.1016/j.ab.2020.113608),\" Analytical Biochemistry 593: article 1136082020 (2020).\n\n\n\n\nThis answer (https://stats.stackexchange.com/a/518168/28500) points out that differences between gels and blots sometimes overwhelm the differences due to treatments. Your results will be most believable if you run samples that you want to compare on the same gel and blot, even if your quantitation is OK. Current best practice expects you to provide annotated images of the entire blots anyway, at least in supplemental data.\n\n\n\n\nTechnical versus biological replicates\n\n\n\n\nWith all cells obtained from only 1 organ, the best you can do is test whether the protein level was associated with the treatment for the 1 organ you dissociated. The 3 samples at each combination of time and treatment are technical replicates. Differences among the 3 samples at any such combination represent technical differences in culturing the cells, extracting proteins, running the gels, exposing the Western blots, quantifying the bands, and (perhaps) normalizing against a \"housekeeping\" protein not expected to be affected by treatment.\n\n\n\n\nYou need to have multiple biological replicates to support any more general hypothesis about the results. In your situation, that would at least involve organs from multiple animals from different litters, possibly of different sexes, maybe also of different ages or even different species, depending on how general you want the results to be. The Technical Perspective by the Pollards explains the difference between technical and biological replicates.\n\n\n\n\nStatistical analysis\n\n\n\n\nAlthough you can only examine differences for this 1 organ, the following general principles also apply to experiments with biological replicates.\n\n\n\n\nYou have a continuous outcome (protein level via Western blot) with treatment/control and time-point (4 values) as factors. Following Figure 2 of the Technical Report by the Pollards, you could do ANOVA (analysis of variance) or a linear regression model. (ANOVA is simply a specific form of a linear regression model, so that distinction isn't very important.)\n\n\n\n\nIf \"the effect of treatment on protein levels changes with incubation time,\" there isn't a single \"effect of treatment on protein levels (regardless of time)\" or a single \"effect of time on protein levels (regardless of treatment).\" A 2-way ANOVA, with treatment/control in one direction and time-point in the other direction, can test whether \"the effect of treatment on protein levels changes with incubation time.\" If it doesn't, then you can estimate the \"effect of treatment on protein levels (regardless of time)\" and the \"effect of time on protein levels (regardless of treatment).\" If it does, you can use associated \"post-hoc\" tests to evaluate the difference between any treatment/time-point combinations.\n\n\n\n\nIn response to comment\n\n\n\n\nWith treatment/control and 4 time points, you presumably have 3 interaction coefficients. When you say \"2 Way ANOVA resulted in (mostly) not significant results for treatment * time interactions,\" I suspect that means you only found one of those coefficients to be \"statistically significantly\" different from 0. What that means depends on how the software codes the predictors, which can vary among software implementations and how you call their functios. You can get an overall estimate of the interaction by comparing models with and without the interaction term, for example via a likelihood-ratio test (https://en.wikipedia.org/wiki/Likelihood-ratio_test). Some implementations of 2-way ANOVA will do that automatically.\n\n\n\n\nFor t-tests between treatment and control at each time point, it's best to start with a 2-way ANOVA. A t-test is based on the estimate of the variance of observed values around the model's predictions. If you perform a t-test at each time point, ignoring all the other time points, each test only uses the number of observations at that time point. You thus get imprecise variance estimates that can differ substantially among time points. A 2-way ANOVA instead uses all the observations/predictions to get a pooled variance estimate, which you use for all the time points.* In R, packages like emmeans (https://cran.r-project.org/package=emmeans) can help with that.\n\n\n\n\nThat said, I've seen lots of plots with separate analyses for each time point. In cell biology, you typically need visually compelling differences to convince your audience. If the differences are very visually compelling, they are likely to be \"statistically significant\" even if the statistical tests aren't optimal.\n\n\n\n\nYou also should be aware of the multiple comparisons problem (https://en.wikipedia.org/wiki/Multiple_comparisons_problem). The more tests you run, the more likely you are to find a \"significant\" result just by chance. There are two things you can control to minimize that problem: the \"family-wise error rate\" (FWER), the probability that none of the comparisons is falsely positive, or the \"false-discovery rate\" (FDR), the fraction of apparent positive results likely to be false positives. In large-scale experiments in genomics and proteomics, FDR control is the usual choice.\n\n\n\n\n\n\n\n*Using pooled variance estimates becomes very important in large-scale experiments like gene-expression studies on 20,000 or so genes, in which single-gene variance estimates can vary widely. The Bioconductor limma package (https://doi.org/doi:10.18129/B9.bioc.limma) uses an \"empirical Bayes\" variance estimate for each gene, which starts with individual variance estimates but then \"squeezes\" the estimates toward a common value. The package's author outlines that method here (https://stats.stackexchange.com/a/670944/28500), with references.", "answer_url": "https://stats.stackexchange.com/a/677084", "author": "EdM", "author_url": "https://stats.stackexchange.com/users/28500/edm", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-05T21:54:12+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677078, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-09-05T21:54:12+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "2464CE21-544C-49EC-A65A-6F86849F9B4D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/2464CE21-544C-49EC-A65A-6F86849F9B4D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-09-07T16:19:27+00:00", "raw_file": "raw/codex_api_v1/3f959895a29b33d83894e5370d82e1c0cf87f20ac57fa423ebc923738357c657_1790825253957066500_0.json", "raw_sha256": "ddd8808039e410ca99f97e2a7f12c307f046c4e5c3e184683bc12f816e6f49fc", "revision_guid": "B613000D-ABDF-47BA-BDB2-301FB5C608F6", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/B613000D-ABDF-47BA-BDB2-301FB5C608F6/view-source"}], "score": 6, "updated_at": "2026-09-07T16:19:27+00:00"}], "domain": "statistics", "external_links": ["https://cran.r-project.org/package=emmeans", "https://doi.org/10.1016/j.ab.2020.113608", "https://doi.org/10.1091/mbc.E15-02-0076", "https://doi.org/doi:10.18129/B9.bioc.limma", "https://en.wikipedia.org/wiki/Likelihood-ratio_test", "https://en.wikipedia.org/wiki/Multiple_comparisons_problem"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "user503965", "question_author_url": "https://stats.stackexchange.com/users/516304/user503965", "question_author_user_type": "registered", "question_created_at": "2026-09-05T09:13:22+00:00", "question_html": "

A few FYI to start:

\n\n

I had cells extracted from an organ (1 organ). Cells were separated into different wells and plates. My end goal is to check for changes in protein "X" levels using western blot.\nTwo factors are included: Control vs Treatment and Incubation Time (how long cells have been incubated with or without the treatment).

\n

Wells were divided as so:\n30 minutes incubation: 3 controls + 3 medications.\n1 hour: 3 controls + 3 medications.\n2 hours: 3 + 3\n3 hours: 3 + 3.

\n

All samples originate from the same organ lysate (organ was lysed and cells collected -> samples from lysate tube were plated in different wells) 6 wells (3 control + 3 treatment) were the "30m" group, 6 were "1hour" group, and so on...

\n

I could extrapolate several points of data: 1) effects of treatment on protein levels (regardless of time); 2) effects of time on protein levels (Regardless of treatment) and 3) Does the effect of treatment on protein levels changes with incubation time?

\n

Would really appreciate some recommendations for tests (+some theory about the test you think would fit best).

\n", "question_id": 677078, "question_license": "CC BY-SA 4.0", "question_score": 5, "question_text": "A few FYI to start:\n\n\n\n\n\nI am doing a research project to finish my bachelors in life sciences.\n\n\n\n\nI studied Probability for scientists (intro level).\n\n\n\n\nI didn't study statistical inference. Instead I chose Calculus 1.\nI need to statistically analyze my results but I don't know how. I also have no time to read full introductions to statistical analysis.\n\n\n\n\n\nI had cells extracted from an organ (1 organ). Cells were separated into different wells and plates. My end goal is to check for changes in protein \"X\" levels using western blot.\nTwo factors are included: Control vs Treatment and Incubation Time (how long cells have been incubated with or without the treatment).\n\n\n\n\nWells were divided as so:\n30 minutes incubation: 3 controls + 3 medications.\n1 hour: 3 controls + 3 medications.\n2 hours: 3 + 3\n3 hours: 3 + 3.\n\n\n\n\nAll samples originate from the same organ lysate (organ was lysed and cells collected -> samples from lysate tube were plated in different wells) 6 wells (3 control + 3 treatment) were the \"30m\" group, 6 were \"1hour\" group, and so on...\n\n\n\n\nI could extrapolate several points of data: 1) effects of treatment on protein levels (regardless of time); 2) effects of time on protein levels (Regardless of treatment) and 3) Does the effect of treatment on protein levels changes with incubation time?\n\n\n\n\nWould really appreciate some recommendations for tests (+some theory about the test you think would fit best).", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "user503965", "profile_url": "https://stats.stackexchange.com/users/516304/user503965", "user_type": "registered"}, "created_at": "2026-09-05T09:13:22+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "28593582-B344-42B2-A1B1-A0C00CBD588F", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/28593582-B344-42B2-A1B1-A0C00CBD588F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "user503965", "profile_url": "https://stats.stackexchange.com/users/516304/user503965", "user_type": "registered"}, "created_at": "2026-09-05T09:19:27+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "691E0983-9880-4E86-92A1-95DEDF3C24AB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/691E0983-9880-4E86-92A1-95DEDF3C24AB/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Rick Hass", "profile_url": "https://stats.stackexchange.com/users/97844/rick-hass", "user_type": "registered"}, "created_at": "2026-09-05T17:00:39+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "BC5FAF19-81E4-4449-9AB1-A58BE937A472", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/BC5FAF19-81E4-4449-9AB1-A58BE937A472/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-09-05T23:14:16+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "4D24D3DB-1EB5-48B8-8CFC-DD98AA684452", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/4D24D3DB-1EB5-48B8-8CFC-DD98AA684452/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/677078/time-course-experiment-which-statistical-analysis-fits-best", "split": "test", "split_group": "cbb822688bb3d1bc11e31ae26d9e8a7ea2167dad6d35dc44f96db014cfd3c90f", "tags": ["inference", "experiment-design"], "thread_id": "stats:677078", "title": "Time course experiment - which statistical analysis fits best?"}} {"citation_context": "r example, by Pillai-Kastoori et al., \"A systematic approach to quantitative Western blot analysis (https://doi.org/10.1016/j.ab.2020.113608),\" Analytical Biochemistry 593: article 1136082020 (2020).\n\n\n\n\nThis answer (https://stats.stackexch", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": "10.1016/j.ab.2020.113608", "external_url": "https://doi.org/10.1016/j.ab.2020.113608", "kind": "doi_url", "post_id": 677084, "post_url": "https://stats.stackexchange.com/a/677084", "product": "citations", "record_id": "Scientific-Citation-Graph:e709a6533c59e092e64b3b8f", "split": "test", "thread": {"accepted_answer_id": 677084, "answers": [{"answer_html": "

The 2019 Technical Perspective by Daniel, Thomas and Katherine Pollard, "Empowering statistical methods for cellular and molecular biologists" Molecular Biology of the Cell 30: 1359-1368 is a good practical introduction to study design and statistical analysis for studies like yours. I have quibbles with some details of their recommendations, but you should find it very helpful particularly as you design and analyze future experiments.

\n

Subject-matter preliminaries

\n

Subject-matter knowledge is important before you design or analyze experiments. You don't say much about the biological hypothesis per se, but I've run enough Western blots at least to know that quantifying them isn't trivial. The issues are covered, for example, by Pillai-Kastoori et al., "A systematic approach to quantitative Western blot analysis," Analytical Biochemistry 593: article 1136082020 (2020).

\n

This answer points out that differences between gels and blots sometimes overwhelm the differences due to treatments. Your results will be most believable if you run samples that you want to compare on the same gel and blot, even if your quantitation is OK. Current best practice expects you to provide annotated images of the entire blots anyway, at least in supplemental data.

\n

Technical versus biological replicates

\n

With all cells obtained from only 1 organ, the best you can do is test whether the protein level was associated with the treatment for the 1 organ you dissociated. The 3 samples at each combination of time and treatment are technical replicates. Differences among the 3 samples at any such combination represent technical differences in culturing the cells, extracting proteins, running the gels, exposing the Western blots, quantifying the bands, and (perhaps) normalizing against a "housekeeping" protein not expected to be affected by treatment.

\n

You need to have multiple biological replicates to support any more general hypothesis about the results. In your situation, that would at least involve organs from multiple animals from different litters, possibly of different sexes, maybe also of different ages or even different species, depending on how general you want the results to be. The Technical Perspective by the Pollards explains the difference between technical and biological replicates.

\n

Statistical analysis

\n

Although you can only examine differences for this 1 organ, the following general principles also apply to experiments with biological replicates.

\n

You have a continuous outcome (protein level via Western blot) with treatment/control and time-point (4 values) as factors. Following Figure 2 of the Technical Report by the Pollards, you could do ANOVA (analysis of variance) or a linear regression model. (ANOVA is simply a specific form of a linear regression model, so that distinction isn't very important.)

\n

If "the effect of treatment on protein levels changes with incubation time," there isn't a single "effect of treatment on protein levels (regardless of time)" or a single "effect of time on protein levels (regardless of treatment)." A 2-way ANOVA, with treatment/control in one direction and time-point in the other direction, can test whether "the effect of treatment on protein levels changes with incubation time." If it doesn't, then you can estimate the "effect of treatment on protein levels (regardless of time)" and the "effect of time on protein levels (regardless of treatment)." If it does, you can use associated "post-hoc" tests to evaluate the difference between any treatment/time-point combinations.

\n

In response to comment

\n

With treatment/control and 4 time points, you presumably have 3 interaction coefficients. When you say "2 Way ANOVA resulted in (mostly) not significant results for treatment * time interactions," I suspect that means you only found one of those coefficients to be "statistically significantly" different from 0. What that means depends on how the software codes the predictors, which can vary among software implementations and how you call their functios. You can get an overall estimate of the interaction by comparing models with and without the interaction term, for example via a likelihood-ratio test. Some implementations of 2-way ANOVA will do that automatically.

\n

For t-tests between treatment and control at each time point, it's best to start with a 2-way ANOVA. A t-test is based on the estimate of the variance of observed values around the model's predictions. If you perform a t-test at each time point, ignoring all the other time points, each test only uses the number of observations at that time point. You thus get imprecise variance estimates that can differ substantially among time points. A 2-way ANOVA instead uses all the observations/predictions to get a pooled variance estimate, which you use for all the time points.* In R, packages like emmeans can help with that.

\n

That said, I've seen lots of plots with separate analyses for each time point. In cell biology, you typically need visually compelling differences to convince your audience. If the differences are very visually compelling, they are likely to be "statistically significant" even if the statistical tests aren't optimal.

\n

You also should be aware of the multiple comparisons problem. The more tests you run, the more likely you are to find a "significant" result just by chance. There are two things you can control to minimize that problem: the "family-wise error rate" (FWER), the probability that none of the comparisons is falsely positive, or the "false-discovery rate" (FDR), the fraction of apparent positive results likely to be false positives. In large-scale experiments in genomics and proteomics, FDR control is the usual choice.

\n
\n

*Using pooled variance estimates becomes very important in large-scale experiments like gene-expression studies on 20,000 or so genes, in which single-gene variance estimates can vary widely. The Bioconductor limma package uses an "empirical Bayes" variance estimate for each gene, which starts with individual variance estimates but then "squeezes" the estimates toward a common value. The package's author outlines that method here, with references.

\n", "answer_id": 677084, "answer_text": "The 2019 Technical Perspective by Daniel, Thomas and Katherine Pollard, \"Empowering statistical methods for cellular and molecular biologists (https://doi.org/10.1091/mbc.E15-02-0076)\" Molecular Biology of the Cell 30: 1359-1368 is a good practical introduction to study design and statistical analysis for studies like yours. I have quibbles with some details of their recommendations, but you should find it very helpful particularly as you design and analyze future experiments.\n\n\n\n\nSubject-matter preliminaries\n\n\n\n\nSubject-matter knowledge is important before you design or analyze experiments. You don't say much about the biological hypothesis per se, but I've run enough Western blots at least to know that quantifying them isn't trivial. The issues are covered, for example, by Pillai-Kastoori et al., \"A systematic approach to quantitative Western blot analysis (https://doi.org/10.1016/j.ab.2020.113608),\" Analytical Biochemistry 593: article 1136082020 (2020).\n\n\n\n\nThis answer (https://stats.stackexchange.com/a/518168/28500) points out that differences between gels and blots sometimes overwhelm the differences due to treatments. Your results will be most believable if you run samples that you want to compare on the same gel and blot, even if your quantitation is OK. Current best practice expects you to provide annotated images of the entire blots anyway, at least in supplemental data.\n\n\n\n\nTechnical versus biological replicates\n\n\n\n\nWith all cells obtained from only 1 organ, the best you can do is test whether the protein level was associated with the treatment for the 1 organ you dissociated. The 3 samples at each combination of time and treatment are technical replicates. Differences among the 3 samples at any such combination represent technical differences in culturing the cells, extracting proteins, running the gels, exposing the Western blots, quantifying the bands, and (perhaps) normalizing against a \"housekeeping\" protein not expected to be affected by treatment.\n\n\n\n\nYou need to have multiple biological replicates to support any more general hypothesis about the results. In your situation, that would at least involve organs from multiple animals from different litters, possibly of different sexes, maybe also of different ages or even different species, depending on how general you want the results to be. The Technical Perspective by the Pollards explains the difference between technical and biological replicates.\n\n\n\n\nStatistical analysis\n\n\n\n\nAlthough you can only examine differences for this 1 organ, the following general principles also apply to experiments with biological replicates.\n\n\n\n\nYou have a continuous outcome (protein level via Western blot) with treatment/control and time-point (4 values) as factors. Following Figure 2 of the Technical Report by the Pollards, you could do ANOVA (analysis of variance) or a linear regression model. (ANOVA is simply a specific form of a linear regression model, so that distinction isn't very important.)\n\n\n\n\nIf \"the effect of treatment on protein levels changes with incubation time,\" there isn't a single \"effect of treatment on protein levels (regardless of time)\" or a single \"effect of time on protein levels (regardless of treatment).\" A 2-way ANOVA, with treatment/control in one direction and time-point in the other direction, can test whether \"the effect of treatment on protein levels changes with incubation time.\" If it doesn't, then you can estimate the \"effect of treatment on protein levels (regardless of time)\" and the \"effect of time on protein levels (regardless of treatment).\" If it does, you can use associated \"post-hoc\" tests to evaluate the difference between any treatment/time-point combinations.\n\n\n\n\nIn response to comment\n\n\n\n\nWith treatment/control and 4 time points, you presumably have 3 interaction coefficients. When you say \"2 Way ANOVA resulted in (mostly) not significant results for treatment * time interactions,\" I suspect that means you only found one of those coefficients to be \"statistically significantly\" different from 0. What that means depends on how the software codes the predictors, which can vary among software implementations and how you call their functios. You can get an overall estimate of the interaction by comparing models with and without the interaction term, for example via a likelihood-ratio test (https://en.wikipedia.org/wiki/Likelihood-ratio_test). Some implementations of 2-way ANOVA will do that automatically.\n\n\n\n\nFor t-tests between treatment and control at each time point, it's best to start with a 2-way ANOVA. A t-test is based on the estimate of the variance of observed values around the model's predictions. If you perform a t-test at each time point, ignoring all the other time points, each test only uses the number of observations at that time point. You thus get imprecise variance estimates that can differ substantially among time points. A 2-way ANOVA instead uses all the observations/predictions to get a pooled variance estimate, which you use for all the time points.* In R, packages like emmeans (https://cran.r-project.org/package=emmeans) can help with that.\n\n\n\n\nThat said, I've seen lots of plots with separate analyses for each time point. In cell biology, you typically need visually compelling differences to convince your audience. If the differences are very visually compelling, they are likely to be \"statistically significant\" even if the statistical tests aren't optimal.\n\n\n\n\nYou also should be aware of the multiple comparisons problem (https://en.wikipedia.org/wiki/Multiple_comparisons_problem). The more tests you run, the more likely you are to find a \"significant\" result just by chance. There are two things you can control to minimize that problem: the \"family-wise error rate\" (FWER), the probability that none of the comparisons is falsely positive, or the \"false-discovery rate\" (FDR), the fraction of apparent positive results likely to be false positives. In large-scale experiments in genomics and proteomics, FDR control is the usual choice.\n\n\n\n\n\n\n\n*Using pooled variance estimates becomes very important in large-scale experiments like gene-expression studies on 20,000 or so genes, in which single-gene variance estimates can vary widely. The Bioconductor limma package (https://doi.org/doi:10.18129/B9.bioc.limma) uses an \"empirical Bayes\" variance estimate for each gene, which starts with individual variance estimates but then \"squeezes\" the estimates toward a common value. The package's author outlines that method here (https://stats.stackexchange.com/a/670944/28500), with references.", "answer_url": "https://stats.stackexchange.com/a/677084", "author": "EdM", "author_url": "https://stats.stackexchange.com/users/28500/edm", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-05T21:54:12+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677078, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-09-05T21:54:12+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "2464CE21-544C-49EC-A65A-6F86849F9B4D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/2464CE21-544C-49EC-A65A-6F86849F9B4D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-09-07T16:19:27+00:00", "raw_file": "raw/codex_api_v1/3f959895a29b33d83894e5370d82e1c0cf87f20ac57fa423ebc923738357c657_1790825253957066500_0.json", "raw_sha256": "ddd8808039e410ca99f97e2a7f12c307f046c4e5c3e184683bc12f816e6f49fc", "revision_guid": "B613000D-ABDF-47BA-BDB2-301FB5C608F6", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/B613000D-ABDF-47BA-BDB2-301FB5C608F6/view-source"}], "score": 6, "updated_at": "2026-09-07T16:19:27+00:00"}], "domain": "statistics", "external_links": ["https://cran.r-project.org/package=emmeans", "https://doi.org/10.1016/j.ab.2020.113608", "https://doi.org/10.1091/mbc.E15-02-0076", "https://doi.org/doi:10.18129/B9.bioc.limma", "https://en.wikipedia.org/wiki/Likelihood-ratio_test", "https://en.wikipedia.org/wiki/Multiple_comparisons_problem"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "user503965", "question_author_url": "https://stats.stackexchange.com/users/516304/user503965", "question_author_user_type": "registered", "question_created_at": "2026-09-05T09:13:22+00:00", "question_html": "

A few FYI to start:

\n\n

I had cells extracted from an organ (1 organ). Cells were separated into different wells and plates. My end goal is to check for changes in protein "X" levels using western blot.\nTwo factors are included: Control vs Treatment and Incubation Time (how long cells have been incubated with or without the treatment).

\n

Wells were divided as so:\n30 minutes incubation: 3 controls + 3 medications.\n1 hour: 3 controls + 3 medications.\n2 hours: 3 + 3\n3 hours: 3 + 3.

\n

All samples originate from the same organ lysate (organ was lysed and cells collected -> samples from lysate tube were plated in different wells) 6 wells (3 control + 3 treatment) were the "30m" group, 6 were "1hour" group, and so on...

\n

I could extrapolate several points of data: 1) effects of treatment on protein levels (regardless of time); 2) effects of time on protein levels (Regardless of treatment) and 3) Does the effect of treatment on protein levels changes with incubation time?

\n

Would really appreciate some recommendations for tests (+some theory about the test you think would fit best).

\n", "question_id": 677078, "question_license": "CC BY-SA 4.0", "question_score": 5, "question_text": "A few FYI to start:\n\n\n\n\n\nI am doing a research project to finish my bachelors in life sciences.\n\n\n\n\nI studied Probability for scientists (intro level).\n\n\n\n\nI didn't study statistical inference. Instead I chose Calculus 1.\nI need to statistically analyze my results but I don't know how. I also have no time to read full introductions to statistical analysis.\n\n\n\n\n\nI had cells extracted from an organ (1 organ). Cells were separated into different wells and plates. My end goal is to check for changes in protein \"X\" levels using western blot.\nTwo factors are included: Control vs Treatment and Incubation Time (how long cells have been incubated with or without the treatment).\n\n\n\n\nWells were divided as so:\n30 minutes incubation: 3 controls + 3 medications.\n1 hour: 3 controls + 3 medications.\n2 hours: 3 + 3\n3 hours: 3 + 3.\n\n\n\n\nAll samples originate from the same organ lysate (organ was lysed and cells collected -> samples from lysate tube were plated in different wells) 6 wells (3 control + 3 treatment) were the \"30m\" group, 6 were \"1hour\" group, and so on...\n\n\n\n\nI could extrapolate several points of data: 1) effects of treatment on protein levels (regardless of time); 2) effects of time on protein levels (Regardless of treatment) and 3) Does the effect of treatment on protein levels changes with incubation time?\n\n\n\n\nWould really appreciate some recommendations for tests (+some theory about the test you think would fit best).", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "user503965", "profile_url": "https://stats.stackexchange.com/users/516304/user503965", "user_type": "registered"}, "created_at": "2026-09-05T09:13:22+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "28593582-B344-42B2-A1B1-A0C00CBD588F", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/28593582-B344-42B2-A1B1-A0C00CBD588F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "user503965", "profile_url": "https://stats.stackexchange.com/users/516304/user503965", "user_type": "registered"}, "created_at": "2026-09-05T09:19:27+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "691E0983-9880-4E86-92A1-95DEDF3C24AB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/691E0983-9880-4E86-92A1-95DEDF3C24AB/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Rick Hass", "profile_url": "https://stats.stackexchange.com/users/97844/rick-hass", "user_type": "registered"}, "created_at": "2026-09-05T17:00:39+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "BC5FAF19-81E4-4449-9AB1-A58BE937A472", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/BC5FAF19-81E4-4449-9AB1-A58BE937A472/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-09-05T23:14:16+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "4D24D3DB-1EB5-48B8-8CFC-DD98AA684452", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/4D24D3DB-1EB5-48B8-8CFC-DD98AA684452/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/677078/time-course-experiment-which-statistical-analysis-fits-best", "split": "test", "split_group": "cbb822688bb3d1bc11e31ae26d9e8a7ea2167dad6d35dc44f96db014cfd3c90f", "tags": ["inference", "experiment-design"], "thread_id": "stats:677078", "title": "Time course experiment - which statistical analysis fits best?"}} {"citation_context": "homas and Katherine Pollard, \"Empowering statistical methods for cellular and molecular biologists (https://doi.org/10.1091/mbc.E15-02-0076)\" Molecular Biology of the Cell 30: 1359-1368 is a good practical introduction to study design and ", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": "10.1091/mbc.E15-02-0076", "external_url": "https://doi.org/10.1091/mbc.E15-02-0076", "kind": "doi_url", "post_id": 677084, "post_url": "https://stats.stackexchange.com/a/677084", "product": "citations", "record_id": "Scientific-Citation-Graph:7bef289f2d10ff48d206e123", "split": "test", "thread": {"accepted_answer_id": 677084, "answers": [{"answer_html": "

The 2019 Technical Perspective by Daniel, Thomas and Katherine Pollard, "Empowering statistical methods for cellular and molecular biologists" Molecular Biology of the Cell 30: 1359-1368 is a good practical introduction to study design and statistical analysis for studies like yours. I have quibbles with some details of their recommendations, but you should find it very helpful particularly as you design and analyze future experiments.

\n

Subject-matter preliminaries

\n

Subject-matter knowledge is important before you design or analyze experiments. You don't say much about the biological hypothesis per se, but I've run enough Western blots at least to know that quantifying them isn't trivial. The issues are covered, for example, by Pillai-Kastoori et al., "A systematic approach to quantitative Western blot analysis," Analytical Biochemistry 593: article 1136082020 (2020).

\n

This answer points out that differences between gels and blots sometimes overwhelm the differences due to treatments. Your results will be most believable if you run samples that you want to compare on the same gel and blot, even if your quantitation is OK. Current best practice expects you to provide annotated images of the entire blots anyway, at least in supplemental data.

\n

Technical versus biological replicates

\n

With all cells obtained from only 1 organ, the best you can do is test whether the protein level was associated with the treatment for the 1 organ you dissociated. The 3 samples at each combination of time and treatment are technical replicates. Differences among the 3 samples at any such combination represent technical differences in culturing the cells, extracting proteins, running the gels, exposing the Western blots, quantifying the bands, and (perhaps) normalizing against a "housekeeping" protein not expected to be affected by treatment.

\n

You need to have multiple biological replicates to support any more general hypothesis about the results. In your situation, that would at least involve organs from multiple animals from different litters, possibly of different sexes, maybe also of different ages or even different species, depending on how general you want the results to be. The Technical Perspective by the Pollards explains the difference between technical and biological replicates.

\n

Statistical analysis

\n

Although you can only examine differences for this 1 organ, the following general principles also apply to experiments with biological replicates.

\n

You have a continuous outcome (protein level via Western blot) with treatment/control and time-point (4 values) as factors. Following Figure 2 of the Technical Report by the Pollards, you could do ANOVA (analysis of variance) or a linear regression model. (ANOVA is simply a specific form of a linear regression model, so that distinction isn't very important.)

\n

If "the effect of treatment on protein levels changes with incubation time," there isn't a single "effect of treatment on protein levels (regardless of time)" or a single "effect of time on protein levels (regardless of treatment)." A 2-way ANOVA, with treatment/control in one direction and time-point in the other direction, can test whether "the effect of treatment on protein levels changes with incubation time." If it doesn't, then you can estimate the "effect of treatment on protein levels (regardless of time)" and the "effect of time on protein levels (regardless of treatment)." If it does, you can use associated "post-hoc" tests to evaluate the difference between any treatment/time-point combinations.

\n

In response to comment

\n

With treatment/control and 4 time points, you presumably have 3 interaction coefficients. When you say "2 Way ANOVA resulted in (mostly) not significant results for treatment * time interactions," I suspect that means you only found one of those coefficients to be "statistically significantly" different from 0. What that means depends on how the software codes the predictors, which can vary among software implementations and how you call their functios. You can get an overall estimate of the interaction by comparing models with and without the interaction term, for example via a likelihood-ratio test. Some implementations of 2-way ANOVA will do that automatically.

\n

For t-tests between treatment and control at each time point, it's best to start with a 2-way ANOVA. A t-test is based on the estimate of the variance of observed values around the model's predictions. If you perform a t-test at each time point, ignoring all the other time points, each test only uses the number of observations at that time point. You thus get imprecise variance estimates that can differ substantially among time points. A 2-way ANOVA instead uses all the observations/predictions to get a pooled variance estimate, which you use for all the time points.* In R, packages like emmeans can help with that.

\n

That said, I've seen lots of plots with separate analyses for each time point. In cell biology, you typically need visually compelling differences to convince your audience. If the differences are very visually compelling, they are likely to be "statistically significant" even if the statistical tests aren't optimal.

\n

You also should be aware of the multiple comparisons problem. The more tests you run, the more likely you are to find a "significant" result just by chance. There are two things you can control to minimize that problem: the "family-wise error rate" (FWER), the probability that none of the comparisons is falsely positive, or the "false-discovery rate" (FDR), the fraction of apparent positive results likely to be false positives. In large-scale experiments in genomics and proteomics, FDR control is the usual choice.

\n
\n

*Using pooled variance estimates becomes very important in large-scale experiments like gene-expression studies on 20,000 or so genes, in which single-gene variance estimates can vary widely. The Bioconductor limma package uses an "empirical Bayes" variance estimate for each gene, which starts with individual variance estimates but then "squeezes" the estimates toward a common value. The package's author outlines that method here, with references.

\n", "answer_id": 677084, "answer_text": "The 2019 Technical Perspective by Daniel, Thomas and Katherine Pollard, \"Empowering statistical methods for cellular and molecular biologists (https://doi.org/10.1091/mbc.E15-02-0076)\" Molecular Biology of the Cell 30: 1359-1368 is a good practical introduction to study design and statistical analysis for studies like yours. I have quibbles with some details of their recommendations, but you should find it very helpful particularly as you design and analyze future experiments.\n\n\n\n\nSubject-matter preliminaries\n\n\n\n\nSubject-matter knowledge is important before you design or analyze experiments. You don't say much about the biological hypothesis per se, but I've run enough Western blots at least to know that quantifying them isn't trivial. The issues are covered, for example, by Pillai-Kastoori et al., \"A systematic approach to quantitative Western blot analysis (https://doi.org/10.1016/j.ab.2020.113608),\" Analytical Biochemistry 593: article 1136082020 (2020).\n\n\n\n\nThis answer (https://stats.stackexchange.com/a/518168/28500) points out that differences between gels and blots sometimes overwhelm the differences due to treatments. Your results will be most believable if you run samples that you want to compare on the same gel and blot, even if your quantitation is OK. Current best practice expects you to provide annotated images of the entire blots anyway, at least in supplemental data.\n\n\n\n\nTechnical versus biological replicates\n\n\n\n\nWith all cells obtained from only 1 organ, the best you can do is test whether the protein level was associated with the treatment for the 1 organ you dissociated. The 3 samples at each combination of time and treatment are technical replicates. Differences among the 3 samples at any such combination represent technical differences in culturing the cells, extracting proteins, running the gels, exposing the Western blots, quantifying the bands, and (perhaps) normalizing against a \"housekeeping\" protein not expected to be affected by treatment.\n\n\n\n\nYou need to have multiple biological replicates to support any more general hypothesis about the results. In your situation, that would at least involve organs from multiple animals from different litters, possibly of different sexes, maybe also of different ages or even different species, depending on how general you want the results to be. The Technical Perspective by the Pollards explains the difference between technical and biological replicates.\n\n\n\n\nStatistical analysis\n\n\n\n\nAlthough you can only examine differences for this 1 organ, the following general principles also apply to experiments with biological replicates.\n\n\n\n\nYou have a continuous outcome (protein level via Western blot) with treatment/control and time-point (4 values) as factors. Following Figure 2 of the Technical Report by the Pollards, you could do ANOVA (analysis of variance) or a linear regression model. (ANOVA is simply a specific form of a linear regression model, so that distinction isn't very important.)\n\n\n\n\nIf \"the effect of treatment on protein levels changes with incubation time,\" there isn't a single \"effect of treatment on protein levels (regardless of time)\" or a single \"effect of time on protein levels (regardless of treatment).\" A 2-way ANOVA, with treatment/control in one direction and time-point in the other direction, can test whether \"the effect of treatment on protein levels changes with incubation time.\" If it doesn't, then you can estimate the \"effect of treatment on protein levels (regardless of time)\" and the \"effect of time on protein levels (regardless of treatment).\" If it does, you can use associated \"post-hoc\" tests to evaluate the difference between any treatment/time-point combinations.\n\n\n\n\nIn response to comment\n\n\n\n\nWith treatment/control and 4 time points, you presumably have 3 interaction coefficients. When you say \"2 Way ANOVA resulted in (mostly) not significant results for treatment * time interactions,\" I suspect that means you only found one of those coefficients to be \"statistically significantly\" different from 0. What that means depends on how the software codes the predictors, which can vary among software implementations and how you call their functios. You can get an overall estimate of the interaction by comparing models with and without the interaction term, for example via a likelihood-ratio test (https://en.wikipedia.org/wiki/Likelihood-ratio_test). Some implementations of 2-way ANOVA will do that automatically.\n\n\n\n\nFor t-tests between treatment and control at each time point, it's best to start with a 2-way ANOVA. A t-test is based on the estimate of the variance of observed values around the model's predictions. If you perform a t-test at each time point, ignoring all the other time points, each test only uses the number of observations at that time point. You thus get imprecise variance estimates that can differ substantially among time points. A 2-way ANOVA instead uses all the observations/predictions to get a pooled variance estimate, which you use for all the time points.* In R, packages like emmeans (https://cran.r-project.org/package=emmeans) can help with that.\n\n\n\n\nThat said, I've seen lots of plots with separate analyses for each time point. In cell biology, you typically need visually compelling differences to convince your audience. If the differences are very visually compelling, they are likely to be \"statistically significant\" even if the statistical tests aren't optimal.\n\n\n\n\nYou also should be aware of the multiple comparisons problem (https://en.wikipedia.org/wiki/Multiple_comparisons_problem). The more tests you run, the more likely you are to find a \"significant\" result just by chance. There are two things you can control to minimize that problem: the \"family-wise error rate\" (FWER), the probability that none of the comparisons is falsely positive, or the \"false-discovery rate\" (FDR), the fraction of apparent positive results likely to be false positives. In large-scale experiments in genomics and proteomics, FDR control is the usual choice.\n\n\n\n\n\n\n\n*Using pooled variance estimates becomes very important in large-scale experiments like gene-expression studies on 20,000 or so genes, in which single-gene variance estimates can vary widely. The Bioconductor limma package (https://doi.org/doi:10.18129/B9.bioc.limma) uses an \"empirical Bayes\" variance estimate for each gene, which starts with individual variance estimates but then \"squeezes\" the estimates toward a common value. The package's author outlines that method here (https://stats.stackexchange.com/a/670944/28500), with references.", "answer_url": "https://stats.stackexchange.com/a/677084", "author": "EdM", "author_url": "https://stats.stackexchange.com/users/28500/edm", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-05T21:54:12+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677078, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-09-05T21:54:12+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "2464CE21-544C-49EC-A65A-6F86849F9B4D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/2464CE21-544C-49EC-A65A-6F86849F9B4D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-09-07T16:19:27+00:00", "raw_file": "raw/codex_api_v1/3f959895a29b33d83894e5370d82e1c0cf87f20ac57fa423ebc923738357c657_1790825253957066500_0.json", "raw_sha256": "ddd8808039e410ca99f97e2a7f12c307f046c4e5c3e184683bc12f816e6f49fc", "revision_guid": "B613000D-ABDF-47BA-BDB2-301FB5C608F6", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/B613000D-ABDF-47BA-BDB2-301FB5C608F6/view-source"}], "score": 6, "updated_at": "2026-09-07T16:19:27+00:00"}], "domain": "statistics", "external_links": ["https://cran.r-project.org/package=emmeans", "https://doi.org/10.1016/j.ab.2020.113608", "https://doi.org/10.1091/mbc.E15-02-0076", "https://doi.org/doi:10.18129/B9.bioc.limma", "https://en.wikipedia.org/wiki/Likelihood-ratio_test", "https://en.wikipedia.org/wiki/Multiple_comparisons_problem"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "user503965", "question_author_url": "https://stats.stackexchange.com/users/516304/user503965", "question_author_user_type": "registered", "question_created_at": "2026-09-05T09:13:22+00:00", "question_html": "

A few FYI to start:

\n\n

I had cells extracted from an organ (1 organ). Cells were separated into different wells and plates. My end goal is to check for changes in protein "X" levels using western blot.\nTwo factors are included: Control vs Treatment and Incubation Time (how long cells have been incubated with or without the treatment).

\n

Wells were divided as so:\n30 minutes incubation: 3 controls + 3 medications.\n1 hour: 3 controls + 3 medications.\n2 hours: 3 + 3\n3 hours: 3 + 3.

\n

All samples originate from the same organ lysate (organ was lysed and cells collected -> samples from lysate tube were plated in different wells) 6 wells (3 control + 3 treatment) were the "30m" group, 6 were "1hour" group, and so on...

\n

I could extrapolate several points of data: 1) effects of treatment on protein levels (regardless of time); 2) effects of time on protein levels (Regardless of treatment) and 3) Does the effect of treatment on protein levels changes with incubation time?

\n

Would really appreciate some recommendations for tests (+some theory about the test you think would fit best).

\n", "question_id": 677078, "question_license": "CC BY-SA 4.0", "question_score": 5, "question_text": "A few FYI to start:\n\n\n\n\n\nI am doing a research project to finish my bachelors in life sciences.\n\n\n\n\nI studied Probability for scientists (intro level).\n\n\n\n\nI didn't study statistical inference. Instead I chose Calculus 1.\nI need to statistically analyze my results but I don't know how. I also have no time to read full introductions to statistical analysis.\n\n\n\n\n\nI had cells extracted from an organ (1 organ). Cells were separated into different wells and plates. My end goal is to check for changes in protein \"X\" levels using western blot.\nTwo factors are included: Control vs Treatment and Incubation Time (how long cells have been incubated with or without the treatment).\n\n\n\n\nWells were divided as so:\n30 minutes incubation: 3 controls + 3 medications.\n1 hour: 3 controls + 3 medications.\n2 hours: 3 + 3\n3 hours: 3 + 3.\n\n\n\n\nAll samples originate from the same organ lysate (organ was lysed and cells collected -> samples from lysate tube were plated in different wells) 6 wells (3 control + 3 treatment) were the \"30m\" group, 6 were \"1hour\" group, and so on...\n\n\n\n\nI could extrapolate several points of data: 1) effects of treatment on protein levels (regardless of time); 2) effects of time on protein levels (Regardless of treatment) and 3) Does the effect of treatment on protein levels changes with incubation time?\n\n\n\n\nWould really appreciate some recommendations for tests (+some theory about the test you think would fit best).", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "user503965", "profile_url": "https://stats.stackexchange.com/users/516304/user503965", "user_type": "registered"}, "created_at": "2026-09-05T09:13:22+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "28593582-B344-42B2-A1B1-A0C00CBD588F", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/28593582-B344-42B2-A1B1-A0C00CBD588F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "user503965", "profile_url": "https://stats.stackexchange.com/users/516304/user503965", "user_type": "registered"}, "created_at": "2026-09-05T09:19:27+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "691E0983-9880-4E86-92A1-95DEDF3C24AB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/691E0983-9880-4E86-92A1-95DEDF3C24AB/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Rick Hass", "profile_url": "https://stats.stackexchange.com/users/97844/rick-hass", "user_type": "registered"}, "created_at": "2026-09-05T17:00:39+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "BC5FAF19-81E4-4449-9AB1-A58BE937A472", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/BC5FAF19-81E4-4449-9AB1-A58BE937A472/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-09-05T23:14:16+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "4D24D3DB-1EB5-48B8-8CFC-DD98AA684452", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/4D24D3DB-1EB5-48B8-8CFC-DD98AA684452/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/677078/time-course-experiment-which-statistical-analysis-fits-best", "split": "test", "split_group": "cbb822688bb3d1bc11e31ae26d9e8a7ea2167dad6d35dc44f96db014cfd3c90f", "tags": ["inference", "experiment-design"], "thread_id": "stats:677078", "title": "Time course experiment - which statistical analysis fits best?"}} {"citation_context": " so genes, in which single-gene variance estimates can vary widely. The Bioconductor limma package (https://doi.org/doi:10.18129/B9.bioc.limma) uses an \"empirical Bayes\" variance estimate for each gene, which starts with individual variance e", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": "10.18129/B9.bioc.limma", "external_url": "https://doi.org/doi:10.18129/B9.bioc.limma", "kind": "doi_url", "post_id": 677084, "post_url": "https://stats.stackexchange.com/a/677084", "product": "citations", "record_id": "Scientific-Citation-Graph:c7ca6c8f0ef04e95541a41ab", "split": "test", "thread": {"accepted_answer_id": 677084, "answers": [{"answer_html": "

The 2019 Technical Perspective by Daniel, Thomas and Katherine Pollard, "Empowering statistical methods for cellular and molecular biologists" Molecular Biology of the Cell 30: 1359-1368 is a good practical introduction to study design and statistical analysis for studies like yours. I have quibbles with some details of their recommendations, but you should find it very helpful particularly as you design and analyze future experiments.

\n

Subject-matter preliminaries

\n

Subject-matter knowledge is important before you design or analyze experiments. You don't say much about the biological hypothesis per se, but I've run enough Western blots at least to know that quantifying them isn't trivial. The issues are covered, for example, by Pillai-Kastoori et al., "A systematic approach to quantitative Western blot analysis," Analytical Biochemistry 593: article 1136082020 (2020).

\n

This answer points out that differences between gels and blots sometimes overwhelm the differences due to treatments. Your results will be most believable if you run samples that you want to compare on the same gel and blot, even if your quantitation is OK. Current best practice expects you to provide annotated images of the entire blots anyway, at least in supplemental data.

\n

Technical versus biological replicates

\n

With all cells obtained from only 1 organ, the best you can do is test whether the protein level was associated with the treatment for the 1 organ you dissociated. The 3 samples at each combination of time and treatment are technical replicates. Differences among the 3 samples at any such combination represent technical differences in culturing the cells, extracting proteins, running the gels, exposing the Western blots, quantifying the bands, and (perhaps) normalizing against a "housekeeping" protein not expected to be affected by treatment.

\n

You need to have multiple biological replicates to support any more general hypothesis about the results. In your situation, that would at least involve organs from multiple animals from different litters, possibly of different sexes, maybe also of different ages or even different species, depending on how general you want the results to be. The Technical Perspective by the Pollards explains the difference between technical and biological replicates.

\n

Statistical analysis

\n

Although you can only examine differences for this 1 organ, the following general principles also apply to experiments with biological replicates.

\n

You have a continuous outcome (protein level via Western blot) with treatment/control and time-point (4 values) as factors. Following Figure 2 of the Technical Report by the Pollards, you could do ANOVA (analysis of variance) or a linear regression model. (ANOVA is simply a specific form of a linear regression model, so that distinction isn't very important.)

\n

If "the effect of treatment on protein levels changes with incubation time," there isn't a single "effect of treatment on protein levels (regardless of time)" or a single "effect of time on protein levels (regardless of treatment)." A 2-way ANOVA, with treatment/control in one direction and time-point in the other direction, can test whether "the effect of treatment on protein levels changes with incubation time." If it doesn't, then you can estimate the "effect of treatment on protein levels (regardless of time)" and the "effect of time on protein levels (regardless of treatment)." If it does, you can use associated "post-hoc" tests to evaluate the difference between any treatment/time-point combinations.

\n

In response to comment

\n

With treatment/control and 4 time points, you presumably have 3 interaction coefficients. When you say "2 Way ANOVA resulted in (mostly) not significant results for treatment * time interactions," I suspect that means you only found one of those coefficients to be "statistically significantly" different from 0. What that means depends on how the software codes the predictors, which can vary among software implementations and how you call their functios. You can get an overall estimate of the interaction by comparing models with and without the interaction term, for example via a likelihood-ratio test. Some implementations of 2-way ANOVA will do that automatically.

\n

For t-tests between treatment and control at each time point, it's best to start with a 2-way ANOVA. A t-test is based on the estimate of the variance of observed values around the model's predictions. If you perform a t-test at each time point, ignoring all the other time points, each test only uses the number of observations at that time point. You thus get imprecise variance estimates that can differ substantially among time points. A 2-way ANOVA instead uses all the observations/predictions to get a pooled variance estimate, which you use for all the time points.* In R, packages like emmeans can help with that.

\n

That said, I've seen lots of plots with separate analyses for each time point. In cell biology, you typically need visually compelling differences to convince your audience. If the differences are very visually compelling, they are likely to be "statistically significant" even if the statistical tests aren't optimal.

\n

You also should be aware of the multiple comparisons problem. The more tests you run, the more likely you are to find a "significant" result just by chance. There are two things you can control to minimize that problem: the "family-wise error rate" (FWER), the probability that none of the comparisons is falsely positive, or the "false-discovery rate" (FDR), the fraction of apparent positive results likely to be false positives. In large-scale experiments in genomics and proteomics, FDR control is the usual choice.

\n
\n

*Using pooled variance estimates becomes very important in large-scale experiments like gene-expression studies on 20,000 or so genes, in which single-gene variance estimates can vary widely. The Bioconductor limma package uses an "empirical Bayes" variance estimate for each gene, which starts with individual variance estimates but then "squeezes" the estimates toward a common value. The package's author outlines that method here, with references.

\n", "answer_id": 677084, "answer_text": "The 2019 Technical Perspective by Daniel, Thomas and Katherine Pollard, \"Empowering statistical methods for cellular and molecular biologists (https://doi.org/10.1091/mbc.E15-02-0076)\" Molecular Biology of the Cell 30: 1359-1368 is a good practical introduction to study design and statistical analysis for studies like yours. I have quibbles with some details of their recommendations, but you should find it very helpful particularly as you design and analyze future experiments.\n\n\n\n\nSubject-matter preliminaries\n\n\n\n\nSubject-matter knowledge is important before you design or analyze experiments. You don't say much about the biological hypothesis per se, but I've run enough Western blots at least to know that quantifying them isn't trivial. The issues are covered, for example, by Pillai-Kastoori et al., \"A systematic approach to quantitative Western blot analysis (https://doi.org/10.1016/j.ab.2020.113608),\" Analytical Biochemistry 593: article 1136082020 (2020).\n\n\n\n\nThis answer (https://stats.stackexchange.com/a/518168/28500) points out that differences between gels and blots sometimes overwhelm the differences due to treatments. Your results will be most believable if you run samples that you want to compare on the same gel and blot, even if your quantitation is OK. Current best practice expects you to provide annotated images of the entire blots anyway, at least in supplemental data.\n\n\n\n\nTechnical versus biological replicates\n\n\n\n\nWith all cells obtained from only 1 organ, the best you can do is test whether the protein level was associated with the treatment for the 1 organ you dissociated. The 3 samples at each combination of time and treatment are technical replicates. Differences among the 3 samples at any such combination represent technical differences in culturing the cells, extracting proteins, running the gels, exposing the Western blots, quantifying the bands, and (perhaps) normalizing against a \"housekeeping\" protein not expected to be affected by treatment.\n\n\n\n\nYou need to have multiple biological replicates to support any more general hypothesis about the results. In your situation, that would at least involve organs from multiple animals from different litters, possibly of different sexes, maybe also of different ages or even different species, depending on how general you want the results to be. The Technical Perspective by the Pollards explains the difference between technical and biological replicates.\n\n\n\n\nStatistical analysis\n\n\n\n\nAlthough you can only examine differences for this 1 organ, the following general principles also apply to experiments with biological replicates.\n\n\n\n\nYou have a continuous outcome (protein level via Western blot) with treatment/control and time-point (4 values) as factors. Following Figure 2 of the Technical Report by the Pollards, you could do ANOVA (analysis of variance) or a linear regression model. (ANOVA is simply a specific form of a linear regression model, so that distinction isn't very important.)\n\n\n\n\nIf \"the effect of treatment on protein levels changes with incubation time,\" there isn't a single \"effect of treatment on protein levels (regardless of time)\" or a single \"effect of time on protein levels (regardless of treatment).\" A 2-way ANOVA, with treatment/control in one direction and time-point in the other direction, can test whether \"the effect of treatment on protein levels changes with incubation time.\" If it doesn't, then you can estimate the \"effect of treatment on protein levels (regardless of time)\" and the \"effect of time on protein levels (regardless of treatment).\" If it does, you can use associated \"post-hoc\" tests to evaluate the difference between any treatment/time-point combinations.\n\n\n\n\nIn response to comment\n\n\n\n\nWith treatment/control and 4 time points, you presumably have 3 interaction coefficients. When you say \"2 Way ANOVA resulted in (mostly) not significant results for treatment * time interactions,\" I suspect that means you only found one of those coefficients to be \"statistically significantly\" different from 0. What that means depends on how the software codes the predictors, which can vary among software implementations and how you call their functios. You can get an overall estimate of the interaction by comparing models with and without the interaction term, for example via a likelihood-ratio test (https://en.wikipedia.org/wiki/Likelihood-ratio_test). Some implementations of 2-way ANOVA will do that automatically.\n\n\n\n\nFor t-tests between treatment and control at each time point, it's best to start with a 2-way ANOVA. A t-test is based on the estimate of the variance of observed values around the model's predictions. If you perform a t-test at each time point, ignoring all the other time points, each test only uses the number of observations at that time point. You thus get imprecise variance estimates that can differ substantially among time points. A 2-way ANOVA instead uses all the observations/predictions to get a pooled variance estimate, which you use for all the time points.* In R, packages like emmeans (https://cran.r-project.org/package=emmeans) can help with that.\n\n\n\n\nThat said, I've seen lots of plots with separate analyses for each time point. In cell biology, you typically need visually compelling differences to convince your audience. If the differences are very visually compelling, they are likely to be \"statistically significant\" even if the statistical tests aren't optimal.\n\n\n\n\nYou also should be aware of the multiple comparisons problem (https://en.wikipedia.org/wiki/Multiple_comparisons_problem). The more tests you run, the more likely you are to find a \"significant\" result just by chance. There are two things you can control to minimize that problem: the \"family-wise error rate\" (FWER), the probability that none of the comparisons is falsely positive, or the \"false-discovery rate\" (FDR), the fraction of apparent positive results likely to be false positives. In large-scale experiments in genomics and proteomics, FDR control is the usual choice.\n\n\n\n\n\n\n\n*Using pooled variance estimates becomes very important in large-scale experiments like gene-expression studies on 20,000 or so genes, in which single-gene variance estimates can vary widely. The Bioconductor limma package (https://doi.org/doi:10.18129/B9.bioc.limma) uses an \"empirical Bayes\" variance estimate for each gene, which starts with individual variance estimates but then \"squeezes\" the estimates toward a common value. The package's author outlines that method here (https://stats.stackexchange.com/a/670944/28500), with references.", "answer_url": "https://stats.stackexchange.com/a/677084", "author": "EdM", "author_url": "https://stats.stackexchange.com/users/28500/edm", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-05T21:54:12+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677078, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-09-05T21:54:12+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "2464CE21-544C-49EC-A65A-6F86849F9B4D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/2464CE21-544C-49EC-A65A-6F86849F9B4D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-09-07T16:19:27+00:00", "raw_file": "raw/codex_api_v1/3f959895a29b33d83894e5370d82e1c0cf87f20ac57fa423ebc923738357c657_1790825253957066500_0.json", "raw_sha256": "ddd8808039e410ca99f97e2a7f12c307f046c4e5c3e184683bc12f816e6f49fc", "revision_guid": "B613000D-ABDF-47BA-BDB2-301FB5C608F6", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/B613000D-ABDF-47BA-BDB2-301FB5C608F6/view-source"}], "score": 6, "updated_at": "2026-09-07T16:19:27+00:00"}], "domain": "statistics", "external_links": ["https://cran.r-project.org/package=emmeans", "https://doi.org/10.1016/j.ab.2020.113608", "https://doi.org/10.1091/mbc.E15-02-0076", "https://doi.org/doi:10.18129/B9.bioc.limma", "https://en.wikipedia.org/wiki/Likelihood-ratio_test", "https://en.wikipedia.org/wiki/Multiple_comparisons_problem"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "user503965", "question_author_url": "https://stats.stackexchange.com/users/516304/user503965", "question_author_user_type": "registered", "question_created_at": "2026-09-05T09:13:22+00:00", "question_html": "

A few FYI to start:

\n\n

I had cells extracted from an organ (1 organ). Cells were separated into different wells and plates. My end goal is to check for changes in protein "X" levels using western blot.\nTwo factors are included: Control vs Treatment and Incubation Time (how long cells have been incubated with or without the treatment).

\n

Wells were divided as so:\n30 minutes incubation: 3 controls + 3 medications.\n1 hour: 3 controls + 3 medications.\n2 hours: 3 + 3\n3 hours: 3 + 3.

\n

All samples originate from the same organ lysate (organ was lysed and cells collected -> samples from lysate tube were plated in different wells) 6 wells (3 control + 3 treatment) were the "30m" group, 6 were "1hour" group, and so on...

\n

I could extrapolate several points of data: 1) effects of treatment on protein levels (regardless of time); 2) effects of time on protein levels (Regardless of treatment) and 3) Does the effect of treatment on protein levels changes with incubation time?

\n

Would really appreciate some recommendations for tests (+some theory about the test you think would fit best).

\n", "question_id": 677078, "question_license": "CC BY-SA 4.0", "question_score": 5, "question_text": "A few FYI to start:\n\n\n\n\n\nI am doing a research project to finish my bachelors in life sciences.\n\n\n\n\nI studied Probability for scientists (intro level).\n\n\n\n\nI didn't study statistical inference. Instead I chose Calculus 1.\nI need to statistically analyze my results but I don't know how. I also have no time to read full introductions to statistical analysis.\n\n\n\n\n\nI had cells extracted from an organ (1 organ). Cells were separated into different wells and plates. My end goal is to check for changes in protein \"X\" levels using western blot.\nTwo factors are included: Control vs Treatment and Incubation Time (how long cells have been incubated with or without the treatment).\n\n\n\n\nWells were divided as so:\n30 minutes incubation: 3 controls + 3 medications.\n1 hour: 3 controls + 3 medications.\n2 hours: 3 + 3\n3 hours: 3 + 3.\n\n\n\n\nAll samples originate from the same organ lysate (organ was lysed and cells collected -> samples from lysate tube were plated in different wells) 6 wells (3 control + 3 treatment) were the \"30m\" group, 6 were \"1hour\" group, and so on...\n\n\n\n\nI could extrapolate several points of data: 1) effects of treatment on protein levels (regardless of time); 2) effects of time on protein levels (Regardless of treatment) and 3) Does the effect of treatment on protein levels changes with incubation time?\n\n\n\n\nWould really appreciate some recommendations for tests (+some theory about the test you think would fit best).", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "user503965", "profile_url": "https://stats.stackexchange.com/users/516304/user503965", "user_type": "registered"}, "created_at": "2026-09-05T09:13:22+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "28593582-B344-42B2-A1B1-A0C00CBD588F", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/28593582-B344-42B2-A1B1-A0C00CBD588F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "user503965", "profile_url": "https://stats.stackexchange.com/users/516304/user503965", "user_type": "registered"}, "created_at": "2026-09-05T09:19:27+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "691E0983-9880-4E86-92A1-95DEDF3C24AB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/691E0983-9880-4E86-92A1-95DEDF3C24AB/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Rick Hass", "profile_url": "https://stats.stackexchange.com/users/97844/rick-hass", "user_type": "registered"}, "created_at": "2026-09-05T17:00:39+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "BC5FAF19-81E4-4449-9AB1-A58BE937A472", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/BC5FAF19-81E4-4449-9AB1-A58BE937A472/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-09-05T23:14:16+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "4D24D3DB-1EB5-48B8-8CFC-DD98AA684452", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/4D24D3DB-1EB5-48B8-8CFC-DD98AA684452/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/677078/time-course-experiment-which-statistical-analysis-fits-best", "split": "test", "split_group": "cbb822688bb3d1bc11e31ae26d9e8a7ea2167dad6d35dc44f96db014cfd3c90f", "tags": ["inference", "experiment-design"], "thread_id": "stats:677078", "title": "Time course experiment - which statistical analysis fits best?"}} {"citation_context": "by comparing models with and without the interaction term, for example via a likelihood-ratio test (https://en.wikipedia.org/wiki/Likelihood-ratio_test). Some implementations of 2-way ANOVA will do that automatically.\n\n\n\n\nFor t-tests between treatment", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Likelihood-ratio_test", "kind": "external_url", "post_id": 677084, "post_url": "https://stats.stackexchange.com/a/677084", "product": "citations", "record_id": "Scientific-Citation-Graph:638cb61e640a2fcbc65a125c", "split": "test", "thread": {"accepted_answer_id": 677084, "answers": [{"answer_html": "

The 2019 Technical Perspective by Daniel, Thomas and Katherine Pollard, "Empowering statistical methods for cellular and molecular biologists" Molecular Biology of the Cell 30: 1359-1368 is a good practical introduction to study design and statistical analysis for studies like yours. I have quibbles with some details of their recommendations, but you should find it very helpful particularly as you design and analyze future experiments.

\n

Subject-matter preliminaries

\n

Subject-matter knowledge is important before you design or analyze experiments. You don't say much about the biological hypothesis per se, but I've run enough Western blots at least to know that quantifying them isn't trivial. The issues are covered, for example, by Pillai-Kastoori et al., "A systematic approach to quantitative Western blot analysis," Analytical Biochemistry 593: article 1136082020 (2020).

\n

This answer points out that differences between gels and blots sometimes overwhelm the differences due to treatments. Your results will be most believable if you run samples that you want to compare on the same gel and blot, even if your quantitation is OK. Current best practice expects you to provide annotated images of the entire blots anyway, at least in supplemental data.

\n

Technical versus biological replicates

\n

With all cells obtained from only 1 organ, the best you can do is test whether the protein level was associated with the treatment for the 1 organ you dissociated. The 3 samples at each combination of time and treatment are technical replicates. Differences among the 3 samples at any such combination represent technical differences in culturing the cells, extracting proteins, running the gels, exposing the Western blots, quantifying the bands, and (perhaps) normalizing against a "housekeeping" protein not expected to be affected by treatment.

\n

You need to have multiple biological replicates to support any more general hypothesis about the results. In your situation, that would at least involve organs from multiple animals from different litters, possibly of different sexes, maybe also of different ages or even different species, depending on how general you want the results to be. The Technical Perspective by the Pollards explains the difference between technical and biological replicates.

\n

Statistical analysis

\n

Although you can only examine differences for this 1 organ, the following general principles also apply to experiments with biological replicates.

\n

You have a continuous outcome (protein level via Western blot) with treatment/control and time-point (4 values) as factors. Following Figure 2 of the Technical Report by the Pollards, you could do ANOVA (analysis of variance) or a linear regression model. (ANOVA is simply a specific form of a linear regression model, so that distinction isn't very important.)

\n

If "the effect of treatment on protein levels changes with incubation time," there isn't a single "effect of treatment on protein levels (regardless of time)" or a single "effect of time on protein levels (regardless of treatment)." A 2-way ANOVA, with treatment/control in one direction and time-point in the other direction, can test whether "the effect of treatment on protein levels changes with incubation time." If it doesn't, then you can estimate the "effect of treatment on protein levels (regardless of time)" and the "effect of time on protein levels (regardless of treatment)." If it does, you can use associated "post-hoc" tests to evaluate the difference between any treatment/time-point combinations.

\n

In response to comment

\n

With treatment/control and 4 time points, you presumably have 3 interaction coefficients. When you say "2 Way ANOVA resulted in (mostly) not significant results for treatment * time interactions," I suspect that means you only found one of those coefficients to be "statistically significantly" different from 0. What that means depends on how the software codes the predictors, which can vary among software implementations and how you call their functios. You can get an overall estimate of the interaction by comparing models with and without the interaction term, for example via a likelihood-ratio test. Some implementations of 2-way ANOVA will do that automatically.

\n

For t-tests between treatment and control at each time point, it's best to start with a 2-way ANOVA. A t-test is based on the estimate of the variance of observed values around the model's predictions. If you perform a t-test at each time point, ignoring all the other time points, each test only uses the number of observations at that time point. You thus get imprecise variance estimates that can differ substantially among time points. A 2-way ANOVA instead uses all the observations/predictions to get a pooled variance estimate, which you use for all the time points.* In R, packages like emmeans can help with that.

\n

That said, I've seen lots of plots with separate analyses for each time point. In cell biology, you typically need visually compelling differences to convince your audience. If the differences are very visually compelling, they are likely to be "statistically significant" even if the statistical tests aren't optimal.

\n

You also should be aware of the multiple comparisons problem. The more tests you run, the more likely you are to find a "significant" result just by chance. There are two things you can control to minimize that problem: the "family-wise error rate" (FWER), the probability that none of the comparisons is falsely positive, or the "false-discovery rate" (FDR), the fraction of apparent positive results likely to be false positives. In large-scale experiments in genomics and proteomics, FDR control is the usual choice.

\n
\n

*Using pooled variance estimates becomes very important in large-scale experiments like gene-expression studies on 20,000 or so genes, in which single-gene variance estimates can vary widely. The Bioconductor limma package uses an "empirical Bayes" variance estimate for each gene, which starts with individual variance estimates but then "squeezes" the estimates toward a common value. The package's author outlines that method here, with references.

\n", "answer_id": 677084, "answer_text": "The 2019 Technical Perspective by Daniel, Thomas and Katherine Pollard, \"Empowering statistical methods for cellular and molecular biologists (https://doi.org/10.1091/mbc.E15-02-0076)\" Molecular Biology of the Cell 30: 1359-1368 is a good practical introduction to study design and statistical analysis for studies like yours. I have quibbles with some details of their recommendations, but you should find it very helpful particularly as you design and analyze future experiments.\n\n\n\n\nSubject-matter preliminaries\n\n\n\n\nSubject-matter knowledge is important before you design or analyze experiments. You don't say much about the biological hypothesis per se, but I've run enough Western blots at least to know that quantifying them isn't trivial. The issues are covered, for example, by Pillai-Kastoori et al., \"A systematic approach to quantitative Western blot analysis (https://doi.org/10.1016/j.ab.2020.113608),\" Analytical Biochemistry 593: article 1136082020 (2020).\n\n\n\n\nThis answer (https://stats.stackexchange.com/a/518168/28500) points out that differences between gels and blots sometimes overwhelm the differences due to treatments. Your results will be most believable if you run samples that you want to compare on the same gel and blot, even if your quantitation is OK. Current best practice expects you to provide annotated images of the entire blots anyway, at least in supplemental data.\n\n\n\n\nTechnical versus biological replicates\n\n\n\n\nWith all cells obtained from only 1 organ, the best you can do is test whether the protein level was associated with the treatment for the 1 organ you dissociated. The 3 samples at each combination of time and treatment are technical replicates. Differences among the 3 samples at any such combination represent technical differences in culturing the cells, extracting proteins, running the gels, exposing the Western blots, quantifying the bands, and (perhaps) normalizing against a \"housekeeping\" protein not expected to be affected by treatment.\n\n\n\n\nYou need to have multiple biological replicates to support any more general hypothesis about the results. In your situation, that would at least involve organs from multiple animals from different litters, possibly of different sexes, maybe also of different ages or even different species, depending on how general you want the results to be. The Technical Perspective by the Pollards explains the difference between technical and biological replicates.\n\n\n\n\nStatistical analysis\n\n\n\n\nAlthough you can only examine differences for this 1 organ, the following general principles also apply to experiments with biological replicates.\n\n\n\n\nYou have a continuous outcome (protein level via Western blot) with treatment/control and time-point (4 values) as factors. Following Figure 2 of the Technical Report by the Pollards, you could do ANOVA (analysis of variance) or a linear regression model. (ANOVA is simply a specific form of a linear regression model, so that distinction isn't very important.)\n\n\n\n\nIf \"the effect of treatment on protein levels changes with incubation time,\" there isn't a single \"effect of treatment on protein levels (regardless of time)\" or a single \"effect of time on protein levels (regardless of treatment).\" A 2-way ANOVA, with treatment/control in one direction and time-point in the other direction, can test whether \"the effect of treatment on protein levels changes with incubation time.\" If it doesn't, then you can estimate the \"effect of treatment on protein levels (regardless of time)\" and the \"effect of time on protein levels (regardless of treatment).\" If it does, you can use associated \"post-hoc\" tests to evaluate the difference between any treatment/time-point combinations.\n\n\n\n\nIn response to comment\n\n\n\n\nWith treatment/control and 4 time points, you presumably have 3 interaction coefficients. When you say \"2 Way ANOVA resulted in (mostly) not significant results for treatment * time interactions,\" I suspect that means you only found one of those coefficients to be \"statistically significantly\" different from 0. What that means depends on how the software codes the predictors, which can vary among software implementations and how you call their functios. You can get an overall estimate of the interaction by comparing models with and without the interaction term, for example via a likelihood-ratio test (https://en.wikipedia.org/wiki/Likelihood-ratio_test). Some implementations of 2-way ANOVA will do that automatically.\n\n\n\n\nFor t-tests between treatment and control at each time point, it's best to start with a 2-way ANOVA. A t-test is based on the estimate of the variance of observed values around the model's predictions. If you perform a t-test at each time point, ignoring all the other time points, each test only uses the number of observations at that time point. You thus get imprecise variance estimates that can differ substantially among time points. A 2-way ANOVA instead uses all the observations/predictions to get a pooled variance estimate, which you use for all the time points.* In R, packages like emmeans (https://cran.r-project.org/package=emmeans) can help with that.\n\n\n\n\nThat said, I've seen lots of plots with separate analyses for each time point. In cell biology, you typically need visually compelling differences to convince your audience. If the differences are very visually compelling, they are likely to be \"statistically significant\" even if the statistical tests aren't optimal.\n\n\n\n\nYou also should be aware of the multiple comparisons problem (https://en.wikipedia.org/wiki/Multiple_comparisons_problem). The more tests you run, the more likely you are to find a \"significant\" result just by chance. There are two things you can control to minimize that problem: the \"family-wise error rate\" (FWER), the probability that none of the comparisons is falsely positive, or the \"false-discovery rate\" (FDR), the fraction of apparent positive results likely to be false positives. In large-scale experiments in genomics and proteomics, FDR control is the usual choice.\n\n\n\n\n\n\n\n*Using pooled variance estimates becomes very important in large-scale experiments like gene-expression studies on 20,000 or so genes, in which single-gene variance estimates can vary widely. The Bioconductor limma package (https://doi.org/doi:10.18129/B9.bioc.limma) uses an \"empirical Bayes\" variance estimate for each gene, which starts with individual variance estimates but then \"squeezes\" the estimates toward a common value. The package's author outlines that method here (https://stats.stackexchange.com/a/670944/28500), with references.", "answer_url": "https://stats.stackexchange.com/a/677084", "author": "EdM", "author_url": "https://stats.stackexchange.com/users/28500/edm", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-05T21:54:12+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677078, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-09-05T21:54:12+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "2464CE21-544C-49EC-A65A-6F86849F9B4D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/2464CE21-544C-49EC-A65A-6F86849F9B4D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-09-07T16:19:27+00:00", "raw_file": "raw/codex_api_v1/3f959895a29b33d83894e5370d82e1c0cf87f20ac57fa423ebc923738357c657_1790825253957066500_0.json", "raw_sha256": "ddd8808039e410ca99f97e2a7f12c307f046c4e5c3e184683bc12f816e6f49fc", "revision_guid": "B613000D-ABDF-47BA-BDB2-301FB5C608F6", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/B613000D-ABDF-47BA-BDB2-301FB5C608F6/view-source"}], "score": 6, "updated_at": "2026-09-07T16:19:27+00:00"}], "domain": "statistics", "external_links": ["https://cran.r-project.org/package=emmeans", "https://doi.org/10.1016/j.ab.2020.113608", "https://doi.org/10.1091/mbc.E15-02-0076", "https://doi.org/doi:10.18129/B9.bioc.limma", "https://en.wikipedia.org/wiki/Likelihood-ratio_test", "https://en.wikipedia.org/wiki/Multiple_comparisons_problem"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "user503965", "question_author_url": "https://stats.stackexchange.com/users/516304/user503965", "question_author_user_type": "registered", "question_created_at": "2026-09-05T09:13:22+00:00", "question_html": "

A few FYI to start:

\n\n

I had cells extracted from an organ (1 organ). Cells were separated into different wells and plates. My end goal is to check for changes in protein "X" levels using western blot.\nTwo factors are included: Control vs Treatment and Incubation Time (how long cells have been incubated with or without the treatment).

\n

Wells were divided as so:\n30 minutes incubation: 3 controls + 3 medications.\n1 hour: 3 controls + 3 medications.\n2 hours: 3 + 3\n3 hours: 3 + 3.

\n

All samples originate from the same organ lysate (organ was lysed and cells collected -> samples from lysate tube were plated in different wells) 6 wells (3 control + 3 treatment) were the "30m" group, 6 were "1hour" group, and so on...

\n

I could extrapolate several points of data: 1) effects of treatment on protein levels (regardless of time); 2) effects of time on protein levels (Regardless of treatment) and 3) Does the effect of treatment on protein levels changes with incubation time?

\n

Would really appreciate some recommendations for tests (+some theory about the test you think would fit best).

\n", "question_id": 677078, "question_license": "CC BY-SA 4.0", "question_score": 5, "question_text": "A few FYI to start:\n\n\n\n\n\nI am doing a research project to finish my bachelors in life sciences.\n\n\n\n\nI studied Probability for scientists (intro level).\n\n\n\n\nI didn't study statistical inference. Instead I chose Calculus 1.\nI need to statistically analyze my results but I don't know how. I also have no time to read full introductions to statistical analysis.\n\n\n\n\n\nI had cells extracted from an organ (1 organ). Cells were separated into different wells and plates. My end goal is to check for changes in protein \"X\" levels using western blot.\nTwo factors are included: Control vs Treatment and Incubation Time (how long cells have been incubated with or without the treatment).\n\n\n\n\nWells were divided as so:\n30 minutes incubation: 3 controls + 3 medications.\n1 hour: 3 controls + 3 medications.\n2 hours: 3 + 3\n3 hours: 3 + 3.\n\n\n\n\nAll samples originate from the same organ lysate (organ was lysed and cells collected -> samples from lysate tube were plated in different wells) 6 wells (3 control + 3 treatment) were the \"30m\" group, 6 were \"1hour\" group, and so on...\n\n\n\n\nI could extrapolate several points of data: 1) effects of treatment on protein levels (regardless of time); 2) effects of time on protein levels (Regardless of treatment) and 3) Does the effect of treatment on protein levels changes with incubation time?\n\n\n\n\nWould really appreciate some recommendations for tests (+some theory about the test you think would fit best).", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "user503965", "profile_url": "https://stats.stackexchange.com/users/516304/user503965", "user_type": "registered"}, "created_at": "2026-09-05T09:13:22+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "28593582-B344-42B2-A1B1-A0C00CBD588F", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/28593582-B344-42B2-A1B1-A0C00CBD588F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "user503965", "profile_url": "https://stats.stackexchange.com/users/516304/user503965", "user_type": "registered"}, "created_at": "2026-09-05T09:19:27+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "691E0983-9880-4E86-92A1-95DEDF3C24AB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/691E0983-9880-4E86-92A1-95DEDF3C24AB/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Rick Hass", "profile_url": "https://stats.stackexchange.com/users/97844/rick-hass", "user_type": "registered"}, "created_at": "2026-09-05T17:00:39+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "BC5FAF19-81E4-4449-9AB1-A58BE937A472", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/BC5FAF19-81E4-4449-9AB1-A58BE937A472/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-09-05T23:14:16+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "4D24D3DB-1EB5-48B8-8CFC-DD98AA684452", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/4D24D3DB-1EB5-48B8-8CFC-DD98AA684452/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/677078/time-course-experiment-which-statistical-analysis-fits-best", "split": "test", "split_group": "cbb822688bb3d1bc11e31ae26d9e8a7ea2167dad6d35dc44f96db014cfd3c90f", "tags": ["inference", "experiment-design"], "thread_id": "stats:677078", "title": "Time course experiment - which statistical analysis fits best?"}} {"citation_context": "statistical tests aren't optimal.\n\n\n\n\nYou also should be aware of the multiple comparisons problem (https://en.wikipedia.org/wiki/Multiple_comparisons_problem). The more tests you run, the more likely you are to find a \"significant\" result just by chance. Th", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Multiple_comparisons_problem", "kind": "external_url", "post_id": 677084, "post_url": "https://stats.stackexchange.com/a/677084", "product": "citations", "record_id": "Scientific-Citation-Graph:bd2a7f75683452363aa72082", "split": "test", "thread": {"accepted_answer_id": 677084, "answers": [{"answer_html": "

The 2019 Technical Perspective by Daniel, Thomas and Katherine Pollard, "Empowering statistical methods for cellular and molecular biologists" Molecular Biology of the Cell 30: 1359-1368 is a good practical introduction to study design and statistical analysis for studies like yours. I have quibbles with some details of their recommendations, but you should find it very helpful particularly as you design and analyze future experiments.

\n

Subject-matter preliminaries

\n

Subject-matter knowledge is important before you design or analyze experiments. You don't say much about the biological hypothesis per se, but I've run enough Western blots at least to know that quantifying them isn't trivial. The issues are covered, for example, by Pillai-Kastoori et al., "A systematic approach to quantitative Western blot analysis," Analytical Biochemistry 593: article 1136082020 (2020).

\n

This answer points out that differences between gels and blots sometimes overwhelm the differences due to treatments. Your results will be most believable if you run samples that you want to compare on the same gel and blot, even if your quantitation is OK. Current best practice expects you to provide annotated images of the entire blots anyway, at least in supplemental data.

\n

Technical versus biological replicates

\n

With all cells obtained from only 1 organ, the best you can do is test whether the protein level was associated with the treatment for the 1 organ you dissociated. The 3 samples at each combination of time and treatment are technical replicates. Differences among the 3 samples at any such combination represent technical differences in culturing the cells, extracting proteins, running the gels, exposing the Western blots, quantifying the bands, and (perhaps) normalizing against a "housekeeping" protein not expected to be affected by treatment.

\n

You need to have multiple biological replicates to support any more general hypothesis about the results. In your situation, that would at least involve organs from multiple animals from different litters, possibly of different sexes, maybe also of different ages or even different species, depending on how general you want the results to be. The Technical Perspective by the Pollards explains the difference between technical and biological replicates.

\n

Statistical analysis

\n

Although you can only examine differences for this 1 organ, the following general principles also apply to experiments with biological replicates.

\n

You have a continuous outcome (protein level via Western blot) with treatment/control and time-point (4 values) as factors. Following Figure 2 of the Technical Report by the Pollards, you could do ANOVA (analysis of variance) or a linear regression model. (ANOVA is simply a specific form of a linear regression model, so that distinction isn't very important.)

\n

If "the effect of treatment on protein levels changes with incubation time," there isn't a single "effect of treatment on protein levels (regardless of time)" or a single "effect of time on protein levels (regardless of treatment)." A 2-way ANOVA, with treatment/control in one direction and time-point in the other direction, can test whether "the effect of treatment on protein levels changes with incubation time." If it doesn't, then you can estimate the "effect of treatment on protein levels (regardless of time)" and the "effect of time on protein levels (regardless of treatment)." If it does, you can use associated "post-hoc" tests to evaluate the difference between any treatment/time-point combinations.

\n

In response to comment

\n

With treatment/control and 4 time points, you presumably have 3 interaction coefficients. When you say "2 Way ANOVA resulted in (mostly) not significant results for treatment * time interactions," I suspect that means you only found one of those coefficients to be "statistically significantly" different from 0. What that means depends on how the software codes the predictors, which can vary among software implementations and how you call their functios. You can get an overall estimate of the interaction by comparing models with and without the interaction term, for example via a likelihood-ratio test. Some implementations of 2-way ANOVA will do that automatically.

\n

For t-tests between treatment and control at each time point, it's best to start with a 2-way ANOVA. A t-test is based on the estimate of the variance of observed values around the model's predictions. If you perform a t-test at each time point, ignoring all the other time points, each test only uses the number of observations at that time point. You thus get imprecise variance estimates that can differ substantially among time points. A 2-way ANOVA instead uses all the observations/predictions to get a pooled variance estimate, which you use for all the time points.* In R, packages like emmeans can help with that.

\n

That said, I've seen lots of plots with separate analyses for each time point. In cell biology, you typically need visually compelling differences to convince your audience. If the differences are very visually compelling, they are likely to be "statistically significant" even if the statistical tests aren't optimal.

\n

You also should be aware of the multiple comparisons problem. The more tests you run, the more likely you are to find a "significant" result just by chance. There are two things you can control to minimize that problem: the "family-wise error rate" (FWER), the probability that none of the comparisons is falsely positive, or the "false-discovery rate" (FDR), the fraction of apparent positive results likely to be false positives. In large-scale experiments in genomics and proteomics, FDR control is the usual choice.

\n
\n

*Using pooled variance estimates becomes very important in large-scale experiments like gene-expression studies on 20,000 or so genes, in which single-gene variance estimates can vary widely. The Bioconductor limma package uses an "empirical Bayes" variance estimate for each gene, which starts with individual variance estimates but then "squeezes" the estimates toward a common value. The package's author outlines that method here, with references.

\n", "answer_id": 677084, "answer_text": "The 2019 Technical Perspective by Daniel, Thomas and Katherine Pollard, \"Empowering statistical methods for cellular and molecular biologists (https://doi.org/10.1091/mbc.E15-02-0076)\" Molecular Biology of the Cell 30: 1359-1368 is a good practical introduction to study design and statistical analysis for studies like yours. I have quibbles with some details of their recommendations, but you should find it very helpful particularly as you design and analyze future experiments.\n\n\n\n\nSubject-matter preliminaries\n\n\n\n\nSubject-matter knowledge is important before you design or analyze experiments. You don't say much about the biological hypothesis per se, but I've run enough Western blots at least to know that quantifying them isn't trivial. The issues are covered, for example, by Pillai-Kastoori et al., \"A systematic approach to quantitative Western blot analysis (https://doi.org/10.1016/j.ab.2020.113608),\" Analytical Biochemistry 593: article 1136082020 (2020).\n\n\n\n\nThis answer (https://stats.stackexchange.com/a/518168/28500) points out that differences between gels and blots sometimes overwhelm the differences due to treatments. Your results will be most believable if you run samples that you want to compare on the same gel and blot, even if your quantitation is OK. Current best practice expects you to provide annotated images of the entire blots anyway, at least in supplemental data.\n\n\n\n\nTechnical versus biological replicates\n\n\n\n\nWith all cells obtained from only 1 organ, the best you can do is test whether the protein level was associated with the treatment for the 1 organ you dissociated. The 3 samples at each combination of time and treatment are technical replicates. Differences among the 3 samples at any such combination represent technical differences in culturing the cells, extracting proteins, running the gels, exposing the Western blots, quantifying the bands, and (perhaps) normalizing against a \"housekeeping\" protein not expected to be affected by treatment.\n\n\n\n\nYou need to have multiple biological replicates to support any more general hypothesis about the results. In your situation, that would at least involve organs from multiple animals from different litters, possibly of different sexes, maybe also of different ages or even different species, depending on how general you want the results to be. The Technical Perspective by the Pollards explains the difference between technical and biological replicates.\n\n\n\n\nStatistical analysis\n\n\n\n\nAlthough you can only examine differences for this 1 organ, the following general principles also apply to experiments with biological replicates.\n\n\n\n\nYou have a continuous outcome (protein level via Western blot) with treatment/control and time-point (4 values) as factors. Following Figure 2 of the Technical Report by the Pollards, you could do ANOVA (analysis of variance) or a linear regression model. (ANOVA is simply a specific form of a linear regression model, so that distinction isn't very important.)\n\n\n\n\nIf \"the effect of treatment on protein levels changes with incubation time,\" there isn't a single \"effect of treatment on protein levels (regardless of time)\" or a single \"effect of time on protein levels (regardless of treatment).\" A 2-way ANOVA, with treatment/control in one direction and time-point in the other direction, can test whether \"the effect of treatment on protein levels changes with incubation time.\" If it doesn't, then you can estimate the \"effect of treatment on protein levels (regardless of time)\" and the \"effect of time on protein levels (regardless of treatment).\" If it does, you can use associated \"post-hoc\" tests to evaluate the difference between any treatment/time-point combinations.\n\n\n\n\nIn response to comment\n\n\n\n\nWith treatment/control and 4 time points, you presumably have 3 interaction coefficients. When you say \"2 Way ANOVA resulted in (mostly) not significant results for treatment * time interactions,\" I suspect that means you only found one of those coefficients to be \"statistically significantly\" different from 0. What that means depends on how the software codes the predictors, which can vary among software implementations and how you call their functios. You can get an overall estimate of the interaction by comparing models with and without the interaction term, for example via a likelihood-ratio test (https://en.wikipedia.org/wiki/Likelihood-ratio_test). Some implementations of 2-way ANOVA will do that automatically.\n\n\n\n\nFor t-tests between treatment and control at each time point, it's best to start with a 2-way ANOVA. A t-test is based on the estimate of the variance of observed values around the model's predictions. If you perform a t-test at each time point, ignoring all the other time points, each test only uses the number of observations at that time point. You thus get imprecise variance estimates that can differ substantially among time points. A 2-way ANOVA instead uses all the observations/predictions to get a pooled variance estimate, which you use for all the time points.* In R, packages like emmeans (https://cran.r-project.org/package=emmeans) can help with that.\n\n\n\n\nThat said, I've seen lots of plots with separate analyses for each time point. In cell biology, you typically need visually compelling differences to convince your audience. If the differences are very visually compelling, they are likely to be \"statistically significant\" even if the statistical tests aren't optimal.\n\n\n\n\nYou also should be aware of the multiple comparisons problem (https://en.wikipedia.org/wiki/Multiple_comparisons_problem). The more tests you run, the more likely you are to find a \"significant\" result just by chance. There are two things you can control to minimize that problem: the \"family-wise error rate\" (FWER), the probability that none of the comparisons is falsely positive, or the \"false-discovery rate\" (FDR), the fraction of apparent positive results likely to be false positives. In large-scale experiments in genomics and proteomics, FDR control is the usual choice.\n\n\n\n\n\n\n\n*Using pooled variance estimates becomes very important in large-scale experiments like gene-expression studies on 20,000 or so genes, in which single-gene variance estimates can vary widely. The Bioconductor limma package (https://doi.org/doi:10.18129/B9.bioc.limma) uses an \"empirical Bayes\" variance estimate for each gene, which starts with individual variance estimates but then \"squeezes\" the estimates toward a common value. The package's author outlines that method here (https://stats.stackexchange.com/a/670944/28500), with references.", "answer_url": "https://stats.stackexchange.com/a/677084", "author": "EdM", "author_url": "https://stats.stackexchange.com/users/28500/edm", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-05T21:54:12+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677078, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-09-05T21:54:12+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "2464CE21-544C-49EC-A65A-6F86849F9B4D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/2464CE21-544C-49EC-A65A-6F86849F9B4D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "EdM", "profile_url": "https://stats.stackexchange.com/users/28500/edm", "user_type": "registered"}, "created_at": "2026-09-07T16:19:27+00:00", "raw_file": "raw/codex_api_v1/3f959895a29b33d83894e5370d82e1c0cf87f20ac57fa423ebc923738357c657_1790825253957066500_0.json", "raw_sha256": "ddd8808039e410ca99f97e2a7f12c307f046c4e5c3e184683bc12f816e6f49fc", "revision_guid": "B613000D-ABDF-47BA-BDB2-301FB5C608F6", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/B613000D-ABDF-47BA-BDB2-301FB5C608F6/view-source"}], "score": 6, "updated_at": "2026-09-07T16:19:27+00:00"}], "domain": "statistics", "external_links": ["https://cran.r-project.org/package=emmeans", "https://doi.org/10.1016/j.ab.2020.113608", "https://doi.org/10.1091/mbc.E15-02-0076", "https://doi.org/doi:10.18129/B9.bioc.limma", "https://en.wikipedia.org/wiki/Likelihood-ratio_test", "https://en.wikipedia.org/wiki/Multiple_comparisons_problem"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "user503965", "question_author_url": "https://stats.stackexchange.com/users/516304/user503965", "question_author_user_type": "registered", "question_created_at": "2026-09-05T09:13:22+00:00", "question_html": "

A few FYI to start:

\n\n

I had cells extracted from an organ (1 organ). Cells were separated into different wells and plates. My end goal is to check for changes in protein "X" levels using western blot.\nTwo factors are included: Control vs Treatment and Incubation Time (how long cells have been incubated with or without the treatment).

\n

Wells were divided as so:\n30 minutes incubation: 3 controls + 3 medications.\n1 hour: 3 controls + 3 medications.\n2 hours: 3 + 3\n3 hours: 3 + 3.

\n

All samples originate from the same organ lysate (organ was lysed and cells collected -> samples from lysate tube were plated in different wells) 6 wells (3 control + 3 treatment) were the "30m" group, 6 were "1hour" group, and so on...

\n

I could extrapolate several points of data: 1) effects of treatment on protein levels (regardless of time); 2) effects of time on protein levels (Regardless of treatment) and 3) Does the effect of treatment on protein levels changes with incubation time?

\n

Would really appreciate some recommendations for tests (+some theory about the test you think would fit best).

\n", "question_id": 677078, "question_license": "CC BY-SA 4.0", "question_score": 5, "question_text": "A few FYI to start:\n\n\n\n\n\nI am doing a research project to finish my bachelors in life sciences.\n\n\n\n\nI studied Probability for scientists (intro level).\n\n\n\n\nI didn't study statistical inference. Instead I chose Calculus 1.\nI need to statistically analyze my results but I don't know how. I also have no time to read full introductions to statistical analysis.\n\n\n\n\n\nI had cells extracted from an organ (1 organ). Cells were separated into different wells and plates. My end goal is to check for changes in protein \"X\" levels using western blot.\nTwo factors are included: Control vs Treatment and Incubation Time (how long cells have been incubated with or without the treatment).\n\n\n\n\nWells were divided as so:\n30 minutes incubation: 3 controls + 3 medications.\n1 hour: 3 controls + 3 medications.\n2 hours: 3 + 3\n3 hours: 3 + 3.\n\n\n\n\nAll samples originate from the same organ lysate (organ was lysed and cells collected -> samples from lysate tube were plated in different wells) 6 wells (3 control + 3 treatment) were the \"30m\" group, 6 were \"1hour\" group, and so on...\n\n\n\n\nI could extrapolate several points of data: 1) effects of treatment on protein levels (regardless of time); 2) effects of time on protein levels (Regardless of treatment) and 3) Does the effect of treatment on protein levels changes with incubation time?\n\n\n\n\nWould really appreciate some recommendations for tests (+some theory about the test you think would fit best).", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "user503965", "profile_url": "https://stats.stackexchange.com/users/516304/user503965", "user_type": "registered"}, "created_at": "2026-09-05T09:13:22+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "28593582-B344-42B2-A1B1-A0C00CBD588F", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/28593582-B344-42B2-A1B1-A0C00CBD588F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "user503965", "profile_url": "https://stats.stackexchange.com/users/516304/user503965", "user_type": "registered"}, "created_at": "2026-09-05T09:19:27+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "691E0983-9880-4E86-92A1-95DEDF3C24AB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/691E0983-9880-4E86-92A1-95DEDF3C24AB/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Rick Hass", "profile_url": "https://stats.stackexchange.com/users/97844/rick-hass", "user_type": "registered"}, "created_at": "2026-09-05T17:00:39+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "BC5FAF19-81E4-4449-9AB1-A58BE937A472", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/BC5FAF19-81E4-4449-9AB1-A58BE937A472/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-09-05T23:14:16+00:00", "raw_file": "raw/codex_api_v1/64ee278f47b21ead17c9e9fc156835d607f15cff0518af0117a527463a68df8a_1790825256327661600_0.json", "raw_sha256": "18d894000304f6d836d0b21a9f2f35d37c183b3d25e32a897338c6dff012df04", "revision_guid": "4D24D3DB-1EB5-48B8-8CFC-DD98AA684452", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/4D24D3DB-1EB5-48B8-8CFC-DD98AA684452/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/677078/time-course-experiment-which-statistical-analysis-fits-best", "split": "test", "split_group": "cbb822688bb3d1bc11e31ae26d9e8a7ea2167dad6d35dc44f96db014cfd3c90f", "tags": ["inference", "experiment-design"], "thread_id": "stats:677078", "title": "Time course experiment - which statistical analysis fits best?"}} {"citation_context": "et/kEDelnub.png] (https://i.sstatic.net/kEDelnub.png)\n[image: enter image description here; source: https://i.sstatic.net/H3ywscwO.png] (https://i.sstatic.net/H3ywscwO.png)\n\n\n\n\nPrior to running this script, I would have thought that l", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://i.sstatic.net/H3ywscwO.png", "kind": "external_url", "post_id": 677094, "post_url": "https://stats.stackexchange.com/questions/677094/can-coverage-probability-decrease-as-sample-size-increases", "product": "citations", "record_id": "Scientific-Citation-Graph:22a95558db7d00ac44a375f3", "split": "test", "thread": {"accepted_answer_id": 677117, "answers": [{"answer_html": "

The suspicion expressed in the comments is well-founded: your MLE function tends to not arrive at the true MLE. Since it is performing a search, I would expect a good MLE function to use the moment estimators as the starting point. Using the function below, the behavior you observed disappears, as shown by the equivalent plots.

\n

My fit_mle function is inspired by Rfast::betabinom.mle, adapted to handle edge cases.

\n
fit_mle <- function(x, k) {\n  m1 <- mean(x)\n  \n  if (k == 1 || all(x == 0) || all(x == k)) {\n    a <- max(m1*100/k, 1e-5)\n    b <- max(100 - a, 1e-5)\n    V <- NA\n  } else {\n    n <- length(x)\n    z1 <- sort(unique(x))\n    n1 <- tabulate(match(x, z1))\n    z2 <- sort(unique(k - x))\n    n2 <- tabulate(match(k - x, z2))\n    m2 <- mean(x^2)\n    d <- 1/(k*(m2/m1 - m1) - k + m1)\n    a <- (k*m1 - m2)*d\n    b <- (k - m1)*(k - m2/m1)*d\n    \n    if (!is.finite(a) || d < 0) {\n      a <- max(m1*100/k, 1e-5)\n      b <- max(100 - a, 1e-5)\n    } else if (a <= 0 || b <= 0) {\n      a <- max(m1*0.1/k, 1e-5)\n      b <- max(0.1 - a, 1e-5)\n    }\n    \n    for (i in 1:100) {\n      ab <- a + b\n      t1 <- digamma(ab) - digamma(k + ab)\n      S1 <- a*(sum(digamma(z1 + a)*n1) + n*(t1 - digamma(a)))\n      S2 <- b*(sum(digamma(z2 + b)*n2) + n*(t1 - digamma(b)))\n      t2 <- trigamma(ab) - trigamma(k + ab)\n      J11 <- a^2*(sum(trigamma(z1 + a)*n1) + n*(t2 - trigamma(a))) + S1\n      J22 <- b^2*(sum(trigamma(z2 + b)*n2) + n*(t2 - trigamma(b))) + S2\n      J12 <- a*b*t2*n\n      if (abs(detJ <- J11*J22 - J12^2) < 1e-12) break\n      step1 <- (J22*S1 - J12*S2)/detJ\n      step2 <- (J11*S2 - J12*S1)/detJ\n      if (abs(step1) + abs(step2) < 1e-8) break\n      step_norm <- 2/sqrt(step1^2 + step2^2)\n      \n      if (step_norm < 1) {\n        step1 <- step1*step_norm\n        step2 <- step2*step_norm\n      }\n      \n      a <- a*exp(-step1)\n      b <- b*exp(-step2)\n    }\n    \n    g <- a*b/(a + b)^2\n    V <- -(J11 + J22 + 2*J12)*g^2/detJ\n  }\n  \n  c(a/(a + b), if (is.finite(V) && V > 0 && V < 1 / (4 * n)) V else NA)\n}\n
\n

\"enter

\n

\"enter

\n

Full code:

\n
library(MASS)\n\nz <- qnorm(0.975)\n\n## Simulate \nmu_true <- 0.5\nv_true  <- 0.249\nn_vals  <- c(5, 10, 15, 20, 25, 50, 100, 200, 500,1000)\nk_vals  <- c(1, 2, 3, 4, 5, 6,7,8,9)\nR       <- 1000\n\n\nsim_data <- function(n, k, mu, v) {\n  nu <- mu * (1 - mu) / v - 1\n  rbinom(n, k, rbeta(n, mu * nu, (1 - mu) * nu))\n}\n\n## MLE \nfit_mle <- function(x, k) {\n  xx <<- x\n  kk <<- k\n  m1 <- mean(x)\n  \n  if (k == 1 || all(x == 0) || all(x == k)) {\n    a <- max(m1*100/k, 1e-5)\n    b <- max(100 - a, 1e-5)\n    V <- NA\n  } else {\n    n <- length(x)\n    z1 <- sort(unique(x))\n    n1 <- tabulate(match(x, z1))\n    z2 <- sort(unique(k - x))\n    n2 <- tabulate(match(k - x, z2))\n    m2 <- mean(x^2)\n    d <- 1/(k*(m2/m1 - m1) - k + m1)\n    a <- (k*m1 - m2)*d\n    b <- (k - m1)*(k - m2/m1)*d\n    \n    if (!is.finite(a) || d < 0) {\n      a <- max(m1*100/k, 1e-5)\n      b <- max(100 - a, 1e-5)\n    } else if (a <= 0 || b <= 0) {\n      a <- max(m1*0.1/k, 1e-5)\n      b <- max(0.1 - a, 1e-5)\n    }\n    \n    for (i in 1:100) {\n      ab <- a + b\n      t1 <- digamma(ab) - digamma(k + ab)\n      S1 <- a*(sum(digamma(z1 + a)*n1) + n*(t1 - digamma(a)))\n      S2 <- b*(sum(digamma(z2 + b)*n2) + n*(t1 - digamma(b)))\n      t2 <- trigamma(ab) - trigamma(k + ab)\n      J11 <- a^2*(sum(trigamma(z1 + a)*n1) + n*(t2 - trigamma(a))) + S1\n      J22 <- b^2*(sum(trigamma(z2 + b)*n2) + n*(t2 - trigamma(b))) + S2\n      J12 <- a*b*t2*n\n      if (abs(detJ <- J11*J22 - J12^2) < 1e-12) break\n      step1 <- (J22*S1 - J12*S2)/detJ\n      step2 <- (J11*S2 - J12*S1)/detJ\n      if (abs(step1) + abs(step2) < 1e-8) break\n      step_norm <- 2/sqrt(step1^2 + step2^2)\n      \n      if (step_norm < 1) {\n        step1 <- step1*step_norm\n        step2 <- step2*step_norm\n      }\n      \n      a <- a*exp(-step1)\n      b <- b*exp(-step2)\n    }\n    \n    g <- a*b/(a + b)^2\n    V <- -(J11 + J22 + 2*J12)*g^2/detJ\n  }\n  \n  c(a/(a + b), if (is.finite(V) && V > 0 && V < 1 / (4 * n)) V else NA)\n}\n\n## Moments\nfit_mom <- function(x, k) {\n  p <- x / k\n  c(mean(p), var(p) / length(p))\n}\n\nscore <- function(m, V, mu) {\n  s <- sqrt(V); ok <- is.finite(m)\n  data.frame(mean_estimate      = mean(m[ok]),\n             bias               = mean(m[ok]) - mu,\n             mc_se              = sd(m[ok]) / sqrt(sum(ok)),\n             sd_estimate        = sd(m[ok]),\n             variance_estimate  = mean(V, na.rm = TRUE),\n             length_of_interval = mean(2 * z * s, na.rm = TRUE),\n             coverage           = mean(abs(m - mu) <= z * s, na.rm = TRUE))\n}\n\nrun_cell <- function(mu, v, n, k, R, i, tot, t0) {\n  cat(sprintf("[%2d/%2d] n = %3d, k = %d ... ", i, tot, n, k))\n  e <- replicate(R, { x <- sim_data(n, k, mu, v)\n  rbind(fit_mom(x, k), fit_mle(x, k)) })\n  cat(sprintf("done (%.1fs elapsed)\\n",\n              as.numeric(difftime(Sys.time(), t0, units = "secs"))))\n  cbind(true_mean = mu, true_variance = v, n = n, k = k,\n        true_var_of_mean = (v + (mu * (1 - mu) - v) / k) / n,\n        method = c("moments", "mle"),\n        rbind(score(e[1, 1, ], e[1, 2, ], mu),\n              score(e[2, 1, ], e[2, 2, ], mu)))\n}\n\n#Estimation\nset.seed(1)\nt0 <- Sys.time()\ng  <- expand.grid(n = n_vals, k = k_vals)\nres <- do.call(rbind, Map(run_cell, mu_true, v_true, g$n, g$k,\n                          MoreArgs = list(R = R), i = seq_len(nrow(g)),\n                          tot = nrow(g), t0 = t0))\n\nlibrary(ggplot2)\nlibrary(patchwork)\n\nres_df <- as.data.frame(res, stringsAsFactors = FALSE)\nnum_cols <- c("true_mean", "true_variance", "n", "k", "true_var_of_mean", \n              "mean_estimate", "bias", "mc_se", "sd_estimate", \n              "variance_estimate", "length_of_interval", "coverage")\nres_df[num_cols] <- lapply(res_df[num_cols], as.numeric)\nres_df$k_factor <- as.factor(res_df$k)\n\ndf_mom <- subset(res_df, method == "moments")\ndf_mle <- subset(res_df, method == "mle")\n\n# Helper function to generate the panels\nmake_panel <- function(data, metric_col, title, subtitle, y_label, hline = NULL) {\n  p <- ggplot(data, aes(x = n, y = .data[[metric_col]], color = k_factor)) +\n    geom_line(linewidth = 0.5) +\n    geom_point(size = 1.5) +\n    labs(title = title, subtitle = subtitle, x = "n", y = y_label, color = "k") +\n    theme_bw() +\n    theme(legend.position = "bottom",\n          plot.title = element_text(hjust = 0),\n          plot.subtitle = element_text(hjust = 0))\n  \n  if (!is.null(hline)) {\n    p <- p + geom_hline(yintercept = hline, linetype = "dashed", linewidth = 0.5)\n  }\n  return(p)\n}\n\np1 <- make_panel(df_mom, "bias", "Moments: bias of the estimated mean", \n                 "Average estimate minus the truth. Dashed line at 0.", "bias", 0)\np2 <- make_panel(df_mle, "bias", "MLE: bias of the estimated mean", \n                 "Average estimate minus the truth. Dashed line at 0.", "bias", 0)\np3 <- make_panel(df_mom, "sd_estimate", "Moments: SD of the estimated mean", \n                 "Spread of the estimate across studies.", "SD")\np4 <- make_panel(df_mle, "sd_estimate", "MLE: SD of the estimated mean", \n                 "Spread of the estimate across studies.", "SD")\n\n# Combine using patchwork\ncombined_grid <- (p1 + p2) / (p3 + p4)\nprint(combined_grid)\n\np_cov <- ggplot(res_df, aes(x = n, y = coverage, color = method)) +\n  geom_line(linewidth = 0.5) +\n  geom_point(size = 1.5) +\n  geom_hline(yintercept = 0.95, linetype = "dashed") +\n  facet_grid(~ k, labeller = label_both) +\n  labs(title = "Coverage of the nominal 95% interval",\n       subtitle = "Share of 1000 intervals containing the true mean. Dashed line at 0.95.",\n       x = "n",\n       y = "coverage",\n       color = "method") +\n  theme_bw() +\n  theme(legend.position = "bottom",\n        strip.background = element_rect(fill = "grey90"))\n\nprint(p_cov)\n
\n", "answer_id": 677117, "answer_text": "The suspicion expressed in the comments is well-founded: your MLE function tends to not arrive at the true MLE. Since it is performing a search, I would expect a good MLE function to use the moment estimators as the starting point. Using the function below, the behavior you observed disappears, as shown by the equivalent plots.\n\n\n\n\nMy fit_mle function is inspired by Rfast::betabinom.mle, adapted to handle edge cases.\n\n\n\n\nfit_mle <- function(x, k) {\n m1 <- mean(x)\n \n if (k == 1 || all(x == 0) || all(x == k)) {\n a <- max(m1*100/k, 1e-5)\n b <- max(100 - a, 1e-5)\n V <- NA\n } else {\n n <- length(x)\n z1 <- sort(unique(x))\n n1 <- tabulate(match(x, z1))\n z2 <- sort(unique(k - x))\n n2 <- tabulate(match(k - x, z2))\n m2 <- mean(x^2)\n d <- 1/(k*(m2/m1 - m1) - k + m1)\n a <- (k*m1 - m2)*d\n b <- (k - m1)*(k - m2/m1)*d\n \n if (!is.finite(a) || d < 0) {\n a <- max(m1*100/k, 1e-5)\n b <- max(100 - a, 1e-5)\n } else if (a <= 0 || b <= 0) {\n a <- max(m1*0.1/k, 1e-5)\n b <- max(0.1 - a, 1e-5)\n }\n \n for (i in 1:100) {\n ab <- a + b\n t1 <- digamma(ab) - digamma(k + ab)\n S1 <- a*(sum(digamma(z1 + a)*n1) + n*(t1 - digamma(a)))\n S2 <- b*(sum(digamma(z2 + b)*n2) + n*(t1 - digamma(b)))\n t2 <- trigamma(ab) - trigamma(k + ab)\n J11 <- a^2*(sum(trigamma(z1 + a)*n1) + n*(t2 - trigamma(a))) + S1\n J22 <- b^2*(sum(trigamma(z2 + b)*n2) + n*(t2 - trigamma(b))) + S2\n J12 <- a*b*t2*n\n if (abs(detJ <- J11*J22 - J12^2) < 1e-12) break\n step1 <- (J22*S1 - J12*S2)/detJ\n step2 <- (J11*S2 - J12*S1)/detJ\n if (abs(step1) + abs(step2) < 1e-8) break\n step_norm <- 2/sqrt(step1^2 + step2^2)\n \n if (step_norm < 1) {\n step1 <- step1*step_norm\n step2 <- step2*step_norm\n }\n \n a <- a*exp(-step1)\n b <- b*exp(-step2)\n }\n \n g <- a*b/(a + b)^2\n V <- -(J11 + J22 + 2*J12)*g^2/detJ\n }\n \n c(a/(a + b), if (is.finite(V) && V > 0 && V < 1 / (4 * n)) V else NA)\n}\n\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/yrEHvkk0.png] (https://i.sstatic.net/yrEHvkk0.png)\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/9nEiiFBK.png] (https://i.sstatic.net/9nEiiFBK.png)\n\n\n\n\nFull code:\n\n\n\n\nlibrary(MASS)\n\nz <- qnorm(0.975)\n\n## Simulate \nmu_true <- 0.5\nv_true <- 0.249\nn_vals <- c(5, 10, 15, 20, 25, 50, 100, 200, 500,1000)\nk_vals <- c(1, 2, 3, 4, 5, 6,7,8,9)\nR <- 1000\n\n\nsim_data <- function(n, k, mu, v) {\n nu <- mu * (1 - mu) / v - 1\n rbinom(n, k, rbeta(n, mu * nu, (1 - mu) * nu))\n}\n\n## MLE \nfit_mle <- function(x, k) {\n xx <<- x\n kk <<- k\n m1 <- mean(x)\n \n if (k == 1 || all(x == 0) || all(x == k)) {\n a <- max(m1*100/k, 1e-5)\n b <- max(100 - a, 1e-5)\n V <- NA\n } else {\n n <- length(x)\n z1 <- sort(unique(x))\n n1 <- tabulate(match(x, z1))\n z2 <- sort(unique(k - x))\n n2 <- tabulate(match(k - x, z2))\n m2 <- mean(x^2)\n d <- 1/(k*(m2/m1 - m1) - k + m1)\n a <- (k*m1 - m2)*d\n b <- (k - m1)*(k - m2/m1)*d\n \n if (!is.finite(a) || d < 0) {\n a <- max(m1*100/k, 1e-5)\n b <- max(100 - a, 1e-5)\n } else if (a <= 0 || b <= 0) {\n a <- max(m1*0.1/k, 1e-5)\n b <- max(0.1 - a, 1e-5)\n }\n \n for (i in 1:100) {\n ab <- a + b\n t1 <- digamma(ab) - digamma(k + ab)\n S1 <- a*(sum(digamma(z1 + a)*n1) + n*(t1 - digamma(a)))\n S2 <- b*(sum(digamma(z2 + b)*n2) + n*(t1 - digamma(b)))\n t2 <- trigamma(ab) - trigamma(k + ab)\n J11 <- a^2*(sum(trigamma(z1 + a)*n1) + n*(t2 - trigamma(a))) + S1\n J22 <- b^2*(sum(trigamma(z2 + b)*n2) + n*(t2 - trigamma(b))) + S2\n J12 <- a*b*t2*n\n if (abs(detJ <- J11*J22 - J12^2) < 1e-12) break\n step1 <- (J22*S1 - J12*S2)/detJ\n step2 <- (J11*S2 - J12*S1)/detJ\n if (abs(step1) + abs(step2) < 1e-8) break\n step_norm <- 2/sqrt(step1^2 + step2^2)\n \n if (step_norm < 1) {\n step1 <- step1*step_norm\n step2 <- step2*step_norm\n }\n \n a <- a*exp(-step1)\n b <- b*exp(-step2)\n }\n \n g <- a*b/(a + b)^2\n V <- -(J11 + J22 + 2*J12)*g^2/detJ\n }\n \n c(a/(a + b), if (is.finite(V) && V > 0 && V < 1 / (4 * n)) V else NA)\n}\n\n## Moments\nfit_mom <- function(x, k) {\n p <- x / k\n c(mean(p), var(p) / length(p))\n}\n\nscore <- function(m, V, mu) {\n s <- sqrt(V); ok <- is.finite(m)\n data.frame(mean_estimate = mean(m[ok]),\n bias = mean(m[ok]) - mu,\n mc_se = sd(m[ok]) / sqrt(sum(ok)),\n sd_estimate = sd(m[ok]),\n variance_estimate = mean(V, na.rm = TRUE),\n length_of_interval = mean(2 * z * s, na.rm = TRUE),\n coverage = mean(abs(m - mu) <= z * s, na.rm = TRUE))\n}\n\nrun_cell <- function(mu, v, n, k, R, i, tot, t0) {\n cat(sprintf(\"[%2d/%2d] n = %3d, k = %d ... \", i, tot, n, k))\n e <- replicate(R, { x <- sim_data(n, k, mu, v)\n rbind(fit_mom(x, k), fit_mle(x, k)) })\n cat(sprintf(\"done (%.1fs elapsed)\\n\",\n as.numeric(difftime(Sys.time(), t0, units = \"secs\"))))\n cbind(true_mean = mu, true_variance = v, n = n, k = k,\n true_var_of_mean = (v + (mu * (1 - mu) - v) / k) / n,\n method = c(\"moments\", \"mle\"),\n rbind(score(e[1, 1, ], e[1, 2, ], mu),\n score(e[2, 1, ], e[2, 2, ], mu)))\n}\n\n#Estimation\nset.seed(1)\nt0 <- Sys.time()\ng <- expand.grid(n = n_vals, k = k_vals)\nres <- do.call(rbind, Map(run_cell, mu_true, v_true, g$n, g$k,\n MoreArgs = list(R = R), i = seq_len(nrow(g)),\n tot = nrow(g), t0 = t0))\n\nlibrary(ggplot2)\nlibrary(patchwork)\n\nres_df <- as.data.frame(res, stringsAsFactors = FALSE)\nnum_cols <- c(\"true_mean\", \"true_variance\", \"n\", \"k\", \"true_var_of_mean\", \n \"mean_estimate\", \"bias\", \"mc_se\", \"sd_estimate\", \n \"variance_estimate\", \"length_of_interval\", \"coverage\")\nres_df[num_cols] <- lapply(res_df[num_cols], as.numeric)\nres_df$k_factor <- as.factor(res_df$k)\n\ndf_mom <- subset(res_df, method == \"moments\")\ndf_mle <- subset(res_df, method == \"mle\")\n\n# Helper function to generate the panels\nmake_panel <- function(data, metric_col, title, subtitle, y_label, hline = NULL) {\n p <- ggplot(data, aes(x = n, y = .data[[metric_col]], color = k_factor)) +\n geom_line(linewidth = 0.5) +\n geom_point(size = 1.5) +\n labs(title = title, subtitle = subtitle, x = \"n\", y = y_label, color = \"k\") +\n theme_bw() +\n theme(legend.position = \"bottom\",\n plot.title = element_text(hjust = 0),\n plot.subtitle = element_text(hjust = 0))\n \n if (!is.null(hline)) {\n p <- p + geom_hline(yintercept = hline, linetype = \"dashed\", linewidth = 0.5)\n }\n return(p)\n}\n\np1 <- make_panel(df_mom, \"bias\", \"Moments: bias of the estimated mean\", \n \"Average estimate minus the truth. Dashed line at 0.\", \"bias\", 0)\np2 <- make_panel(df_mle, \"bias\", \"MLE: bias of the estimated mean\", \n \"Average estimate minus the truth. Dashed line at 0.\", \"bias\", 0)\np3 <- make_panel(df_mom, \"sd_estimate\", \"Moments: SD of the estimated mean\", \n \"Spread of the estimate across studies.\", \"SD\")\np4 <- make_panel(df_mle, \"sd_estimate\", \"MLE: SD of the estimated mean\", \n \"Spread of the estimate across studies.\", \"SD\")\n\n# Combine using patchwork\ncombined_grid <- (p1 + p2) / (p3 + p4)\nprint(combined_grid)\n\np_cov <- ggplot(res_df, aes(x = n, y = coverage, color = method)) +\n geom_line(linewidth = 0.5) +\n geom_point(size = 1.5) +\n geom_hline(yintercept = 0.95, linetype = \"dashed\") +\n facet_grid(~ k, labeller = label_both) +\n labs(title = \"Coverage of the nominal 95% interval\",\n subtitle = \"Share of 1000 intervals containing the true mean. Dashed line at 0.95.\",\n x = \"n\",\n y = \"coverage\",\n color = \"method\") +\n theme_bw() +\n theme(legend.position = \"bottom\",\n strip.background = element_rect(fill = \"grey90\"))\n\nprint(p_cov)", "answer_url": "https://stats.stackexchange.com/a/677117", "author": "jblood94", "author_url": "https://stats.stackexchange.com/users/214015/jblood94", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-09T13:02:57+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677094, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "jblood94", "profile_url": "https://stats.stackexchange.com/users/214015/jblood94", "user_type": "registered"}, "created_at": "2026-09-09T13:02:57+00:00", "raw_file": "raw/codex_api_v1/3f959895a29b33d83894e5370d82e1c0cf87f20ac57fa423ebc923738357c657_1790825253957066500_0.json", "raw_sha256": "ddd8808039e410ca99f97e2a7f12c307f046c4e5c3e184683bc12f816e6f49fc", "revision_guid": "09E52470-6B69-4568-A8B3-D52476EA341B", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/09E52470-6B69-4568-A8B3-D52476EA341B/view-source"}, {"content_license": null, "contributor": {"display_name": "adamkostanov", "profile_url": "https://stats.stackexchange.com/users/512554/adamkostanov", "user_type": "registered"}, "created_at": "2026-09-16T13:07:32+00:00", "raw_file": "raw/codex_api_v1/59f98009db0ac38325a869c60e3993040b07f5fbd07014051415831400b70d25_1790825251781774200_0.json", "raw_sha256": "2876465103b1eeb5d593dd46b1ec52a862c1da72f8e4767e5f8ee70ff0564119", "revision_guid": "20C3E36B-1564-462F-9257-5BBE5B9B70EF", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/20C3E36B-1564-462F-9257-5BBE5B9B70EF/view-source"}], "score": 3, "updated_at": "2026-09-09T13:02:57+00:00"}], "domain": "statistics", "external_links": ["https://i.sstatic.net/9nEiiFBK.png", "https://i.sstatic.net/H3ywscwO.png", "https://i.sstatic.net/kEDelnub.png", "https://i.sstatic.net/yrEHvkk0.png"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "adamkostanov", "question_author_url": "https://stats.stackexchange.com/users/512554/adamkostanov", "question_author_user_type": "registered", "question_created_at": "2026-09-07T06:07:31+00:00", "question_html": "

Here is a beta-binomial model (treated like repeated measures - $i$ is an index for each individual, $n$ total individuals, and exactly $k$ measurements per individual):

\n

$$\\theta_i \\stackrel{\\text{iid}}{\\sim} \\mathrm{Beta}(a,b), \\qquad x_i \\mid \\theta_i \\sim \\mathrm{Binomial}(k,\\theta_i), \\qquad \\hat p_i = \\frac{x_i}{k}, \\qquad i = 1,\\dots,n$$

\n

$$\\mu = E[\\theta_i] = \\frac{a}{a+b}$$

\n

$$\\sigma^2 = \\operatorname{Var}(\\theta_i) = \\frac{ab}{(a+b)^2(a+b+1)}$$

\n

$$\\tau^2 = E[\\theta_i(1-\\theta_i)] = \\mu(1-\\mu) - \\sigma^2$$

\n

For a single unit,

\n

$$E[\\hat p_i] = \\mu, \\qquad \\operatorname{Var}(\\hat p_i) = \\sigma^2 + \\frac{\\tau^2}{k}$$

\n

and

\n

$$\\operatorname{Var}(\\hat\\mu) = \\frac{1}{n}\\left(\\sigma^2 + \\frac{\\tau^2}{k}\\right)$$

\n

There are two ways to estimate parameters I am interested in (I am interested in mean estimate and the variance of the mean estimate).

\n

The first way is with moments (I can show the manipulations if needed):

\n

$$\\hat\\mu = \\frac{1}{n}\\sum_{i=1}^{n}\\hat p_i \\qquad \\text{estimates } \\mu$$

\n

$$S^2 = \\frac{1}{n-1}\\sum_{i=1}^{n}(\\hat p_i - \\hat\\mu)^2 \\qquad \\text{estimates } \\sigma^2 + \\frac{\\tau^2}{k}$$

\n

$$\\widehat{\\operatorname{Var}}(\\hat\\mu) = \\frac{S^2}{n} \\qquad \\text{estimates } \\operatorname{Var}(\\hat\\mu)$$

\n

And the second way is using MLE (delta method for variances and log/exp constraint for optimization).

\n

Here is an R script that simulates data, and compares estimates, precision and coverage for both methods. I made it so that mean and variance can be specified in the simulation (instead of a and b from the Beta distribution) at different values of $n,k$ for some fixed true mean and variance. I discard MLE fits with invalid Hessians/variance and I specifically chose the case where there is a large true variance):

\n
library(MASS)\n\nz <- qnorm(0.975)\n\n## Simulate \nmu_true <- 0.5\nv_true  <- 0.249\nn_vals  <- c(5, 10, 15, 20, 25, 50, 100, 200, 500,1000)\nk_vals  <- c(1, 2, 3, 4, 5, 6,7,8,9)\nR       <- 1000\n\n\nsim_data <- function(n, k, mu, v) {\n  nu <- mu * (1 - mu) / v - 1\n  rbinom(n, k, rbeta(n, mu * nu, (1 - mu) * nu))\n}\n\n## MLE \nbb_nll <- function(q, x, k)\n  length(x) * lbeta(exp(q[1]), exp(q[2])) -\n  sum(lbeta(exp(q[1]) + x, exp(q[2]) + k - x))\n\nfit_mle <- function(x, k) {\n  n <- length(x)\n  o <- try(optim(c(0, 0), bb_nll, x = x, k = k, method = "BFGS",\n                 hessian = TRUE), silent = TRUE)\n  if (inherits(o, "try-error")) return(c(NA, NA))\n  a <- exp(o$par[1]); b <- exp(o$par[2])\n  g <- a * b / (a + b)^2 * c(1, -1)\n  V <- try(drop(crossprod(g, ginv(o$hessian) %*% g)), silent = TRUE)\n  ok <- !inherits(V, \"try-error\") && is.finite(V) && V > 0 &&\n        V < 1 / (4 * n) && rcond(o$hessian) > 1e-10\n  c(a / (a + b), if (ok) V else NA)\n}\n\n## Moments\nfit_mom <- function(x, k) {\n  p <- x / k\n  c(mean(p), var(p) / length(p))\n}\n\nscore <- function(m, V, mu) {\n  s <- sqrt(V); ok <- is.finite(m)\n  data.frame(mean_estimate      = mean(m[ok]),\n             bias               = mean(m[ok]) - mu,\n             mc_se              = sd(m[ok]) / sqrt(sum(ok)),\n             sd_estimate        = sd(m[ok]),\n             variance_estimate  = mean(V, na.rm = TRUE),\n             length_of_interval = mean(2 * z * s, na.rm = TRUE),\n             coverage           = mean(abs(m - mu) <= z * s, na.rm = TRUE))\n}\n\nrun_cell <- function(mu, v, n, k, R, i, tot, t0) {\n  cat(sprintf("[%2d/%2d] n = %3d, k = %d ... ", i, tot, n, k))\n  e <- replicate(R, { x <- sim_data(n, k, mu, v)\n                      rbind(fit_mom(x, k), fit_mle(x, k)) })\n  cat(sprintf("done (%.1fs elapsed)\\n",\n              as.numeric(difftime(Sys.time(), t0, units = "secs"))))\n  cbind(true_mean = mu, true_variance = v, n = n, k = k,\n        true_var_of_mean = (v + (mu * (1 - mu) - v) / k) / n,\n        method = c("moments", "mle"),\n        rbind(score(e[1, 1, ], e[1, 2, ], mu),\n              score(e[2, 1, ], e[2, 2, ], mu)))\n}\n\n#Estimation\nset.seed(1)\ng  <- expand.grid(n = n_vals, k = k_vals)\nres <- do.call(rbind, Map(run_cell, mu_true, v_true, g$n, g$k,\n                          MoreArgs = list(R = R), i = seq_len(nrow(g)),\n                          tot = nrow(g), t0 = t0))\n
\n

Here are the results:

\n

\"enter\n\"enter

\n

Prior to running this script, I would have thought that larger $n,k$ combinations would produce less bias, tighter variances and better coverage rates. But for the MLE, it looks like this is not true. And for both Moments and MLE, it seems that sometimes coverage can sometimes decrease as $n$ increases (jagged pattern).

\n

Why is this happening?

\n", "question_id": 677094, "question_license": "CC BY-SA 4.0", "question_score": 3, "question_text": "Here is a beta-binomial model (treated like repeated measures - $i$ is an index for each individual, $n$ total individuals, and exactly $k$ measurements per individual):\n\n\n\n\n$$\\theta_i \\stackrel{\\text{iid}}{\\sim} \\mathrm{Beta}(a,b), \\qquad x_i \\mid \\theta_i \\sim \\mathrm{Binomial}(k,\\theta_i), \\qquad \\hat p_i = \\frac{x_i}{k}, \\qquad i = 1,\\dots,n$$\n\n\n\n\n$$\\mu = E[\\theta_i] = \\frac{a}{a+b}$$\n\n\n\n\n$$\\sigma^2 = \\operatorname{Var}(\\theta_i) = \\frac{ab}{(a+b)^2(a+b+1)}$$\n\n\n\n\n$$\\tau^2 = E[\\theta_i(1-\\theta_i)] = \\mu(1-\\mu) - \\sigma^2$$\n\n\n\n\nFor a single unit,\n\n\n\n\n$$E[\\hat p_i] = \\mu, \\qquad \\operatorname{Var}(\\hat p_i) = \\sigma^2 + \\frac{\\tau^2}{k}$$\n\n\n\n\nand\n\n\n\n\n$$\\operatorname{Var}(\\hat\\mu) = \\frac{1}{n}\\left(\\sigma^2 + \\frac{\\tau^2}{k}\\right)$$\n\n\n\n\nThere are two ways to estimate parameters I am interested in (I am interested in mean estimate and the variance of the mean estimate).\n\n\n\n\nThe first way is with moments (I can show the manipulations if needed):\n\n\n\n\n$$\\hat\\mu = \\frac{1}{n}\\sum_{i=1}^{n}\\hat p_i \\qquad \\text{estimates } \\mu$$\n\n\n\n\n$$S^2 = \\frac{1}{n-1}\\sum_{i=1}^{n}(\\hat p_i - \\hat\\mu)^2 \\qquad \\text{estimates } \\sigma^2 + \\frac{\\tau^2}{k}$$\n\n\n\n\n$$\\widehat{\\operatorname{Var}}(\\hat\\mu) = \\frac{S^2}{n} \\qquad \\text{estimates } \\operatorname{Var}(\\hat\\mu)$$\n\n\n\n\nAnd the second way is using MLE (delta method for variances and log/exp constraint for optimization).\n\n\n\n\nHere is an R script that simulates data, and compares estimates, precision and coverage for both methods. I made it so that mean and variance can be specified in the simulation (instead of a and b from the Beta distribution) at different values of $n,k$ for some fixed true mean and variance. I discard MLE fits with invalid Hessians/variance and I specifically chose the case where there is a large true variance):\n\n\n\n\nlibrary(MASS)\n\nz <- qnorm(0.975)\n\n## Simulate \nmu_true <- 0.5\nv_true <- 0.249\nn_vals <- c(5, 10, 15, 20, 25, 50, 100, 200, 500,1000)\nk_vals <- c(1, 2, 3, 4, 5, 6,7,8,9)\nR <- 1000\n\n\nsim_data <- function(n, k, mu, v) {\n nu <- mu * (1 - mu) / v - 1\n rbinom(n, k, rbeta(n, mu * nu, (1 - mu) * nu))\n}\n\n## MLE \nbb_nll <- function(q, x, k)\n length(x) * lbeta(exp(q[1]), exp(q[2])) -\n sum(lbeta(exp(q[1]) + x, exp(q[2]) + k - x))\n\nfit_mle <- function(x, k) {\n n <- length(x)\n o <- try(optim(c(0, 0), bb_nll, x = x, k = k, method = \"BFGS\",\n hessian = TRUE), silent = TRUE)\n if (inherits(o, \"try-error\")) return(c(NA, NA))\n a <- exp(o$par[1]); b <- exp(o$par[2])\n g <- a * b / (a + b)^2 * c(1, -1)\n V <- try(drop(crossprod(g, ginv(o$hessian) %*% g)), silent = TRUE)\n ok <- !inherits(V, \"try-error\") && is.finite(V) && V > 0 &&\n V < 1 / (4 * n) && rcond(o$hessian) > 1e-10\n c(a / (a + b), if (ok) V else NA)\n}\n\n## Moments\nfit_mom <- function(x, k) {\n p <- x / k\n c(mean(p), var(p) / length(p))\n}\n\nscore <- function(m, V, mu) {\n s <- sqrt(V); ok <- is.finite(m)\n data.frame(mean_estimate = mean(m[ok]),\n bias = mean(m[ok]) - mu,\n mc_se = sd(m[ok]) / sqrt(sum(ok)),\n sd_estimate = sd(m[ok]),\n variance_estimate = mean(V, na.rm = TRUE),\n length_of_interval = mean(2 * z * s, na.rm = TRUE),\n coverage = mean(abs(m - mu) <= z * s, na.rm = TRUE))\n}\n\nrun_cell <- function(mu, v, n, k, R, i, tot, t0) {\n cat(sprintf(\"[%2d/%2d] n = %3d, k = %d ... \", i, tot, n, k))\n e <- replicate(R, { x <- sim_data(n, k, mu, v)\n rbind(fit_mom(x, k), fit_mle(x, k)) })\n cat(sprintf(\"done (%.1fs elapsed)\\n\",\n as.numeric(difftime(Sys.time(), t0, units = \"secs\"))))\n cbind(true_mean = mu, true_variance = v, n = n, k = k,\n true_var_of_mean = (v + (mu * (1 - mu) - v) / k) / n,\n method = c(\"moments\", \"mle\"),\n rbind(score(e[1, 1, ], e[1, 2, ], mu),\n score(e[2, 1, ], e[2, 2, ], mu)))\n}\n\n#Estimation\nset.seed(1)\ng <- expand.grid(n = n_vals, k = k_vals)\nres <- do.call(rbind, Map(run_cell, mu_true, v_true, g$n, g$k,\n MoreArgs = list(R = R), i = seq_len(nrow(g)),\n tot = nrow(g), t0 = t0))\n\n\n\n\n\nHere are the results:\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/kEDelnub.png] (https://i.sstatic.net/kEDelnub.png)\n[image: enter image description here; source: https://i.sstatic.net/H3ywscwO.png] (https://i.sstatic.net/H3ywscwO.png)\n\n\n\n\nPrior to running this script, I would have thought that larger $n,k$ combinations would produce less bias, tighter variances and better coverage rates. But for the MLE, it looks like this is not true. And for both Moments and MLE, it seems that sometimes coverage can sometimes decrease as $n$ increases (jagged pattern).\n\n\n\n\nWhy is this happening?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "adamkostanov", "profile_url": "https://stats.stackexchange.com/users/512554/adamkostanov", "user_type": "registered"}, "created_at": "2026-09-07T06:07:31+00:00", "raw_file": "raw/codex_api_v1/3f959895a29b33d83894e5370d82e1c0cf87f20ac57fa423ebc923738357c657_1790825253957066500_0.json", "raw_sha256": "ddd8808039e410ca99f97e2a7f12c307f046c4e5c3e184683bc12f816e6f49fc", "revision_guid": "BE06C153-8C52-4CC0-883B-294D30B035A1", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/BE06C153-8C52-4CC0-883B-294D30B035A1/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "adamkostanov", "profile_url": "https://stats.stackexchange.com/users/512554/adamkostanov", 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677117, "answers": [{"answer_html": "

The suspicion expressed in the comments is well-founded: your MLE function tends to not arrive at the true MLE. Since it is performing a search, I would expect a good MLE function to use the moment estimators as the starting point. Using the function below, the behavior you observed disappears, as shown by the equivalent plots.

\n

My fit_mle function is inspired by Rfast::betabinom.mle, adapted to handle edge cases.

\n
fit_mle <- function(x, k) {\n  m1 <- mean(x)\n  \n  if (k == 1 || all(x == 0) || all(x == k)) {\n    a <- max(m1*100/k, 1e-5)\n    b <- max(100 - a, 1e-5)\n    V <- NA\n  } else {\n    n <- length(x)\n    z1 <- sort(unique(x))\n    n1 <- tabulate(match(x, z1))\n    z2 <- sort(unique(k - x))\n    n2 <- tabulate(match(k - x, z2))\n    m2 <- mean(x^2)\n    d <- 1/(k*(m2/m1 - m1) - k + m1)\n    a <- (k*m1 - m2)*d\n    b <- (k - m1)*(k - m2/m1)*d\n    \n    if (!is.finite(a) || d < 0) {\n      a <- max(m1*100/k, 1e-5)\n      b <- max(100 - a, 1e-5)\n    } else if (a <= 0 || b <= 0) {\n      a <- max(m1*0.1/k, 1e-5)\n      b <- max(0.1 - a, 1e-5)\n    }\n    \n    for (i in 1:100) {\n      ab <- a + b\n      t1 <- digamma(ab) - digamma(k + ab)\n      S1 <- a*(sum(digamma(z1 + a)*n1) + n*(t1 - digamma(a)))\n      S2 <- b*(sum(digamma(z2 + b)*n2) + n*(t1 - digamma(b)))\n      t2 <- trigamma(ab) - trigamma(k + ab)\n      J11 <- a^2*(sum(trigamma(z1 + a)*n1) + n*(t2 - trigamma(a))) + S1\n      J22 <- b^2*(sum(trigamma(z2 + b)*n2) + n*(t2 - trigamma(b))) + S2\n      J12 <- a*b*t2*n\n      if (abs(detJ <- J11*J22 - J12^2) < 1e-12) break\n      step1 <- (J22*S1 - J12*S2)/detJ\n      step2 <- (J11*S2 - J12*S1)/detJ\n      if (abs(step1) + abs(step2) < 1e-8) break\n      step_norm <- 2/sqrt(step1^2 + step2^2)\n      \n      if (step_norm < 1) {\n        step1 <- step1*step_norm\n        step2 <- step2*step_norm\n      }\n      \n      a <- a*exp(-step1)\n      b <- b*exp(-step2)\n    }\n    \n    g <- a*b/(a + b)^2\n    V <- -(J11 + J22 + 2*J12)*g^2/detJ\n  }\n  \n  c(a/(a + b), if (is.finite(V) && V > 0 && V < 1 / (4 * n)) V else NA)\n}\n
\n

\"enter

\n

\"enter

\n

Full code:

\n
library(MASS)\n\nz <- qnorm(0.975)\n\n## Simulate \nmu_true <- 0.5\nv_true  <- 0.249\nn_vals  <- c(5, 10, 15, 20, 25, 50, 100, 200, 500,1000)\nk_vals  <- c(1, 2, 3, 4, 5, 6,7,8,9)\nR       <- 1000\n\n\nsim_data <- function(n, k, mu, v) {\n  nu <- mu * (1 - mu) / v - 1\n  rbinom(n, k, rbeta(n, mu * nu, (1 - mu) * nu))\n}\n\n## MLE \nfit_mle <- function(x, k) {\n  xx <<- x\n  kk <<- k\n  m1 <- mean(x)\n  \n  if (k == 1 || all(x == 0) || all(x == k)) {\n    a <- max(m1*100/k, 1e-5)\n    b <- max(100 - a, 1e-5)\n    V <- NA\n  } else {\n    n <- length(x)\n    z1 <- sort(unique(x))\n    n1 <- tabulate(match(x, z1))\n    z2 <- sort(unique(k - x))\n    n2 <- tabulate(match(k - x, z2))\n    m2 <- mean(x^2)\n    d <- 1/(k*(m2/m1 - m1) - k + m1)\n    a <- (k*m1 - m2)*d\n    b <- (k - m1)*(k - m2/m1)*d\n    \n    if (!is.finite(a) || d < 0) {\n      a <- max(m1*100/k, 1e-5)\n      b <- max(100 - a, 1e-5)\n    } else if (a <= 0 || b <= 0) {\n      a <- max(m1*0.1/k, 1e-5)\n      b <- max(0.1 - a, 1e-5)\n    }\n    \n    for (i in 1:100) {\n      ab <- a + b\n      t1 <- digamma(ab) - digamma(k + ab)\n      S1 <- a*(sum(digamma(z1 + a)*n1) + n*(t1 - digamma(a)))\n      S2 <- b*(sum(digamma(z2 + b)*n2) + n*(t1 - digamma(b)))\n      t2 <- trigamma(ab) - trigamma(k + ab)\n      J11 <- a^2*(sum(trigamma(z1 + a)*n1) + n*(t2 - trigamma(a))) + S1\n      J22 <- b^2*(sum(trigamma(z2 + b)*n2) + n*(t2 - trigamma(b))) + S2\n      J12 <- a*b*t2*n\n      if (abs(detJ <- J11*J22 - J12^2) < 1e-12) break\n      step1 <- (J22*S1 - J12*S2)/detJ\n      step2 <- (J11*S2 - J12*S1)/detJ\n      if (abs(step1) + abs(step2) < 1e-8) break\n      step_norm <- 2/sqrt(step1^2 + step2^2)\n      \n      if (step_norm < 1) {\n        step1 <- step1*step_norm\n        step2 <- step2*step_norm\n      }\n      \n      a <- a*exp(-step1)\n      b <- b*exp(-step2)\n    }\n    \n    g <- a*b/(a + b)^2\n    V <- -(J11 + J22 + 2*J12)*g^2/detJ\n  }\n  \n  c(a/(a + b), if (is.finite(V) && V > 0 && V < 1 / (4 * n)) V else NA)\n}\n\n## Moments\nfit_mom <- function(x, k) {\n  p <- x / k\n  c(mean(p), var(p) / length(p))\n}\n\nscore <- function(m, V, mu) {\n  s <- sqrt(V); ok <- is.finite(m)\n  data.frame(mean_estimate      = mean(m[ok]),\n             bias               = mean(m[ok]) - mu,\n             mc_se              = sd(m[ok]) / sqrt(sum(ok)),\n             sd_estimate        = sd(m[ok]),\n             variance_estimate  = mean(V, na.rm = TRUE),\n             length_of_interval = mean(2 * z * s, na.rm = TRUE),\n             coverage           = mean(abs(m - mu) <= z * s, na.rm = TRUE))\n}\n\nrun_cell <- function(mu, v, n, k, R, i, tot, t0) {\n  cat(sprintf("[%2d/%2d] n = %3d, k = %d ... ", i, tot, n, k))\n  e <- replicate(R, { x <- sim_data(n, k, mu, v)\n  rbind(fit_mom(x, k), fit_mle(x, k)) })\n  cat(sprintf("done (%.1fs elapsed)\\n",\n              as.numeric(difftime(Sys.time(), t0, units = "secs"))))\n  cbind(true_mean = mu, true_variance = v, n = n, k = k,\n        true_var_of_mean = (v + (mu * (1 - mu) - v) / k) / n,\n        method = c("moments", "mle"),\n        rbind(score(e[1, 1, ], e[1, 2, ], mu),\n              score(e[2, 1, ], e[2, 2, ], mu)))\n}\n\n#Estimation\nset.seed(1)\nt0 <- Sys.time()\ng  <- expand.grid(n = n_vals, k = k_vals)\nres <- do.call(rbind, Map(run_cell, mu_true, v_true, g$n, g$k,\n                          MoreArgs = list(R = R), i = seq_len(nrow(g)),\n                          tot = nrow(g), t0 = t0))\n\nlibrary(ggplot2)\nlibrary(patchwork)\n\nres_df <- as.data.frame(res, stringsAsFactors = FALSE)\nnum_cols <- c("true_mean", "true_variance", "n", "k", "true_var_of_mean", \n              "mean_estimate", "bias", "mc_se", "sd_estimate", \n              "variance_estimate", "length_of_interval", "coverage")\nres_df[num_cols] <- lapply(res_df[num_cols], as.numeric)\nres_df$k_factor <- as.factor(res_df$k)\n\ndf_mom <- subset(res_df, method == "moments")\ndf_mle <- subset(res_df, method == "mle")\n\n# Helper function to generate the panels\nmake_panel <- function(data, metric_col, title, subtitle, y_label, hline = NULL) {\n  p <- ggplot(data, aes(x = n, y = .data[[metric_col]], color = k_factor)) +\n    geom_line(linewidth = 0.5) +\n    geom_point(size = 1.5) +\n    labs(title = title, subtitle = subtitle, x = "n", y = y_label, color = "k") +\n    theme_bw() +\n    theme(legend.position = "bottom",\n          plot.title = element_text(hjust = 0),\n          plot.subtitle = element_text(hjust = 0))\n  \n  if (!is.null(hline)) {\n    p <- p + geom_hline(yintercept = hline, linetype = "dashed", linewidth = 0.5)\n  }\n  return(p)\n}\n\np1 <- make_panel(df_mom, "bias", "Moments: bias of the estimated mean", \n                 "Average estimate minus the truth. Dashed line at 0.", "bias", 0)\np2 <- make_panel(df_mle, "bias", "MLE: bias of the estimated mean", \n                 "Average estimate minus the truth. Dashed line at 0.", "bias", 0)\np3 <- make_panel(df_mom, "sd_estimate", "Moments: SD of the estimated mean", \n                 "Spread of the estimate across studies.", "SD")\np4 <- make_panel(df_mle, "sd_estimate", "MLE: SD of the estimated mean", \n                 "Spread of the estimate across studies.", "SD")\n\n# Combine using patchwork\ncombined_grid <- (p1 + p2) / (p3 + p4)\nprint(combined_grid)\n\np_cov <- ggplot(res_df, aes(x = n, y = coverage, color = method)) +\n  geom_line(linewidth = 0.5) +\n  geom_point(size = 1.5) +\n  geom_hline(yintercept = 0.95, linetype = "dashed") +\n  facet_grid(~ k, labeller = label_both) +\n  labs(title = "Coverage of the nominal 95% interval",\n       subtitle = "Share of 1000 intervals containing the true mean. Dashed line at 0.95.",\n       x = "n",\n       y = "coverage",\n       color = "method") +\n  theme_bw() +\n  theme(legend.position = "bottom",\n        strip.background = element_rect(fill = "grey90"))\n\nprint(p_cov)\n
\n", "answer_id": 677117, "answer_text": "The suspicion expressed in the comments is well-founded: your MLE function tends to not arrive at the true MLE. Since it is performing a search, I would expect a good MLE function to use the moment estimators as the starting point. Using the function below, the behavior you observed disappears, as shown by the equivalent plots.\n\n\n\n\nMy fit_mle function is inspired by Rfast::betabinom.mle, adapted to handle edge cases.\n\n\n\n\nfit_mle <- function(x, k) {\n m1 <- mean(x)\n \n if (k == 1 || all(x == 0) || all(x == k)) {\n a <- max(m1*100/k, 1e-5)\n b <- max(100 - a, 1e-5)\n V <- NA\n } else {\n n <- length(x)\n z1 <- sort(unique(x))\n n1 <- tabulate(match(x, z1))\n z2 <- sort(unique(k - x))\n n2 <- tabulate(match(k - x, z2))\n m2 <- mean(x^2)\n d <- 1/(k*(m2/m1 - m1) - k + m1)\n a <- (k*m1 - m2)*d\n b <- (k - m1)*(k - m2/m1)*d\n \n if (!is.finite(a) || d < 0) {\n a <- max(m1*100/k, 1e-5)\n b <- max(100 - a, 1e-5)\n } else if (a <= 0 || b <= 0) {\n a <- max(m1*0.1/k, 1e-5)\n b <- max(0.1 - a, 1e-5)\n }\n \n for (i in 1:100) {\n ab <- a + b\n t1 <- digamma(ab) - digamma(k + ab)\n S1 <- a*(sum(digamma(z1 + a)*n1) + n*(t1 - digamma(a)))\n S2 <- b*(sum(digamma(z2 + b)*n2) + n*(t1 - digamma(b)))\n t2 <- trigamma(ab) - trigamma(k + ab)\n J11 <- a^2*(sum(trigamma(z1 + a)*n1) + n*(t2 - trigamma(a))) + S1\n J22 <- b^2*(sum(trigamma(z2 + b)*n2) + n*(t2 - trigamma(b))) + S2\n J12 <- a*b*t2*n\n if (abs(detJ <- J11*J22 - J12^2) < 1e-12) break\n step1 <- (J22*S1 - J12*S2)/detJ\n step2 <- (J11*S2 - J12*S1)/detJ\n if (abs(step1) + abs(step2) < 1e-8) break\n step_norm <- 2/sqrt(step1^2 + step2^2)\n \n if (step_norm < 1) {\n step1 <- step1*step_norm\n step2 <- step2*step_norm\n }\n \n a <- a*exp(-step1)\n b <- b*exp(-step2)\n }\n \n g <- a*b/(a + b)^2\n V <- -(J11 + J22 + 2*J12)*g^2/detJ\n }\n \n c(a/(a + b), if (is.finite(V) && V > 0 && V < 1 / (4 * n)) V else NA)\n}\n\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/yrEHvkk0.png] (https://i.sstatic.net/yrEHvkk0.png)\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/9nEiiFBK.png] (https://i.sstatic.net/9nEiiFBK.png)\n\n\n\n\nFull code:\n\n\n\n\nlibrary(MASS)\n\nz <- qnorm(0.975)\n\n## Simulate \nmu_true <- 0.5\nv_true <- 0.249\nn_vals <- c(5, 10, 15, 20, 25, 50, 100, 200, 500,1000)\nk_vals <- c(1, 2, 3, 4, 5, 6,7,8,9)\nR <- 1000\n\n\nsim_data <- function(n, k, mu, v) {\n nu <- mu * (1 - mu) / v - 1\n rbinom(n, k, rbeta(n, mu * nu, (1 - mu) * nu))\n}\n\n## MLE \nfit_mle <- function(x, k) {\n xx <<- x\n kk <<- k\n m1 <- mean(x)\n \n if (k == 1 || all(x == 0) || all(x == k)) {\n a <- max(m1*100/k, 1e-5)\n b <- max(100 - a, 1e-5)\n V <- NA\n } else {\n n <- length(x)\n z1 <- sort(unique(x))\n n1 <- tabulate(match(x, z1))\n z2 <- sort(unique(k - x))\n n2 <- tabulate(match(k - x, z2))\n m2 <- mean(x^2)\n d <- 1/(k*(m2/m1 - m1) - k + m1)\n a <- (k*m1 - m2)*d\n b <- (k - m1)*(k - m2/m1)*d\n \n if (!is.finite(a) || d < 0) {\n a <- max(m1*100/k, 1e-5)\n b <- max(100 - a, 1e-5)\n } else if (a <= 0 || b <= 0) {\n a <- max(m1*0.1/k, 1e-5)\n b <- max(0.1 - a, 1e-5)\n }\n \n for (i in 1:100) {\n ab <- a + b\n t1 <- digamma(ab) - digamma(k + ab)\n S1 <- a*(sum(digamma(z1 + a)*n1) + n*(t1 - digamma(a)))\n S2 <- b*(sum(digamma(z2 + b)*n2) + n*(t1 - digamma(b)))\n t2 <- trigamma(ab) - trigamma(k + ab)\n J11 <- a^2*(sum(trigamma(z1 + a)*n1) + n*(t2 - trigamma(a))) + S1\n J22 <- b^2*(sum(trigamma(z2 + b)*n2) + n*(t2 - trigamma(b))) + S2\n J12 <- a*b*t2*n\n if (abs(detJ <- J11*J22 - J12^2) < 1e-12) break\n step1 <- (J22*S1 - J12*S2)/detJ\n step2 <- (J11*S2 - J12*S1)/detJ\n if (abs(step1) + abs(step2) < 1e-8) break\n step_norm <- 2/sqrt(step1^2 + step2^2)\n \n if (step_norm < 1) {\n step1 <- step1*step_norm\n step2 <- step2*step_norm\n }\n \n a <- a*exp(-step1)\n b <- b*exp(-step2)\n }\n \n g <- a*b/(a + b)^2\n V <- -(J11 + J22 + 2*J12)*g^2/detJ\n }\n \n c(a/(a + b), if (is.finite(V) && V > 0 && V < 1 / (4 * n)) V else NA)\n}\n\n## Moments\nfit_mom <- function(x, k) {\n p <- x / k\n c(mean(p), var(p) / length(p))\n}\n\nscore <- function(m, V, mu) {\n s <- sqrt(V); ok <- is.finite(m)\n data.frame(mean_estimate = mean(m[ok]),\n bias = mean(m[ok]) - mu,\n mc_se = sd(m[ok]) / sqrt(sum(ok)),\n sd_estimate = sd(m[ok]),\n variance_estimate = mean(V, na.rm = TRUE),\n length_of_interval = mean(2 * z * s, na.rm = TRUE),\n coverage = mean(abs(m - mu) <= z * s, na.rm = TRUE))\n}\n\nrun_cell <- function(mu, v, n, k, R, i, tot, t0) {\n cat(sprintf(\"[%2d/%2d] n = %3d, k = %d ... \", i, tot, n, k))\n e <- replicate(R, { x <- sim_data(n, k, mu, v)\n rbind(fit_mom(x, k), fit_mle(x, k)) })\n cat(sprintf(\"done (%.1fs elapsed)\\n\",\n as.numeric(difftime(Sys.time(), t0, units = \"secs\"))))\n cbind(true_mean = mu, true_variance = v, n = n, k = k,\n true_var_of_mean = (v + (mu * (1 - mu) - v) / k) / n,\n method = c(\"moments\", \"mle\"),\n rbind(score(e[1, 1, ], e[1, 2, ], mu),\n score(e[2, 1, ], e[2, 2, ], mu)))\n}\n\n#Estimation\nset.seed(1)\nt0 <- Sys.time()\ng <- expand.grid(n = n_vals, k = k_vals)\nres <- do.call(rbind, Map(run_cell, mu_true, v_true, g$n, g$k,\n MoreArgs = list(R = R), i = seq_len(nrow(g)),\n tot = nrow(g), t0 = t0))\n\nlibrary(ggplot2)\nlibrary(patchwork)\n\nres_df <- as.data.frame(res, stringsAsFactors = FALSE)\nnum_cols <- c(\"true_mean\", \"true_variance\", \"n\", \"k\", \"true_var_of_mean\", \n \"mean_estimate\", \"bias\", \"mc_se\", \"sd_estimate\", \n \"variance_estimate\", \"length_of_interval\", \"coverage\")\nres_df[num_cols] <- lapply(res_df[num_cols], as.numeric)\nres_df$k_factor <- as.factor(res_df$k)\n\ndf_mom <- subset(res_df, method == \"moments\")\ndf_mle <- subset(res_df, method == \"mle\")\n\n# Helper function to generate the panels\nmake_panel <- function(data, metric_col, title, subtitle, y_label, hline = NULL) {\n p <- ggplot(data, aes(x = n, y = .data[[metric_col]], color = k_factor)) +\n geom_line(linewidth = 0.5) +\n geom_point(size = 1.5) +\n labs(title = title, subtitle = subtitle, x = \"n\", y = y_label, color = \"k\") +\n theme_bw() +\n theme(legend.position = \"bottom\",\n plot.title = element_text(hjust = 0),\n plot.subtitle = element_text(hjust = 0))\n \n if (!is.null(hline)) {\n p <- p + geom_hline(yintercept = hline, linetype = \"dashed\", linewidth = 0.5)\n }\n return(p)\n}\n\np1 <- make_panel(df_mom, \"bias\", \"Moments: bias of the estimated mean\", \n \"Average estimate minus the truth. Dashed line at 0.\", \"bias\", 0)\np2 <- make_panel(df_mle, \"bias\", \"MLE: bias of the estimated mean\", \n \"Average estimate minus the truth. Dashed line at 0.\", \"bias\", 0)\np3 <- make_panel(df_mom, \"sd_estimate\", \"Moments: SD of the estimated mean\", \n \"Spread of the estimate across studies.\", \"SD\")\np4 <- make_panel(df_mle, \"sd_estimate\", \"MLE: SD of the estimated mean\", \n \"Spread of the estimate across studies.\", \"SD\")\n\n# Combine using patchwork\ncombined_grid <- (p1 + p2) / (p3 + p4)\nprint(combined_grid)\n\np_cov <- ggplot(res_df, aes(x = n, y = coverage, color = method)) +\n geom_line(linewidth = 0.5) +\n geom_point(size = 1.5) +\n geom_hline(yintercept = 0.95, linetype = \"dashed\") +\n facet_grid(~ k, labeller = label_both) +\n labs(title = \"Coverage of the nominal 95% interval\",\n subtitle = \"Share of 1000 intervals containing the true mean. Dashed line at 0.95.\",\n x = \"n\",\n y = \"coverage\",\n color = \"method\") +\n theme_bw() +\n theme(legend.position = \"bottom\",\n strip.background = element_rect(fill = \"grey90\"))\n\nprint(p_cov)", "answer_url": "https://stats.stackexchange.com/a/677117", "author": "jblood94", "author_url": "https://stats.stackexchange.com/users/214015/jblood94", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-09T13:02:57+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677094, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "jblood94", "profile_url": "https://stats.stackexchange.com/users/214015/jblood94", "user_type": "registered"}, "created_at": "2026-09-09T13:02:57+00:00", "raw_file": "raw/codex_api_v1/3f959895a29b33d83894e5370d82e1c0cf87f20ac57fa423ebc923738357c657_1790825253957066500_0.json", "raw_sha256": "ddd8808039e410ca99f97e2a7f12c307f046c4e5c3e184683bc12f816e6f49fc", "revision_guid": "09E52470-6B69-4568-A8B3-D52476EA341B", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/09E52470-6B69-4568-A8B3-D52476EA341B/view-source"}, {"content_license": null, "contributor": {"display_name": "adamkostanov", "profile_url": "https://stats.stackexchange.com/users/512554/adamkostanov", "user_type": "registered"}, "created_at": "2026-09-16T13:07:32+00:00", "raw_file": "raw/codex_api_v1/59f98009db0ac38325a869c60e3993040b07f5fbd07014051415831400b70d25_1790825251781774200_0.json", "raw_sha256": "2876465103b1eeb5d593dd46b1ec52a862c1da72f8e4767e5f8ee70ff0564119", "revision_guid": "20C3E36B-1564-462F-9257-5BBE5B9B70EF", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/20C3E36B-1564-462F-9257-5BBE5B9B70EF/view-source"}], "score": 3, "updated_at": "2026-09-09T13:02:57+00:00"}], "domain": "statistics", "external_links": ["https://i.sstatic.net/9nEiiFBK.png", "https://i.sstatic.net/H3ywscwO.png", "https://i.sstatic.net/kEDelnub.png", "https://i.sstatic.net/yrEHvkk0.png"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "adamkostanov", "question_author_url": "https://stats.stackexchange.com/users/512554/adamkostanov", "question_author_user_type": "registered", "question_created_at": "2026-09-07T06:07:31+00:00", "question_html": "

Here is a beta-binomial model (treated like repeated measures - $i$ is an index for each individual, $n$ total individuals, and exactly $k$ measurements per individual):

\n

$$\\theta_i \\stackrel{\\text{iid}}{\\sim} \\mathrm{Beta}(a,b), \\qquad x_i \\mid \\theta_i \\sim \\mathrm{Binomial}(k,\\theta_i), \\qquad \\hat p_i = \\frac{x_i}{k}, \\qquad i = 1,\\dots,n$$

\n

$$\\mu = E[\\theta_i] = \\frac{a}{a+b}$$

\n

$$\\sigma^2 = \\operatorname{Var}(\\theta_i) = \\frac{ab}{(a+b)^2(a+b+1)}$$

\n

$$\\tau^2 = E[\\theta_i(1-\\theta_i)] = \\mu(1-\\mu) - \\sigma^2$$

\n

For a single unit,

\n

$$E[\\hat p_i] = \\mu, \\qquad \\operatorname{Var}(\\hat p_i) = \\sigma^2 + \\frac{\\tau^2}{k}$$

\n

and

\n

$$\\operatorname{Var}(\\hat\\mu) = \\frac{1}{n}\\left(\\sigma^2 + \\frac{\\tau^2}{k}\\right)$$

\n

There are two ways to estimate parameters I am interested in (I am interested in mean estimate and the variance of the mean estimate).

\n

The first way is with moments (I can show the manipulations if needed):

\n

$$\\hat\\mu = \\frac{1}{n}\\sum_{i=1}^{n}\\hat p_i \\qquad \\text{estimates } \\mu$$

\n

$$S^2 = \\frac{1}{n-1}\\sum_{i=1}^{n}(\\hat p_i - \\hat\\mu)^2 \\qquad \\text{estimates } \\sigma^2 + \\frac{\\tau^2}{k}$$

\n

$$\\widehat{\\operatorname{Var}}(\\hat\\mu) = \\frac{S^2}{n} \\qquad \\text{estimates } \\operatorname{Var}(\\hat\\mu)$$

\n

And the second way is using MLE (delta method for variances and log/exp constraint for optimization).

\n

Here is an R script that simulates data, and compares estimates, precision and coverage for both methods. I made it so that mean and variance can be specified in the simulation (instead of a and b from the Beta distribution) at different values of $n,k$ for some fixed true mean and variance. I discard MLE fits with invalid Hessians/variance and I specifically chose the case where there is a large true variance):

\n
library(MASS)\n\nz <- qnorm(0.975)\n\n## Simulate \nmu_true <- 0.5\nv_true  <- 0.249\nn_vals  <- c(5, 10, 15, 20, 25, 50, 100, 200, 500,1000)\nk_vals  <- c(1, 2, 3, 4, 5, 6,7,8,9)\nR       <- 1000\n\n\nsim_data <- function(n, k, mu, v) {\n  nu <- mu * (1 - mu) / v - 1\n  rbinom(n, k, rbeta(n, mu * nu, (1 - mu) * nu))\n}\n\n## MLE \nbb_nll <- function(q, x, k)\n  length(x) * lbeta(exp(q[1]), exp(q[2])) -\n  sum(lbeta(exp(q[1]) + x, exp(q[2]) + k - x))\n\nfit_mle <- function(x, k) {\n  n <- length(x)\n  o <- try(optim(c(0, 0), bb_nll, x = x, k = k, method = "BFGS",\n                 hessian = TRUE), silent = TRUE)\n  if (inherits(o, "try-error")) return(c(NA, NA))\n  a <- exp(o$par[1]); b <- exp(o$par[2])\n  g <- a * b / (a + b)^2 * c(1, -1)\n  V <- try(drop(crossprod(g, ginv(o$hessian) %*% g)), silent = TRUE)\n  ok <- !inherits(V, \"try-error\") && is.finite(V) && V > 0 &&\n        V < 1 / (4 * n) && rcond(o$hessian) > 1e-10\n  c(a / (a + b), if (ok) V else NA)\n}\n\n## Moments\nfit_mom <- function(x, k) {\n  p <- x / k\n  c(mean(p), var(p) / length(p))\n}\n\nscore <- function(m, V, mu) {\n  s <- sqrt(V); ok <- is.finite(m)\n  data.frame(mean_estimate      = mean(m[ok]),\n             bias               = mean(m[ok]) - mu,\n             mc_se              = sd(m[ok]) / sqrt(sum(ok)),\n             sd_estimate        = sd(m[ok]),\n             variance_estimate  = mean(V, na.rm = TRUE),\n             length_of_interval = mean(2 * z * s, na.rm = TRUE),\n             coverage           = mean(abs(m - mu) <= z * s, na.rm = TRUE))\n}\n\nrun_cell <- function(mu, v, n, k, R, i, tot, t0) {\n  cat(sprintf("[%2d/%2d] n = %3d, k = %d ... ", i, tot, n, k))\n  e <- replicate(R, { x <- sim_data(n, k, mu, v)\n                      rbind(fit_mom(x, k), fit_mle(x, k)) })\n  cat(sprintf("done (%.1fs elapsed)\\n",\n              as.numeric(difftime(Sys.time(), t0, units = "secs"))))\n  cbind(true_mean = mu, true_variance = v, n = n, k = k,\n        true_var_of_mean = (v + (mu * (1 - mu) - v) / k) / n,\n        method = c("moments", "mle"),\n        rbind(score(e[1, 1, ], e[1, 2, ], mu),\n              score(e[2, 1, ], e[2, 2, ], mu)))\n}\n\n#Estimation\nset.seed(1)\ng  <- expand.grid(n = n_vals, k = k_vals)\nres <- do.call(rbind, Map(run_cell, mu_true, v_true, g$n, g$k,\n                          MoreArgs = list(R = R), i = seq_len(nrow(g)),\n                          tot = nrow(g), t0 = t0))\n
\n

Here are the results:

\n

\"enter\n\"enter

\n

Prior to running this script, I would have thought that larger $n,k$ combinations would produce less bias, tighter variances and better coverage rates. But for the MLE, it looks like this is not true. And for both Moments and MLE, it seems that sometimes coverage can sometimes decrease as $n$ increases (jagged pattern).

\n

Why is this happening?

\n", "question_id": 677094, "question_license": "CC BY-SA 4.0", "question_score": 3, "question_text": "Here is a beta-binomial model (treated like repeated measures - $i$ is an index for each individual, $n$ total individuals, and exactly $k$ measurements per individual):\n\n\n\n\n$$\\theta_i \\stackrel{\\text{iid}}{\\sim} \\mathrm{Beta}(a,b), \\qquad x_i \\mid \\theta_i \\sim \\mathrm{Binomial}(k,\\theta_i), \\qquad \\hat p_i = \\frac{x_i}{k}, \\qquad i = 1,\\dots,n$$\n\n\n\n\n$$\\mu = E[\\theta_i] = \\frac{a}{a+b}$$\n\n\n\n\n$$\\sigma^2 = \\operatorname{Var}(\\theta_i) = \\frac{ab}{(a+b)^2(a+b+1)}$$\n\n\n\n\n$$\\tau^2 = E[\\theta_i(1-\\theta_i)] = \\mu(1-\\mu) - \\sigma^2$$\n\n\n\n\nFor a single unit,\n\n\n\n\n$$E[\\hat p_i] = \\mu, \\qquad \\operatorname{Var}(\\hat p_i) = \\sigma^2 + \\frac{\\tau^2}{k}$$\n\n\n\n\nand\n\n\n\n\n$$\\operatorname{Var}(\\hat\\mu) = \\frac{1}{n}\\left(\\sigma^2 + \\frac{\\tau^2}{k}\\right)$$\n\n\n\n\nThere are two ways to estimate parameters I am interested in (I am interested in mean estimate and the variance of the mean estimate).\n\n\n\n\nThe first way is with moments (I can show the manipulations if needed):\n\n\n\n\n$$\\hat\\mu = \\frac{1}{n}\\sum_{i=1}^{n}\\hat p_i \\qquad \\text{estimates } \\mu$$\n\n\n\n\n$$S^2 = \\frac{1}{n-1}\\sum_{i=1}^{n}(\\hat p_i - \\hat\\mu)^2 \\qquad \\text{estimates } \\sigma^2 + \\frac{\\tau^2}{k}$$\n\n\n\n\n$$\\widehat{\\operatorname{Var}}(\\hat\\mu) = \\frac{S^2}{n} \\qquad \\text{estimates } \\operatorname{Var}(\\hat\\mu)$$\n\n\n\n\nAnd the second way is using MLE (delta method for variances and log/exp constraint for optimization).\n\n\n\n\nHere is an R script that simulates data, and compares estimates, precision and coverage for both methods. I made it so that mean and variance can be specified in the simulation (instead of a and b from the Beta distribution) at different values of $n,k$ for some fixed true mean and variance. I discard MLE fits with invalid Hessians/variance and I specifically chose the case where there is a large true variance):\n\n\n\n\nlibrary(MASS)\n\nz <- qnorm(0.975)\n\n## Simulate \nmu_true <- 0.5\nv_true <- 0.249\nn_vals <- c(5, 10, 15, 20, 25, 50, 100, 200, 500,1000)\nk_vals <- c(1, 2, 3, 4, 5, 6,7,8,9)\nR <- 1000\n\n\nsim_data <- function(n, k, mu, v) {\n nu <- mu * (1 - mu) / v - 1\n rbinom(n, k, rbeta(n, mu * nu, (1 - mu) * nu))\n}\n\n## MLE \nbb_nll <- function(q, x, k)\n length(x) * lbeta(exp(q[1]), exp(q[2])) -\n sum(lbeta(exp(q[1]) + x, exp(q[2]) + k - x))\n\nfit_mle <- function(x, k) {\n n <- length(x)\n o <- try(optim(c(0, 0), bb_nll, x = x, k = k, method = \"BFGS\",\n hessian = TRUE), silent = TRUE)\n if (inherits(o, \"try-error\")) return(c(NA, NA))\n a <- exp(o$par[1]); b <- exp(o$par[2])\n g <- a * b / (a + b)^2 * c(1, -1)\n V <- try(drop(crossprod(g, ginv(o$hessian) %*% g)), silent = TRUE)\n ok <- !inherits(V, \"try-error\") && is.finite(V) && V > 0 &&\n V < 1 / (4 * n) && rcond(o$hessian) > 1e-10\n c(a / (a + b), if (ok) V else NA)\n}\n\n## Moments\nfit_mom <- function(x, k) {\n p <- x / k\n c(mean(p), var(p) / length(p))\n}\n\nscore <- function(m, V, mu) {\n s <- sqrt(V); ok <- is.finite(m)\n data.frame(mean_estimate = mean(m[ok]),\n bias = mean(m[ok]) - mu,\n mc_se = sd(m[ok]) / sqrt(sum(ok)),\n sd_estimate = sd(m[ok]),\n variance_estimate = mean(V, na.rm = TRUE),\n length_of_interval = mean(2 * z * s, na.rm = TRUE),\n coverage = mean(abs(m - mu) <= z * s, na.rm = TRUE))\n}\n\nrun_cell <- function(mu, v, n, k, R, i, tot, t0) {\n cat(sprintf(\"[%2d/%2d] n = %3d, k = %d ... \", i, tot, n, k))\n e <- replicate(R, { x <- sim_data(n, k, mu, v)\n rbind(fit_mom(x, k), fit_mle(x, k)) })\n cat(sprintf(\"done (%.1fs elapsed)\\n\",\n as.numeric(difftime(Sys.time(), t0, units = \"secs\"))))\n cbind(true_mean = mu, true_variance = v, n = n, k = k,\n true_var_of_mean = (v + (mu * (1 - mu) - v) / k) / n,\n method = c(\"moments\", \"mle\"),\n rbind(score(e[1, 1, ], e[1, 2, ], mu),\n score(e[2, 1, ], e[2, 2, ], mu)))\n}\n\n#Estimation\nset.seed(1)\ng <- expand.grid(n = n_vals, k = k_vals)\nres <- do.call(rbind, Map(run_cell, mu_true, v_true, g$n, g$k,\n MoreArgs = list(R = R), i = seq_len(nrow(g)),\n tot = nrow(g), t0 = t0))\n\n\n\n\n\nHere are the results:\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/kEDelnub.png] (https://i.sstatic.net/kEDelnub.png)\n[image: enter image description here; source: https://i.sstatic.net/H3ywscwO.png] (https://i.sstatic.net/H3ywscwO.png)\n\n\n\n\nPrior to running this script, I would have thought that larger $n,k$ combinations would produce less bias, tighter variances and better coverage rates. But for the MLE, it looks like this is not true. And for both Moments and MLE, it seems that sometimes coverage can sometimes decrease as $n$ increases (jagged pattern).\n\n\n\n\nWhy is this happening?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "adamkostanov", "profile_url": "https://stats.stackexchange.com/users/512554/adamkostanov", "user_type": "registered"}, "created_at": "2026-09-07T06:07:31+00:00", "raw_file": "raw/codex_api_v1/3f959895a29b33d83894e5370d82e1c0cf87f20ac57fa423ebc923738357c657_1790825253957066500_0.json", "raw_sha256": "ddd8808039e410ca99f97e2a7f12c307f046c4e5c3e184683bc12f816e6f49fc", "revision_guid": "BE06C153-8C52-4CC0-883B-294D30B035A1", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/BE06C153-8C52-4CC0-883B-294D30B035A1/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "adamkostanov", "profile_url": "https://stats.stackexchange.com/users/512554/adamkostanov", 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The suspicion expressed in the comments is well-founded: your MLE function tends to not arrive at the true MLE. Since it is performing a search, I would expect a good MLE function to use the moment estimators as the starting point. Using the function below, the behavior you observed disappears, as shown by the equivalent plots.

\n

My fit_mle function is inspired by Rfast::betabinom.mle, adapted to handle edge cases.

\n
fit_mle <- function(x, k) {\n  m1 <- mean(x)\n  \n  if (k == 1 || all(x == 0) || all(x == k)) {\n    a <- max(m1*100/k, 1e-5)\n    b <- max(100 - a, 1e-5)\n    V <- NA\n  } else {\n    n <- length(x)\n    z1 <- sort(unique(x))\n    n1 <- tabulate(match(x, z1))\n    z2 <- sort(unique(k - x))\n    n2 <- tabulate(match(k - x, z2))\n    m2 <- mean(x^2)\n    d <- 1/(k*(m2/m1 - m1) - k + m1)\n    a <- (k*m1 - m2)*d\n    b <- (k - m1)*(k - m2/m1)*d\n    \n    if (!is.finite(a) || d < 0) {\n      a <- max(m1*100/k, 1e-5)\n      b <- max(100 - a, 1e-5)\n    } else if (a <= 0 || b <= 0) {\n      a <- max(m1*0.1/k, 1e-5)\n      b <- max(0.1 - a, 1e-5)\n    }\n    \n    for (i in 1:100) {\n      ab <- a + b\n      t1 <- digamma(ab) - digamma(k + ab)\n      S1 <- a*(sum(digamma(z1 + a)*n1) + n*(t1 - digamma(a)))\n      S2 <- b*(sum(digamma(z2 + b)*n2) + n*(t1 - digamma(b)))\n      t2 <- trigamma(ab) - trigamma(k + ab)\n      J11 <- a^2*(sum(trigamma(z1 + a)*n1) + n*(t2 - trigamma(a))) + S1\n      J22 <- b^2*(sum(trigamma(z2 + b)*n2) + n*(t2 - trigamma(b))) + S2\n      J12 <- a*b*t2*n\n      if (abs(detJ <- J11*J22 - J12^2) < 1e-12) break\n      step1 <- (J22*S1 - J12*S2)/detJ\n      step2 <- (J11*S2 - J12*S1)/detJ\n      if (abs(step1) + abs(step2) < 1e-8) break\n      step_norm <- 2/sqrt(step1^2 + step2^2)\n      \n      if (step_norm < 1) {\n        step1 <- step1*step_norm\n        step2 <- step2*step_norm\n      }\n      \n      a <- a*exp(-step1)\n      b <- b*exp(-step2)\n    }\n    \n    g <- a*b/(a + b)^2\n    V <- -(J11 + J22 + 2*J12)*g^2/detJ\n  }\n  \n  c(a/(a + b), if (is.finite(V) && V > 0 && V < 1 / (4 * n)) V else NA)\n}\n
\n

\"enter

\n

\"enter

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Full code:

\n
library(MASS)\n\nz <- qnorm(0.975)\n\n## Simulate \nmu_true <- 0.5\nv_true  <- 0.249\nn_vals  <- c(5, 10, 15, 20, 25, 50, 100, 200, 500,1000)\nk_vals  <- c(1, 2, 3, 4, 5, 6,7,8,9)\nR       <- 1000\n\n\nsim_data <- function(n, k, mu, v) {\n  nu <- mu * (1 - mu) / v - 1\n  rbinom(n, k, rbeta(n, mu * nu, (1 - mu) * nu))\n}\n\n## MLE \nfit_mle <- function(x, k) {\n  xx <<- x\n  kk <<- k\n  m1 <- mean(x)\n  \n  if (k == 1 || all(x == 0) || all(x == k)) {\n    a <- max(m1*100/k, 1e-5)\n    b <- max(100 - a, 1e-5)\n    V <- NA\n  } else {\n    n <- length(x)\n    z1 <- sort(unique(x))\n    n1 <- tabulate(match(x, z1))\n    z2 <- sort(unique(k - x))\n    n2 <- tabulate(match(k - x, z2))\n    m2 <- mean(x^2)\n    d <- 1/(k*(m2/m1 - m1) - k + m1)\n    a <- (k*m1 - m2)*d\n    b <- (k - m1)*(k - m2/m1)*d\n    \n    if (!is.finite(a) || d < 0) {\n      a <- max(m1*100/k, 1e-5)\n      b <- max(100 - a, 1e-5)\n    } else if (a <= 0 || b <= 0) {\n      a <- max(m1*0.1/k, 1e-5)\n      b <- max(0.1 - a, 1e-5)\n    }\n    \n    for (i in 1:100) {\n      ab <- a + b\n      t1 <- digamma(ab) - digamma(k + ab)\n      S1 <- a*(sum(digamma(z1 + a)*n1) + n*(t1 - digamma(a)))\n      S2 <- b*(sum(digamma(z2 + b)*n2) + n*(t1 - digamma(b)))\n      t2 <- trigamma(ab) - trigamma(k + ab)\n      J11 <- a^2*(sum(trigamma(z1 + a)*n1) + n*(t2 - trigamma(a))) + S1\n      J22 <- b^2*(sum(trigamma(z2 + b)*n2) + n*(t2 - trigamma(b))) + S2\n      J12 <- a*b*t2*n\n      if (abs(detJ <- J11*J22 - J12^2) < 1e-12) break\n      step1 <- (J22*S1 - J12*S2)/detJ\n      step2 <- (J11*S2 - J12*S1)/detJ\n      if (abs(step1) + abs(step2) < 1e-8) break\n      step_norm <- 2/sqrt(step1^2 + step2^2)\n      \n      if (step_norm < 1) {\n        step1 <- step1*step_norm\n        step2 <- step2*step_norm\n      }\n      \n      a <- a*exp(-step1)\n      b <- b*exp(-step2)\n    }\n    \n    g <- a*b/(a + b)^2\n    V <- -(J11 + J22 + 2*J12)*g^2/detJ\n  }\n  \n  c(a/(a + b), if (is.finite(V) && V > 0 && V < 1 / (4 * n)) V else NA)\n}\n\n## Moments\nfit_mom <- function(x, k) {\n  p <- x / k\n  c(mean(p), var(p) / length(p))\n}\n\nscore <- function(m, V, mu) {\n  s <- sqrt(V); ok <- is.finite(m)\n  data.frame(mean_estimate      = mean(m[ok]),\n             bias               = mean(m[ok]) - mu,\n             mc_se              = sd(m[ok]) / sqrt(sum(ok)),\n             sd_estimate        = sd(m[ok]),\n             variance_estimate  = mean(V, na.rm = TRUE),\n             length_of_interval = mean(2 * z * s, na.rm = TRUE),\n             coverage           = mean(abs(m - mu) <= z * s, na.rm = TRUE))\n}\n\nrun_cell <- function(mu, v, n, k, R, i, tot, t0) {\n  cat(sprintf("[%2d/%2d] n = %3d, k = %d ... ", i, tot, n, k))\n  e <- replicate(R, { x <- sim_data(n, k, mu, v)\n  rbind(fit_mom(x, k), fit_mle(x, k)) })\n  cat(sprintf("done (%.1fs elapsed)\\n",\n              as.numeric(difftime(Sys.time(), t0, units = "secs"))))\n  cbind(true_mean = mu, true_variance = v, n = n, k = k,\n        true_var_of_mean = (v + (mu * (1 - mu) - v) / k) / n,\n        method = c("moments", "mle"),\n        rbind(score(e[1, 1, ], e[1, 2, ], mu),\n              score(e[2, 1, ], e[2, 2, ], mu)))\n}\n\n#Estimation\nset.seed(1)\nt0 <- Sys.time()\ng  <- expand.grid(n = n_vals, k = k_vals)\nres <- do.call(rbind, Map(run_cell, mu_true, v_true, g$n, g$k,\n                          MoreArgs = list(R = R), i = seq_len(nrow(g)),\n                          tot = nrow(g), t0 = t0))\n\nlibrary(ggplot2)\nlibrary(patchwork)\n\nres_df <- as.data.frame(res, stringsAsFactors = FALSE)\nnum_cols <- c("true_mean", "true_variance", "n", "k", "true_var_of_mean", \n              "mean_estimate", "bias", "mc_se", "sd_estimate", \n              "variance_estimate", "length_of_interval", "coverage")\nres_df[num_cols] <- lapply(res_df[num_cols], as.numeric)\nres_df$k_factor <- as.factor(res_df$k)\n\ndf_mom <- subset(res_df, method == "moments")\ndf_mle <- subset(res_df, method == "mle")\n\n# Helper function to generate the panels\nmake_panel <- function(data, metric_col, title, subtitle, y_label, hline = NULL) {\n  p <- ggplot(data, aes(x = n, y = .data[[metric_col]], color = k_factor)) +\n    geom_line(linewidth = 0.5) +\n    geom_point(size = 1.5) +\n    labs(title = title, subtitle = subtitle, x = "n", y = y_label, color = "k") +\n    theme_bw() +\n    theme(legend.position = "bottom",\n          plot.title = element_text(hjust = 0),\n          plot.subtitle = element_text(hjust = 0))\n  \n  if (!is.null(hline)) {\n    p <- p + geom_hline(yintercept = hline, linetype = "dashed", linewidth = 0.5)\n  }\n  return(p)\n}\n\np1 <- make_panel(df_mom, "bias", "Moments: bias of the estimated mean", \n                 "Average estimate minus the truth. Dashed line at 0.", "bias", 0)\np2 <- make_panel(df_mle, "bias", "MLE: bias of the estimated mean", \n                 "Average estimate minus the truth. Dashed line at 0.", "bias", 0)\np3 <- make_panel(df_mom, "sd_estimate", "Moments: SD of the estimated mean", \n                 "Spread of the estimate across studies.", "SD")\np4 <- make_panel(df_mle, "sd_estimate", "MLE: SD of the estimated mean", \n                 "Spread of the estimate across studies.", "SD")\n\n# Combine using patchwork\ncombined_grid <- (p1 + p2) / (p3 + p4)\nprint(combined_grid)\n\np_cov <- ggplot(res_df, aes(x = n, y = coverage, color = method)) +\n  geom_line(linewidth = 0.5) +\n  geom_point(size = 1.5) +\n  geom_hline(yintercept = 0.95, linetype = "dashed") +\n  facet_grid(~ k, labeller = label_both) +\n  labs(title = "Coverage of the nominal 95% interval",\n       subtitle = "Share of 1000 intervals containing the true mean. Dashed line at 0.95.",\n       x = "n",\n       y = "coverage",\n       color = "method") +\n  theme_bw() +\n  theme(legend.position = "bottom",\n        strip.background = element_rect(fill = "grey90"))\n\nprint(p_cov)\n
\n", "answer_id": 677117, "answer_text": "The suspicion expressed in the comments is well-founded: your MLE function tends to not arrive at the true MLE. Since it is performing a search, I would expect a good MLE function to use the moment estimators as the starting point. Using the function below, the behavior you observed disappears, as shown by the equivalent plots.\n\n\n\n\nMy fit_mle function is inspired by Rfast::betabinom.mle, adapted to handle edge cases.\n\n\n\n\nfit_mle <- function(x, k) {\n m1 <- mean(x)\n \n if (k == 1 || all(x == 0) || all(x == k)) {\n a <- max(m1*100/k, 1e-5)\n b <- max(100 - a, 1e-5)\n V <- NA\n } else {\n n <- length(x)\n z1 <- sort(unique(x))\n n1 <- tabulate(match(x, z1))\n z2 <- sort(unique(k - x))\n n2 <- tabulate(match(k - x, z2))\n m2 <- mean(x^2)\n d <- 1/(k*(m2/m1 - m1) - k + m1)\n a <- (k*m1 - m2)*d\n b <- (k - m1)*(k - m2/m1)*d\n \n if (!is.finite(a) || d < 0) {\n a <- max(m1*100/k, 1e-5)\n b <- max(100 - a, 1e-5)\n } else if (a <= 0 || b <= 0) {\n a <- max(m1*0.1/k, 1e-5)\n b <- max(0.1 - a, 1e-5)\n }\n \n for (i in 1:100) {\n ab <- a + b\n t1 <- digamma(ab) - digamma(k + ab)\n S1 <- a*(sum(digamma(z1 + a)*n1) + n*(t1 - digamma(a)))\n S2 <- b*(sum(digamma(z2 + b)*n2) + n*(t1 - digamma(b)))\n t2 <- trigamma(ab) - trigamma(k + ab)\n J11 <- a^2*(sum(trigamma(z1 + a)*n1) + n*(t2 - trigamma(a))) + S1\n J22 <- b^2*(sum(trigamma(z2 + b)*n2) + n*(t2 - trigamma(b))) + S2\n J12 <- a*b*t2*n\n if (abs(detJ <- J11*J22 - J12^2) < 1e-12) break\n step1 <- (J22*S1 - J12*S2)/detJ\n step2 <- (J11*S2 - J12*S1)/detJ\n if (abs(step1) + abs(step2) < 1e-8) break\n step_norm <- 2/sqrt(step1^2 + step2^2)\n \n if (step_norm < 1) {\n step1 <- step1*step_norm\n step2 <- step2*step_norm\n }\n \n a <- a*exp(-step1)\n b <- b*exp(-step2)\n }\n \n g <- a*b/(a + b)^2\n V <- -(J11 + J22 + 2*J12)*g^2/detJ\n }\n \n c(a/(a + b), if (is.finite(V) && V > 0 && V < 1 / (4 * n)) V else NA)\n}\n\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/yrEHvkk0.png] (https://i.sstatic.net/yrEHvkk0.png)\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/9nEiiFBK.png] (https://i.sstatic.net/9nEiiFBK.png)\n\n\n\n\nFull code:\n\n\n\n\nlibrary(MASS)\n\nz <- qnorm(0.975)\n\n## Simulate \nmu_true <- 0.5\nv_true <- 0.249\nn_vals <- c(5, 10, 15, 20, 25, 50, 100, 200, 500,1000)\nk_vals <- c(1, 2, 3, 4, 5, 6,7,8,9)\nR <- 1000\n\n\nsim_data <- function(n, k, mu, v) {\n nu <- mu * (1 - mu) / v - 1\n rbinom(n, k, rbeta(n, mu * nu, (1 - mu) * nu))\n}\n\n## MLE \nfit_mle <- function(x, k) {\n xx <<- x\n kk <<- k\n m1 <- mean(x)\n \n if (k == 1 || all(x == 0) || all(x == k)) {\n a <- max(m1*100/k, 1e-5)\n b <- max(100 - a, 1e-5)\n V <- NA\n } else {\n n <- length(x)\n z1 <- sort(unique(x))\n n1 <- tabulate(match(x, z1))\n z2 <- sort(unique(k - x))\n n2 <- tabulate(match(k - x, z2))\n m2 <- mean(x^2)\n d <- 1/(k*(m2/m1 - m1) - k + m1)\n a <- (k*m1 - m2)*d\n b <- (k - m1)*(k - m2/m1)*d\n \n if (!is.finite(a) || d < 0) {\n a <- max(m1*100/k, 1e-5)\n b <- max(100 - a, 1e-5)\n } else if (a <= 0 || b <= 0) {\n a <- max(m1*0.1/k, 1e-5)\n b <- max(0.1 - a, 1e-5)\n }\n \n for (i in 1:100) {\n ab <- a + b\n t1 <- digamma(ab) - digamma(k + ab)\n S1 <- a*(sum(digamma(z1 + a)*n1) + n*(t1 - digamma(a)))\n S2 <- b*(sum(digamma(z2 + b)*n2) + n*(t1 - digamma(b)))\n t2 <- trigamma(ab) - trigamma(k + ab)\n J11 <- a^2*(sum(trigamma(z1 + a)*n1) + n*(t2 - trigamma(a))) + S1\n J22 <- b^2*(sum(trigamma(z2 + b)*n2) + n*(t2 - trigamma(b))) + S2\n J12 <- a*b*t2*n\n if (abs(detJ <- J11*J22 - J12^2) < 1e-12) break\n step1 <- (J22*S1 - J12*S2)/detJ\n step2 <- (J11*S2 - J12*S1)/detJ\n if (abs(step1) + abs(step2) < 1e-8) break\n step_norm <- 2/sqrt(step1^2 + step2^2)\n \n if (step_norm < 1) {\n step1 <- step1*step_norm\n step2 <- step2*step_norm\n }\n \n a <- a*exp(-step1)\n b <- b*exp(-step2)\n }\n \n g <- a*b/(a + b)^2\n V <- -(J11 + J22 + 2*J12)*g^2/detJ\n }\n \n c(a/(a + b), if (is.finite(V) && V > 0 && V < 1 / (4 * n)) V else NA)\n}\n\n## Moments\nfit_mom <- function(x, k) {\n p <- x / k\n c(mean(p), var(p) / length(p))\n}\n\nscore <- function(m, V, mu) {\n s <- sqrt(V); ok <- is.finite(m)\n data.frame(mean_estimate = mean(m[ok]),\n bias = mean(m[ok]) - mu,\n mc_se = sd(m[ok]) / sqrt(sum(ok)),\n sd_estimate = sd(m[ok]),\n variance_estimate = mean(V, na.rm = TRUE),\n length_of_interval = mean(2 * z * s, na.rm = TRUE),\n coverage = mean(abs(m - mu) <= z * s, na.rm = TRUE))\n}\n\nrun_cell <- function(mu, v, n, k, R, i, tot, t0) {\n cat(sprintf(\"[%2d/%2d] n = %3d, k = %d ... \", i, tot, n, k))\n e <- replicate(R, { x <- sim_data(n, k, mu, v)\n rbind(fit_mom(x, k), fit_mle(x, k)) })\n cat(sprintf(\"done (%.1fs elapsed)\\n\",\n as.numeric(difftime(Sys.time(), t0, units = \"secs\"))))\n cbind(true_mean = mu, true_variance = v, n = n, k = k,\n true_var_of_mean = (v + (mu * (1 - mu) - v) / k) / n,\n method = c(\"moments\", \"mle\"),\n rbind(score(e[1, 1, ], e[1, 2, ], mu),\n score(e[2, 1, ], e[2, 2, ], mu)))\n}\n\n#Estimation\nset.seed(1)\nt0 <- Sys.time()\ng <- expand.grid(n = n_vals, k = k_vals)\nres <- do.call(rbind, Map(run_cell, mu_true, v_true, g$n, g$k,\n MoreArgs = list(R = R), i = seq_len(nrow(g)),\n tot = nrow(g), t0 = t0))\n\nlibrary(ggplot2)\nlibrary(patchwork)\n\nres_df <- as.data.frame(res, stringsAsFactors = FALSE)\nnum_cols <- c(\"true_mean\", \"true_variance\", \"n\", \"k\", \"true_var_of_mean\", \n \"mean_estimate\", \"bias\", \"mc_se\", \"sd_estimate\", \n \"variance_estimate\", \"length_of_interval\", \"coverage\")\nres_df[num_cols] <- lapply(res_df[num_cols], as.numeric)\nres_df$k_factor <- as.factor(res_df$k)\n\ndf_mom <- subset(res_df, method == \"moments\")\ndf_mle <- subset(res_df, method == \"mle\")\n\n# Helper function to generate the panels\nmake_panel <- function(data, metric_col, title, subtitle, y_label, hline = NULL) {\n p <- ggplot(data, aes(x = n, y = .data[[metric_col]], color = k_factor)) +\n geom_line(linewidth = 0.5) +\n geom_point(size = 1.5) +\n labs(title = title, subtitle = subtitle, x = \"n\", y = y_label, color = \"k\") +\n theme_bw() +\n theme(legend.position = \"bottom\",\n plot.title = element_text(hjust = 0),\n plot.subtitle = element_text(hjust = 0))\n \n if (!is.null(hline)) {\n p <- p + geom_hline(yintercept = hline, linetype = \"dashed\", linewidth = 0.5)\n }\n return(p)\n}\n\np1 <- make_panel(df_mom, \"bias\", \"Moments: bias of the estimated mean\", \n \"Average estimate minus the truth. Dashed line at 0.\", \"bias\", 0)\np2 <- make_panel(df_mle, \"bias\", \"MLE: bias of the estimated mean\", \n \"Average estimate minus the truth. Dashed line at 0.\", \"bias\", 0)\np3 <- make_panel(df_mom, \"sd_estimate\", \"Moments: SD of the estimated mean\", \n \"Spread of the estimate across studies.\", \"SD\")\np4 <- make_panel(df_mle, \"sd_estimate\", \"MLE: SD of the estimated mean\", \n \"Spread of the estimate across studies.\", \"SD\")\n\n# Combine using patchwork\ncombined_grid <- (p1 + p2) / (p3 + p4)\nprint(combined_grid)\n\np_cov <- ggplot(res_df, aes(x = n, y = coverage, color = method)) +\n geom_line(linewidth = 0.5) +\n geom_point(size = 1.5) +\n geom_hline(yintercept = 0.95, linetype = \"dashed\") +\n facet_grid(~ k, labeller = label_both) +\n labs(title = \"Coverage of the nominal 95% interval\",\n subtitle = \"Share of 1000 intervals containing the true mean. Dashed line at 0.95.\",\n x = \"n\",\n y = \"coverage\",\n color = \"method\") +\n theme_bw() +\n theme(legend.position = \"bottom\",\n strip.background = element_rect(fill = \"grey90\"))\n\nprint(p_cov)", "answer_url": "https://stats.stackexchange.com/a/677117", "author": "jblood94", "author_url": "https://stats.stackexchange.com/users/214015/jblood94", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-09T13:02:57+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677094, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "jblood94", "profile_url": "https://stats.stackexchange.com/users/214015/jblood94", "user_type": "registered"}, "created_at": "2026-09-09T13:02:57+00:00", "raw_file": "raw/codex_api_v1/3f959895a29b33d83894e5370d82e1c0cf87f20ac57fa423ebc923738357c657_1790825253957066500_0.json", "raw_sha256": "ddd8808039e410ca99f97e2a7f12c307f046c4e5c3e184683bc12f816e6f49fc", "revision_guid": "09E52470-6B69-4568-A8B3-D52476EA341B", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/09E52470-6B69-4568-A8B3-D52476EA341B/view-source"}, {"content_license": null, "contributor": {"display_name": "adamkostanov", "profile_url": "https://stats.stackexchange.com/users/512554/adamkostanov", "user_type": "registered"}, "created_at": "2026-09-16T13:07:32+00:00", "raw_file": "raw/codex_api_v1/59f98009db0ac38325a869c60e3993040b07f5fbd07014051415831400b70d25_1790825251781774200_0.json", "raw_sha256": "2876465103b1eeb5d593dd46b1ec52a862c1da72f8e4767e5f8ee70ff0564119", "revision_guid": "20C3E36B-1564-462F-9257-5BBE5B9B70EF", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/20C3E36B-1564-462F-9257-5BBE5B9B70EF/view-source"}], "score": 3, "updated_at": "2026-09-09T13:02:57+00:00"}], "domain": "statistics", "external_links": ["https://i.sstatic.net/9nEiiFBK.png", "https://i.sstatic.net/H3ywscwO.png", "https://i.sstatic.net/kEDelnub.png", "https://i.sstatic.net/yrEHvkk0.png"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "adamkostanov", "question_author_url": "https://stats.stackexchange.com/users/512554/adamkostanov", "question_author_user_type": "registered", "question_created_at": "2026-09-07T06:07:31+00:00", "question_html": "

Here is a beta-binomial model (treated like repeated measures - $i$ is an index for each individual, $n$ total individuals, and exactly $k$ measurements per individual):

\n

$$\\theta_i \\stackrel{\\text{iid}}{\\sim} \\mathrm{Beta}(a,b), \\qquad x_i \\mid \\theta_i \\sim \\mathrm{Binomial}(k,\\theta_i), \\qquad \\hat p_i = \\frac{x_i}{k}, \\qquad i = 1,\\dots,n$$

\n

$$\\mu = E[\\theta_i] = \\frac{a}{a+b}$$

\n

$$\\sigma^2 = \\operatorname{Var}(\\theta_i) = \\frac{ab}{(a+b)^2(a+b+1)}$$

\n

$$\\tau^2 = E[\\theta_i(1-\\theta_i)] = \\mu(1-\\mu) - \\sigma^2$$

\n

For a single unit,

\n

$$E[\\hat p_i] = \\mu, \\qquad \\operatorname{Var}(\\hat p_i) = \\sigma^2 + \\frac{\\tau^2}{k}$$

\n

and

\n

$$\\operatorname{Var}(\\hat\\mu) = \\frac{1}{n}\\left(\\sigma^2 + \\frac{\\tau^2}{k}\\right)$$

\n

There are two ways to estimate parameters I am interested in (I am interested in mean estimate and the variance of the mean estimate).

\n

The first way is with moments (I can show the manipulations if needed):

\n

$$\\hat\\mu = \\frac{1}{n}\\sum_{i=1}^{n}\\hat p_i \\qquad \\text{estimates } \\mu$$

\n

$$S^2 = \\frac{1}{n-1}\\sum_{i=1}^{n}(\\hat p_i - \\hat\\mu)^2 \\qquad \\text{estimates } \\sigma^2 + \\frac{\\tau^2}{k}$$

\n

$$\\widehat{\\operatorname{Var}}(\\hat\\mu) = \\frac{S^2}{n} \\qquad \\text{estimates } \\operatorname{Var}(\\hat\\mu)$$

\n

And the second way is using MLE (delta method for variances and log/exp constraint for optimization).

\n

Here is an R script that simulates data, and compares estimates, precision and coverage for both methods. I made it so that mean and variance can be specified in the simulation (instead of a and b from the Beta distribution) at different values of $n,k$ for some fixed true mean and variance. I discard MLE fits with invalid Hessians/variance and I specifically chose the case where there is a large true variance):

\n
library(MASS)\n\nz <- qnorm(0.975)\n\n## Simulate \nmu_true <- 0.5\nv_true  <- 0.249\nn_vals  <- c(5, 10, 15, 20, 25, 50, 100, 200, 500,1000)\nk_vals  <- c(1, 2, 3, 4, 5, 6,7,8,9)\nR       <- 1000\n\n\nsim_data <- function(n, k, mu, v) {\n  nu <- mu * (1 - mu) / v - 1\n  rbinom(n, k, rbeta(n, mu * nu, (1 - mu) * nu))\n}\n\n## MLE \nbb_nll <- function(q, x, k)\n  length(x) * lbeta(exp(q[1]), exp(q[2])) -\n  sum(lbeta(exp(q[1]) + x, exp(q[2]) + k - x))\n\nfit_mle <- function(x, k) {\n  n <- length(x)\n  o <- try(optim(c(0, 0), bb_nll, x = x, k = k, method = "BFGS",\n                 hessian = TRUE), silent = TRUE)\n  if (inherits(o, "try-error")) return(c(NA, NA))\n  a <- exp(o$par[1]); b <- exp(o$par[2])\n  g <- a * b / (a + b)^2 * c(1, -1)\n  V <- try(drop(crossprod(g, ginv(o$hessian) %*% g)), silent = TRUE)\n  ok <- !inherits(V, \"try-error\") && is.finite(V) && V > 0 &&\n        V < 1 / (4 * n) && rcond(o$hessian) > 1e-10\n  c(a / (a + b), if (ok) V else NA)\n}\n\n## Moments\nfit_mom <- function(x, k) {\n  p <- x / k\n  c(mean(p), var(p) / length(p))\n}\n\nscore <- function(m, V, mu) {\n  s <- sqrt(V); ok <- is.finite(m)\n  data.frame(mean_estimate      = mean(m[ok]),\n             bias               = mean(m[ok]) - mu,\n             mc_se              = sd(m[ok]) / sqrt(sum(ok)),\n             sd_estimate        = sd(m[ok]),\n             variance_estimate  = mean(V, na.rm = TRUE),\n             length_of_interval = mean(2 * z * s, na.rm = TRUE),\n             coverage           = mean(abs(m - mu) <= z * s, na.rm = TRUE))\n}\n\nrun_cell <- function(mu, v, n, k, R, i, tot, t0) {\n  cat(sprintf("[%2d/%2d] n = %3d, k = %d ... ", i, tot, n, k))\n  e <- replicate(R, { x <- sim_data(n, k, mu, v)\n                      rbind(fit_mom(x, k), fit_mle(x, k)) })\n  cat(sprintf("done (%.1fs elapsed)\\n",\n              as.numeric(difftime(Sys.time(), t0, units = "secs"))))\n  cbind(true_mean = mu, true_variance = v, n = n, k = k,\n        true_var_of_mean = (v + (mu * (1 - mu) - v) / k) / n,\n        method = c("moments", "mle"),\n        rbind(score(e[1, 1, ], e[1, 2, ], mu),\n              score(e[2, 1, ], e[2, 2, ], mu)))\n}\n\n#Estimation\nset.seed(1)\ng  <- expand.grid(n = n_vals, k = k_vals)\nres <- do.call(rbind, Map(run_cell, mu_true, v_true, g$n, g$k,\n                          MoreArgs = list(R = R), i = seq_len(nrow(g)),\n                          tot = nrow(g), t0 = t0))\n
\n

Here are the results:

\n

\"enter\n\"enter

\n

Prior to running this script, I would have thought that larger $n,k$ combinations would produce less bias, tighter variances and better coverage rates. But for the MLE, it looks like this is not true. And for both Moments and MLE, it seems that sometimes coverage can sometimes decrease as $n$ increases (jagged pattern).

\n

Why is this happening?

\n", "question_id": 677094, "question_license": "CC BY-SA 4.0", "question_score": 3, "question_text": "Here is a beta-binomial model (treated like repeated measures - $i$ is an index for each individual, $n$ total individuals, and exactly $k$ measurements per individual):\n\n\n\n\n$$\\theta_i \\stackrel{\\text{iid}}{\\sim} \\mathrm{Beta}(a,b), \\qquad x_i \\mid \\theta_i \\sim \\mathrm{Binomial}(k,\\theta_i), \\qquad \\hat p_i = \\frac{x_i}{k}, \\qquad i = 1,\\dots,n$$\n\n\n\n\n$$\\mu = E[\\theta_i] = \\frac{a}{a+b}$$\n\n\n\n\n$$\\sigma^2 = \\operatorname{Var}(\\theta_i) = \\frac{ab}{(a+b)^2(a+b+1)}$$\n\n\n\n\n$$\\tau^2 = E[\\theta_i(1-\\theta_i)] = \\mu(1-\\mu) - \\sigma^2$$\n\n\n\n\nFor a single unit,\n\n\n\n\n$$E[\\hat p_i] = \\mu, \\qquad \\operatorname{Var}(\\hat p_i) = \\sigma^2 + \\frac{\\tau^2}{k}$$\n\n\n\n\nand\n\n\n\n\n$$\\operatorname{Var}(\\hat\\mu) = \\frac{1}{n}\\left(\\sigma^2 + \\frac{\\tau^2}{k}\\right)$$\n\n\n\n\nThere are two ways to estimate parameters I am interested in (I am interested in mean estimate and the variance of the mean estimate).\n\n\n\n\nThe first way is with moments (I can show the manipulations if needed):\n\n\n\n\n$$\\hat\\mu = \\frac{1}{n}\\sum_{i=1}^{n}\\hat p_i \\qquad \\text{estimates } \\mu$$\n\n\n\n\n$$S^2 = \\frac{1}{n-1}\\sum_{i=1}^{n}(\\hat p_i - \\hat\\mu)^2 \\qquad \\text{estimates } \\sigma^2 + \\frac{\\tau^2}{k}$$\n\n\n\n\n$$\\widehat{\\operatorname{Var}}(\\hat\\mu) = \\frac{S^2}{n} \\qquad \\text{estimates } \\operatorname{Var}(\\hat\\mu)$$\n\n\n\n\nAnd the second way is using MLE (delta method for variances and log/exp constraint for optimization).\n\n\n\n\nHere is an R script that simulates data, and compares estimates, precision and coverage for both methods. I made it so that mean and variance can be specified in the simulation (instead of a and b from the Beta distribution) at different values of $n,k$ for some fixed true mean and variance. I discard MLE fits with invalid Hessians/variance and I specifically chose the case where there is a large true variance):\n\n\n\n\nlibrary(MASS)\n\nz <- qnorm(0.975)\n\n## Simulate \nmu_true <- 0.5\nv_true <- 0.249\nn_vals <- c(5, 10, 15, 20, 25, 50, 100, 200, 500,1000)\nk_vals <- c(1, 2, 3, 4, 5, 6,7,8,9)\nR <- 1000\n\n\nsim_data <- function(n, k, mu, v) {\n nu <- mu * (1 - mu) / v - 1\n rbinom(n, k, rbeta(n, mu * nu, (1 - mu) * nu))\n}\n\n## MLE \nbb_nll <- function(q, x, k)\n length(x) * lbeta(exp(q[1]), exp(q[2])) -\n sum(lbeta(exp(q[1]) + x, exp(q[2]) + k - x))\n\nfit_mle <- function(x, k) {\n n <- length(x)\n o <- try(optim(c(0, 0), bb_nll, x = x, k = k, method = \"BFGS\",\n hessian = TRUE), silent = TRUE)\n if (inherits(o, \"try-error\")) return(c(NA, NA))\n a <- exp(o$par[1]); b <- exp(o$par[2])\n g <- a * b / (a + b)^2 * c(1, -1)\n V <- try(drop(crossprod(g, ginv(o$hessian) %*% g)), silent = TRUE)\n ok <- !inherits(V, \"try-error\") && is.finite(V) && V > 0 &&\n V < 1 / (4 * n) && rcond(o$hessian) > 1e-10\n c(a / (a + b), if (ok) V else NA)\n}\n\n## Moments\nfit_mom <- function(x, k) {\n p <- x / k\n c(mean(p), var(p) / length(p))\n}\n\nscore <- function(m, V, mu) {\n s <- sqrt(V); ok <- is.finite(m)\n data.frame(mean_estimate = mean(m[ok]),\n bias = mean(m[ok]) - mu,\n mc_se = sd(m[ok]) / sqrt(sum(ok)),\n sd_estimate = sd(m[ok]),\n variance_estimate = mean(V, na.rm = TRUE),\n length_of_interval = mean(2 * z * s, na.rm = TRUE),\n coverage = mean(abs(m - mu) <= z * s, na.rm = TRUE))\n}\n\nrun_cell <- function(mu, v, n, k, R, i, tot, t0) {\n cat(sprintf(\"[%2d/%2d] n = %3d, k = %d ... \", i, tot, n, k))\n e <- replicate(R, { x <- sim_data(n, k, mu, v)\n rbind(fit_mom(x, k), fit_mle(x, k)) })\n cat(sprintf(\"done (%.1fs elapsed)\\n\",\n as.numeric(difftime(Sys.time(), t0, units = \"secs\"))))\n cbind(true_mean = mu, true_variance = v, n = n, k = k,\n true_var_of_mean = (v + (mu * (1 - mu) - v) / k) / n,\n method = c(\"moments\", \"mle\"),\n rbind(score(e[1, 1, ], e[1, 2, ], mu),\n score(e[2, 1, ], e[2, 2, ], mu)))\n}\n\n#Estimation\nset.seed(1)\ng <- expand.grid(n = n_vals, k = k_vals)\nres <- do.call(rbind, Map(run_cell, mu_true, v_true, g$n, g$k,\n MoreArgs = list(R = R), i = seq_len(nrow(g)),\n tot = nrow(g), t0 = t0))\n\n\n\n\n\nHere are the results:\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/kEDelnub.png] (https://i.sstatic.net/kEDelnub.png)\n[image: enter image description here; source: https://i.sstatic.net/H3ywscwO.png] (https://i.sstatic.net/H3ywscwO.png)\n\n\n\n\nPrior to running this script, I would have thought that larger $n,k$ combinations would produce less bias, tighter variances and better coverage rates. But for the MLE, it looks like this is not true. And for both Moments and MLE, it seems that sometimes coverage can sometimes decrease as $n$ increases (jagged pattern).\n\n\n\n\nWhy is this happening?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "adamkostanov", "profile_url": "https://stats.stackexchange.com/users/512554/adamkostanov", "user_type": "registered"}, "created_at": "2026-09-07T06:07:31+00:00", "raw_file": "raw/codex_api_v1/3f959895a29b33d83894e5370d82e1c0cf87f20ac57fa423ebc923738357c657_1790825253957066500_0.json", "raw_sha256": "ddd8808039e410ca99f97e2a7f12c307f046c4e5c3e184683bc12f816e6f49fc", "revision_guid": "BE06C153-8C52-4CC0-883B-294D30B035A1", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/BE06C153-8C52-4CC0-883B-294D30B035A1/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "adamkostanov", "profile_url": "https://stats.stackexchange.com/users/512554/adamkostanov", 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The suspicion expressed in the comments is well-founded: your MLE function tends to not arrive at the true MLE. Since it is performing a search, I would expect a good MLE function to use the moment estimators as the starting point. Using the function below, the behavior you observed disappears, as shown by the equivalent plots.

\n

My fit_mle function is inspired by Rfast::betabinom.mle, adapted to handle edge cases.

\n
fit_mle <- function(x, k) {\n  m1 <- mean(x)\n  \n  if (k == 1 || all(x == 0) || all(x == k)) {\n    a <- max(m1*100/k, 1e-5)\n    b <- max(100 - a, 1e-5)\n    V <- NA\n  } else {\n    n <- length(x)\n    z1 <- sort(unique(x))\n    n1 <- tabulate(match(x, z1))\n    z2 <- sort(unique(k - x))\n    n2 <- tabulate(match(k - x, z2))\n    m2 <- mean(x^2)\n    d <- 1/(k*(m2/m1 - m1) - k + m1)\n    a <- (k*m1 - m2)*d\n    b <- (k - m1)*(k - m2/m1)*d\n    \n    if (!is.finite(a) || d < 0) {\n      a <- max(m1*100/k, 1e-5)\n      b <- max(100 - a, 1e-5)\n    } else if (a <= 0 || b <= 0) {\n      a <- max(m1*0.1/k, 1e-5)\n      b <- max(0.1 - a, 1e-5)\n    }\n    \n    for (i in 1:100) {\n      ab <- a + b\n      t1 <- digamma(ab) - digamma(k + ab)\n      S1 <- a*(sum(digamma(z1 + a)*n1) + n*(t1 - digamma(a)))\n      S2 <- b*(sum(digamma(z2 + b)*n2) + n*(t1 - digamma(b)))\n      t2 <- trigamma(ab) - trigamma(k + ab)\n      J11 <- a^2*(sum(trigamma(z1 + a)*n1) + n*(t2 - trigamma(a))) + S1\n      J22 <- b^2*(sum(trigamma(z2 + b)*n2) + n*(t2 - trigamma(b))) + S2\n      J12 <- a*b*t2*n\n      if (abs(detJ <- J11*J22 - J12^2) < 1e-12) break\n      step1 <- (J22*S1 - J12*S2)/detJ\n      step2 <- (J11*S2 - J12*S1)/detJ\n      if (abs(step1) + abs(step2) < 1e-8) break\n      step_norm <- 2/sqrt(step1^2 + step2^2)\n      \n      if (step_norm < 1) {\n        step1 <- step1*step_norm\n        step2 <- step2*step_norm\n      }\n      \n      a <- a*exp(-step1)\n      b <- b*exp(-step2)\n    }\n    \n    g <- a*b/(a + b)^2\n    V <- -(J11 + J22 + 2*J12)*g^2/detJ\n  }\n  \n  c(a/(a + b), if (is.finite(V) && V > 0 && V < 1 / (4 * n)) V else NA)\n}\n
\n

\"enter

\n

\"enter

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Full code:

\n
library(MASS)\n\nz <- qnorm(0.975)\n\n## Simulate \nmu_true <- 0.5\nv_true  <- 0.249\nn_vals  <- c(5, 10, 15, 20, 25, 50, 100, 200, 500,1000)\nk_vals  <- c(1, 2, 3, 4, 5, 6,7,8,9)\nR       <- 1000\n\n\nsim_data <- function(n, k, mu, v) {\n  nu <- mu * (1 - mu) / v - 1\n  rbinom(n, k, rbeta(n, mu * nu, (1 - mu) * nu))\n}\n\n## MLE \nfit_mle <- function(x, k) {\n  xx <<- x\n  kk <<- k\n  m1 <- mean(x)\n  \n  if (k == 1 || all(x == 0) || all(x == k)) {\n    a <- max(m1*100/k, 1e-5)\n    b <- max(100 - a, 1e-5)\n    V <- NA\n  } else {\n    n <- length(x)\n    z1 <- sort(unique(x))\n    n1 <- tabulate(match(x, z1))\n    z2 <- sort(unique(k - x))\n    n2 <- tabulate(match(k - x, z2))\n    m2 <- mean(x^2)\n    d <- 1/(k*(m2/m1 - m1) - k + m1)\n    a <- (k*m1 - m2)*d\n    b <- (k - m1)*(k - m2/m1)*d\n    \n    if (!is.finite(a) || d < 0) {\n      a <- max(m1*100/k, 1e-5)\n      b <- max(100 - a, 1e-5)\n    } else if (a <= 0 || b <= 0) {\n      a <- max(m1*0.1/k, 1e-5)\n      b <- max(0.1 - a, 1e-5)\n    }\n    \n    for (i in 1:100) {\n      ab <- a + b\n      t1 <- digamma(ab) - digamma(k + ab)\n      S1 <- a*(sum(digamma(z1 + a)*n1) + n*(t1 - digamma(a)))\n      S2 <- b*(sum(digamma(z2 + b)*n2) + n*(t1 - digamma(b)))\n      t2 <- trigamma(ab) - trigamma(k + ab)\n      J11 <- a^2*(sum(trigamma(z1 + a)*n1) + n*(t2 - trigamma(a))) + S1\n      J22 <- b^2*(sum(trigamma(z2 + b)*n2) + n*(t2 - trigamma(b))) + S2\n      J12 <- a*b*t2*n\n      if (abs(detJ <- J11*J22 - J12^2) < 1e-12) break\n      step1 <- (J22*S1 - J12*S2)/detJ\n      step2 <- (J11*S2 - J12*S1)/detJ\n      if (abs(step1) + abs(step2) < 1e-8) break\n      step_norm <- 2/sqrt(step1^2 + step2^2)\n      \n      if (step_norm < 1) {\n        step1 <- step1*step_norm\n        step2 <- step2*step_norm\n      }\n      \n      a <- a*exp(-step1)\n      b <- b*exp(-step2)\n    }\n    \n    g <- a*b/(a + b)^2\n    V <- -(J11 + J22 + 2*J12)*g^2/detJ\n  }\n  \n  c(a/(a + b), if (is.finite(V) && V > 0 && V < 1 / (4 * n)) V else NA)\n}\n\n## Moments\nfit_mom <- function(x, k) {\n  p <- x / k\n  c(mean(p), var(p) / length(p))\n}\n\nscore <- function(m, V, mu) {\n  s <- sqrt(V); ok <- is.finite(m)\n  data.frame(mean_estimate      = mean(m[ok]),\n             bias               = mean(m[ok]) - mu,\n             mc_se              = sd(m[ok]) / sqrt(sum(ok)),\n             sd_estimate        = sd(m[ok]),\n             variance_estimate  = mean(V, na.rm = TRUE),\n             length_of_interval = mean(2 * z * s, na.rm = TRUE),\n             coverage           = mean(abs(m - mu) <= z * s, na.rm = TRUE))\n}\n\nrun_cell <- function(mu, v, n, k, R, i, tot, t0) {\n  cat(sprintf("[%2d/%2d] n = %3d, k = %d ... ", i, tot, n, k))\n  e <- replicate(R, { x <- sim_data(n, k, mu, v)\n  rbind(fit_mom(x, k), fit_mle(x, k)) })\n  cat(sprintf("done (%.1fs elapsed)\\n",\n              as.numeric(difftime(Sys.time(), t0, units = "secs"))))\n  cbind(true_mean = mu, true_variance = v, n = n, k = k,\n        true_var_of_mean = (v + (mu * (1 - mu) - v) / k) / n,\n        method = c("moments", "mle"),\n        rbind(score(e[1, 1, ], e[1, 2, ], mu),\n              score(e[2, 1, ], e[2, 2, ], mu)))\n}\n\n#Estimation\nset.seed(1)\nt0 <- Sys.time()\ng  <- expand.grid(n = n_vals, k = k_vals)\nres <- do.call(rbind, Map(run_cell, mu_true, v_true, g$n, g$k,\n                          MoreArgs = list(R = R), i = seq_len(nrow(g)),\n                          tot = nrow(g), t0 = t0))\n\nlibrary(ggplot2)\nlibrary(patchwork)\n\nres_df <- as.data.frame(res, stringsAsFactors = FALSE)\nnum_cols <- c("true_mean", "true_variance", "n", "k", "true_var_of_mean", \n              "mean_estimate", "bias", "mc_se", "sd_estimate", \n              "variance_estimate", "length_of_interval", "coverage")\nres_df[num_cols] <- lapply(res_df[num_cols], as.numeric)\nres_df$k_factor <- as.factor(res_df$k)\n\ndf_mom <- subset(res_df, method == "moments")\ndf_mle <- subset(res_df, method == "mle")\n\n# Helper function to generate the panels\nmake_panel <- function(data, metric_col, title, subtitle, y_label, hline = NULL) {\n  p <- ggplot(data, aes(x = n, y = .data[[metric_col]], color = k_factor)) +\n    geom_line(linewidth = 0.5) +\n    geom_point(size = 1.5) +\n    labs(title = title, subtitle = subtitle, x = "n", y = y_label, color = "k") +\n    theme_bw() +\n    theme(legend.position = "bottom",\n          plot.title = element_text(hjust = 0),\n          plot.subtitle = element_text(hjust = 0))\n  \n  if (!is.null(hline)) {\n    p <- p + geom_hline(yintercept = hline, linetype = "dashed", linewidth = 0.5)\n  }\n  return(p)\n}\n\np1 <- make_panel(df_mom, "bias", "Moments: bias of the estimated mean", \n                 "Average estimate minus the truth. Dashed line at 0.", "bias", 0)\np2 <- make_panel(df_mle, "bias", "MLE: bias of the estimated mean", \n                 "Average estimate minus the truth. Dashed line at 0.", "bias", 0)\np3 <- make_panel(df_mom, "sd_estimate", "Moments: SD of the estimated mean", \n                 "Spread of the estimate across studies.", "SD")\np4 <- make_panel(df_mle, "sd_estimate", "MLE: SD of the estimated mean", \n                 "Spread of the estimate across studies.", "SD")\n\n# Combine using patchwork\ncombined_grid <- (p1 + p2) / (p3 + p4)\nprint(combined_grid)\n\np_cov <- ggplot(res_df, aes(x = n, y = coverage, color = method)) +\n  geom_line(linewidth = 0.5) +\n  geom_point(size = 1.5) +\n  geom_hline(yintercept = 0.95, linetype = "dashed") +\n  facet_grid(~ k, labeller = label_both) +\n  labs(title = "Coverage of the nominal 95% interval",\n       subtitle = "Share of 1000 intervals containing the true mean. Dashed line at 0.95.",\n       x = "n",\n       y = "coverage",\n       color = "method") +\n  theme_bw() +\n  theme(legend.position = "bottom",\n        strip.background = element_rect(fill = "grey90"))\n\nprint(p_cov)\n
\n", "answer_id": 677117, "answer_text": "The suspicion expressed in the comments is well-founded: your MLE function tends to not arrive at the true MLE. Since it is performing a search, I would expect a good MLE function to use the moment estimators as the starting point. Using the function below, the behavior you observed disappears, as shown by the equivalent plots.\n\n\n\n\nMy fit_mle function is inspired by Rfast::betabinom.mle, adapted to handle edge cases.\n\n\n\n\nfit_mle <- function(x, k) {\n m1 <- mean(x)\n \n if (k == 1 || all(x == 0) || all(x == k)) {\n a <- max(m1*100/k, 1e-5)\n b <- max(100 - a, 1e-5)\n V <- NA\n } else {\n n <- length(x)\n z1 <- sort(unique(x))\n n1 <- tabulate(match(x, z1))\n z2 <- sort(unique(k - x))\n n2 <- tabulate(match(k - x, z2))\n m2 <- mean(x^2)\n d <- 1/(k*(m2/m1 - m1) - k + m1)\n a <- (k*m1 - m2)*d\n b <- (k - m1)*(k - m2/m1)*d\n \n if (!is.finite(a) || d < 0) {\n a <- max(m1*100/k, 1e-5)\n b <- max(100 - a, 1e-5)\n } else if (a <= 0 || b <= 0) {\n a <- max(m1*0.1/k, 1e-5)\n b <- max(0.1 - a, 1e-5)\n }\n \n for (i in 1:100) {\n ab <- a + b\n t1 <- digamma(ab) - digamma(k + ab)\n S1 <- a*(sum(digamma(z1 + a)*n1) + n*(t1 - digamma(a)))\n S2 <- b*(sum(digamma(z2 + b)*n2) + n*(t1 - digamma(b)))\n t2 <- trigamma(ab) - trigamma(k + ab)\n J11 <- a^2*(sum(trigamma(z1 + a)*n1) + n*(t2 - trigamma(a))) + S1\n J22 <- b^2*(sum(trigamma(z2 + b)*n2) + n*(t2 - trigamma(b))) + S2\n J12 <- a*b*t2*n\n if (abs(detJ <- J11*J22 - J12^2) < 1e-12) break\n step1 <- (J22*S1 - J12*S2)/detJ\n step2 <- (J11*S2 - J12*S1)/detJ\n if (abs(step1) + abs(step2) < 1e-8) break\n step_norm <- 2/sqrt(step1^2 + step2^2)\n \n if (step_norm < 1) {\n step1 <- step1*step_norm\n step2 <- step2*step_norm\n }\n \n a <- a*exp(-step1)\n b <- b*exp(-step2)\n }\n \n g <- a*b/(a + b)^2\n V <- -(J11 + J22 + 2*J12)*g^2/detJ\n }\n \n c(a/(a + b), if (is.finite(V) && V > 0 && V < 1 / (4 * n)) V else NA)\n}\n\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/yrEHvkk0.png] (https://i.sstatic.net/yrEHvkk0.png)\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/9nEiiFBK.png] (https://i.sstatic.net/9nEiiFBK.png)\n\n\n\n\nFull code:\n\n\n\n\nlibrary(MASS)\n\nz <- qnorm(0.975)\n\n## Simulate \nmu_true <- 0.5\nv_true <- 0.249\nn_vals <- c(5, 10, 15, 20, 25, 50, 100, 200, 500,1000)\nk_vals <- c(1, 2, 3, 4, 5, 6,7,8,9)\nR <- 1000\n\n\nsim_data <- function(n, k, mu, v) {\n nu <- mu * (1 - mu) / v - 1\n rbinom(n, k, rbeta(n, mu * nu, (1 - mu) * nu))\n}\n\n## MLE \nfit_mle <- function(x, k) {\n xx <<- x\n kk <<- k\n m1 <- mean(x)\n \n if (k == 1 || all(x == 0) || all(x == k)) {\n a <- max(m1*100/k, 1e-5)\n b <- max(100 - a, 1e-5)\n V <- NA\n } else {\n n <- length(x)\n z1 <- sort(unique(x))\n n1 <- tabulate(match(x, z1))\n z2 <- sort(unique(k - x))\n n2 <- tabulate(match(k - x, z2))\n m2 <- mean(x^2)\n d <- 1/(k*(m2/m1 - m1) - k + m1)\n a <- (k*m1 - m2)*d\n b <- (k - m1)*(k - m2/m1)*d\n \n if (!is.finite(a) || d < 0) {\n a <- max(m1*100/k, 1e-5)\n b <- max(100 - a, 1e-5)\n } else if (a <= 0 || b <= 0) {\n a <- max(m1*0.1/k, 1e-5)\n b <- max(0.1 - a, 1e-5)\n }\n \n for (i in 1:100) {\n ab <- a + b\n t1 <- digamma(ab) - digamma(k + ab)\n S1 <- a*(sum(digamma(z1 + a)*n1) + n*(t1 - digamma(a)))\n S2 <- b*(sum(digamma(z2 + b)*n2) + n*(t1 - digamma(b)))\n t2 <- trigamma(ab) - trigamma(k + ab)\n J11 <- a^2*(sum(trigamma(z1 + a)*n1) + n*(t2 - trigamma(a))) + S1\n J22 <- b^2*(sum(trigamma(z2 + b)*n2) + n*(t2 - trigamma(b))) + S2\n J12 <- a*b*t2*n\n if (abs(detJ <- J11*J22 - J12^2) < 1e-12) break\n step1 <- (J22*S1 - J12*S2)/detJ\n step2 <- (J11*S2 - J12*S1)/detJ\n if (abs(step1) + abs(step2) < 1e-8) break\n step_norm <- 2/sqrt(step1^2 + step2^2)\n \n if (step_norm < 1) {\n step1 <- step1*step_norm\n step2 <- step2*step_norm\n }\n \n a <- a*exp(-step1)\n b <- b*exp(-step2)\n }\n \n g <- a*b/(a + b)^2\n V <- -(J11 + J22 + 2*J12)*g^2/detJ\n }\n \n c(a/(a + b), if (is.finite(V) && V > 0 && V < 1 / (4 * n)) V else NA)\n}\n\n## Moments\nfit_mom <- function(x, k) {\n p <- x / k\n c(mean(p), var(p) / length(p))\n}\n\nscore <- function(m, V, mu) {\n s <- sqrt(V); ok <- is.finite(m)\n data.frame(mean_estimate = mean(m[ok]),\n bias = mean(m[ok]) - mu,\n mc_se = sd(m[ok]) / sqrt(sum(ok)),\n sd_estimate = sd(m[ok]),\n variance_estimate = mean(V, na.rm = TRUE),\n length_of_interval = mean(2 * z * s, na.rm = TRUE),\n coverage = mean(abs(m - mu) <= z * s, na.rm = TRUE))\n}\n\nrun_cell <- function(mu, v, n, k, R, i, tot, t0) {\n cat(sprintf(\"[%2d/%2d] n = %3d, k = %d ... \", i, tot, n, k))\n e <- replicate(R, { x <- sim_data(n, k, mu, v)\n rbind(fit_mom(x, k), fit_mle(x, k)) })\n cat(sprintf(\"done (%.1fs elapsed)\\n\",\n as.numeric(difftime(Sys.time(), t0, units = \"secs\"))))\n cbind(true_mean = mu, true_variance = v, n = n, k = k,\n true_var_of_mean = (v + (mu * (1 - mu) - v) / k) / n,\n method = c(\"moments\", \"mle\"),\n rbind(score(e[1, 1, ], e[1, 2, ], mu),\n score(e[2, 1, ], e[2, 2, ], mu)))\n}\n\n#Estimation\nset.seed(1)\nt0 <- Sys.time()\ng <- expand.grid(n = n_vals, k = k_vals)\nres <- do.call(rbind, Map(run_cell, mu_true, v_true, g$n, g$k,\n MoreArgs = list(R = R), i = seq_len(nrow(g)),\n tot = nrow(g), t0 = t0))\n\nlibrary(ggplot2)\nlibrary(patchwork)\n\nres_df <- as.data.frame(res, stringsAsFactors = FALSE)\nnum_cols <- c(\"true_mean\", \"true_variance\", \"n\", \"k\", \"true_var_of_mean\", \n \"mean_estimate\", \"bias\", \"mc_se\", \"sd_estimate\", \n \"variance_estimate\", \"length_of_interval\", \"coverage\")\nres_df[num_cols] <- lapply(res_df[num_cols], as.numeric)\nres_df$k_factor <- as.factor(res_df$k)\n\ndf_mom <- subset(res_df, method == \"moments\")\ndf_mle <- subset(res_df, method == \"mle\")\n\n# Helper function to generate the panels\nmake_panel <- function(data, metric_col, title, subtitle, y_label, hline = NULL) {\n p <- ggplot(data, aes(x = n, y = .data[[metric_col]], color = k_factor)) +\n geom_line(linewidth = 0.5) +\n geom_point(size = 1.5) +\n labs(title = title, subtitle = subtitle, x = \"n\", y = y_label, color = \"k\") +\n theme_bw() +\n theme(legend.position = \"bottom\",\n plot.title = element_text(hjust = 0),\n plot.subtitle = element_text(hjust = 0))\n \n if (!is.null(hline)) {\n p <- p + geom_hline(yintercept = hline, linetype = \"dashed\", linewidth = 0.5)\n }\n return(p)\n}\n\np1 <- make_panel(df_mom, \"bias\", \"Moments: bias of the estimated mean\", \n \"Average estimate minus the truth. Dashed line at 0.\", \"bias\", 0)\np2 <- make_panel(df_mle, \"bias\", \"MLE: bias of the estimated mean\", \n \"Average estimate minus the truth. Dashed line at 0.\", \"bias\", 0)\np3 <- make_panel(df_mom, \"sd_estimate\", \"Moments: SD of the estimated mean\", \n \"Spread of the estimate across studies.\", \"SD\")\np4 <- make_panel(df_mle, \"sd_estimate\", \"MLE: SD of the estimated mean\", \n \"Spread of the estimate across studies.\", \"SD\")\n\n# Combine using patchwork\ncombined_grid <- (p1 + p2) / (p3 + p4)\nprint(combined_grid)\n\np_cov <- ggplot(res_df, aes(x = n, y = coverage, color = method)) +\n geom_line(linewidth = 0.5) +\n geom_point(size = 1.5) +\n geom_hline(yintercept = 0.95, linetype = \"dashed\") +\n facet_grid(~ k, labeller = label_both) +\n labs(title = \"Coverage of the nominal 95% interval\",\n subtitle = \"Share of 1000 intervals containing the true mean. Dashed line at 0.95.\",\n x = \"n\",\n y = \"coverage\",\n color = \"method\") +\n theme_bw() +\n theme(legend.position = \"bottom\",\n strip.background = element_rect(fill = \"grey90\"))\n\nprint(p_cov)", "answer_url": "https://stats.stackexchange.com/a/677117", "author": "jblood94", "author_url": "https://stats.stackexchange.com/users/214015/jblood94", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-09T13:02:57+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:06.169765+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/9155f81b0f1dac4b0f83fad58469033af46ad34ee8d731e569d063b41b3df6b6_1790825226563497500_0.json", "raw_sha256": "cbac4b1b24e2159f1c17ea9902eaf89a0a5260344e6dba6f75790ba955f0d04b", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677094, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "jblood94", "profile_url": "https://stats.stackexchange.com/users/214015/jblood94", "user_type": "registered"}, "created_at": "2026-09-09T13:02:57+00:00", "raw_file": "raw/codex_api_v1/3f959895a29b33d83894e5370d82e1c0cf87f20ac57fa423ebc923738357c657_1790825253957066500_0.json", "raw_sha256": "ddd8808039e410ca99f97e2a7f12c307f046c4e5c3e184683bc12f816e6f49fc", "revision_guid": "09E52470-6B69-4568-A8B3-D52476EA341B", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/09E52470-6B69-4568-A8B3-D52476EA341B/view-source"}, {"content_license": null, "contributor": {"display_name": "adamkostanov", "profile_url": "https://stats.stackexchange.com/users/512554/adamkostanov", "user_type": "registered"}, "created_at": "2026-09-16T13:07:32+00:00", "raw_file": "raw/codex_api_v1/59f98009db0ac38325a869c60e3993040b07f5fbd07014051415831400b70d25_1790825251781774200_0.json", "raw_sha256": "2876465103b1eeb5d593dd46b1ec52a862c1da72f8e4767e5f8ee70ff0564119", "revision_guid": "20C3E36B-1564-462F-9257-5BBE5B9B70EF", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://stats.stackexchange.com/revisions/20C3E36B-1564-462F-9257-5BBE5B9B70EF/view-source"}], "score": 3, "updated_at": "2026-09-09T13:02:57+00:00"}], "domain": "statistics", "external_links": ["https://i.sstatic.net/9nEiiFBK.png", "https://i.sstatic.net/H3ywscwO.png", "https://i.sstatic.net/kEDelnub.png", "https://i.sstatic.net/yrEHvkk0.png"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "adamkostanov", "question_author_url": "https://stats.stackexchange.com/users/512554/adamkostanov", "question_author_user_type": "registered", "question_created_at": "2026-09-07T06:07:31+00:00", "question_html": "

Here is a beta-binomial model (treated like repeated measures - $i$ is an index for each individual, $n$ total individuals, and exactly $k$ measurements per individual):

\n

$$\\theta_i \\stackrel{\\text{iid}}{\\sim} \\mathrm{Beta}(a,b), \\qquad x_i \\mid \\theta_i \\sim \\mathrm{Binomial}(k,\\theta_i), \\qquad \\hat p_i = \\frac{x_i}{k}, \\qquad i = 1,\\dots,n$$

\n

$$\\mu = E[\\theta_i] = \\frac{a}{a+b}$$

\n

$$\\sigma^2 = \\operatorname{Var}(\\theta_i) = \\frac{ab}{(a+b)^2(a+b+1)}$$

\n

$$\\tau^2 = E[\\theta_i(1-\\theta_i)] = \\mu(1-\\mu) - \\sigma^2$$

\n

For a single unit,

\n

$$E[\\hat p_i] = \\mu, \\qquad \\operatorname{Var}(\\hat p_i) = \\sigma^2 + \\frac{\\tau^2}{k}$$

\n

and

\n

$$\\operatorname{Var}(\\hat\\mu) = \\frac{1}{n}\\left(\\sigma^2 + \\frac{\\tau^2}{k}\\right)$$

\n

There are two ways to estimate parameters I am interested in (I am interested in mean estimate and the variance of the mean estimate).

\n

The first way is with moments (I can show the manipulations if needed):

\n

$$\\hat\\mu = \\frac{1}{n}\\sum_{i=1}^{n}\\hat p_i \\qquad \\text{estimates } \\mu$$

\n

$$S^2 = \\frac{1}{n-1}\\sum_{i=1}^{n}(\\hat p_i - \\hat\\mu)^2 \\qquad \\text{estimates } \\sigma^2 + \\frac{\\tau^2}{k}$$

\n

$$\\widehat{\\operatorname{Var}}(\\hat\\mu) = \\frac{S^2}{n} \\qquad \\text{estimates } \\operatorname{Var}(\\hat\\mu)$$

\n

And the second way is using MLE (delta method for variances and log/exp constraint for optimization).

\n

Here is an R script that simulates data, and compares estimates, precision and coverage for both methods. I made it so that mean and variance can be specified in the simulation (instead of a and b from the Beta distribution) at different values of $n,k$ for some fixed true mean and variance. I discard MLE fits with invalid Hessians/variance and I specifically chose the case where there is a large true variance):

\n
library(MASS)\n\nz <- qnorm(0.975)\n\n## Simulate \nmu_true <- 0.5\nv_true  <- 0.249\nn_vals  <- c(5, 10, 15, 20, 25, 50, 100, 200, 500,1000)\nk_vals  <- c(1, 2, 3, 4, 5, 6,7,8,9)\nR       <- 1000\n\n\nsim_data <- function(n, k, mu, v) {\n  nu <- mu * (1 - mu) / v - 1\n  rbinom(n, k, rbeta(n, mu * nu, (1 - mu) * nu))\n}\n\n## MLE \nbb_nll <- function(q, x, k)\n  length(x) * lbeta(exp(q[1]), exp(q[2])) -\n  sum(lbeta(exp(q[1]) + x, exp(q[2]) + k - x))\n\nfit_mle <- function(x, k) {\n  n <- length(x)\n  o <- try(optim(c(0, 0), bb_nll, x = x, k = k, method = "BFGS",\n                 hessian = TRUE), silent = TRUE)\n  if (inherits(o, "try-error")) return(c(NA, NA))\n  a <- exp(o$par[1]); b <- exp(o$par[2])\n  g <- a * b / (a + b)^2 * c(1, -1)\n  V <- try(drop(crossprod(g, ginv(o$hessian) %*% g)), silent = TRUE)\n  ok <- !inherits(V, \"try-error\") && is.finite(V) && V > 0 &&\n        V < 1 / (4 * n) && rcond(o$hessian) > 1e-10\n  c(a / (a + b), if (ok) V else NA)\n}\n\n## Moments\nfit_mom <- function(x, k) {\n  p <- x / k\n  c(mean(p), var(p) / length(p))\n}\n\nscore <- function(m, V, mu) {\n  s <- sqrt(V); ok <- is.finite(m)\n  data.frame(mean_estimate      = mean(m[ok]),\n             bias               = mean(m[ok]) - mu,\n             mc_se              = sd(m[ok]) / sqrt(sum(ok)),\n             sd_estimate        = sd(m[ok]),\n             variance_estimate  = mean(V, na.rm = TRUE),\n             length_of_interval = mean(2 * z * s, na.rm = TRUE),\n             coverage           = mean(abs(m - mu) <= z * s, na.rm = TRUE))\n}\n\nrun_cell <- function(mu, v, n, k, R, i, tot, t0) {\n  cat(sprintf("[%2d/%2d] n = %3d, k = %d ... ", i, tot, n, k))\n  e <- replicate(R, { x <- sim_data(n, k, mu, v)\n                      rbind(fit_mom(x, k), fit_mle(x, k)) })\n  cat(sprintf("done (%.1fs elapsed)\\n",\n              as.numeric(difftime(Sys.time(), t0, units = "secs"))))\n  cbind(true_mean = mu, true_variance = v, n = n, k = k,\n        true_var_of_mean = (v + (mu * (1 - mu) - v) / k) / n,\n        method = c("moments", "mle"),\n        rbind(score(e[1, 1, ], e[1, 2, ], mu),\n              score(e[2, 1, ], e[2, 2, ], mu)))\n}\n\n#Estimation\nset.seed(1)\ng  <- expand.grid(n = n_vals, k = k_vals)\nres <- do.call(rbind, Map(run_cell, mu_true, v_true, g$n, g$k,\n                          MoreArgs = list(R = R), i = seq_len(nrow(g)),\n                          tot = nrow(g), t0 = t0))\n
\n

Here are the results:

\n

\"enter\n\"enter

\n

Prior to running this script, I would have thought that larger $n,k$ combinations would produce less bias, tighter variances and better coverage rates. But for the MLE, it looks like this is not true. And for both Moments and MLE, it seems that sometimes coverage can sometimes decrease as $n$ increases (jagged pattern).

\n

Why is this happening?

\n", "question_id": 677094, "question_license": "CC BY-SA 4.0", "question_score": 3, "question_text": "Here is a beta-binomial model (treated like repeated measures - $i$ is an index for each individual, $n$ total individuals, and exactly $k$ measurements per individual):\n\n\n\n\n$$\\theta_i \\stackrel{\\text{iid}}{\\sim} \\mathrm{Beta}(a,b), \\qquad x_i \\mid \\theta_i \\sim \\mathrm{Binomial}(k,\\theta_i), \\qquad \\hat p_i = \\frac{x_i}{k}, \\qquad i = 1,\\dots,n$$\n\n\n\n\n$$\\mu = E[\\theta_i] = \\frac{a}{a+b}$$\n\n\n\n\n$$\\sigma^2 = \\operatorname{Var}(\\theta_i) = \\frac{ab}{(a+b)^2(a+b+1)}$$\n\n\n\n\n$$\\tau^2 = E[\\theta_i(1-\\theta_i)] = \\mu(1-\\mu) - \\sigma^2$$\n\n\n\n\nFor a single unit,\n\n\n\n\n$$E[\\hat p_i] = \\mu, \\qquad \\operatorname{Var}(\\hat p_i) = \\sigma^2 + \\frac{\\tau^2}{k}$$\n\n\n\n\nand\n\n\n\n\n$$\\operatorname{Var}(\\hat\\mu) = \\frac{1}{n}\\left(\\sigma^2 + \\frac{\\tau^2}{k}\\right)$$\n\n\n\n\nThere are two ways to estimate parameters I am interested in (I am interested in mean estimate and the variance of the mean estimate).\n\n\n\n\nThe first way is with moments (I can show the manipulations if needed):\n\n\n\n\n$$\\hat\\mu = \\frac{1}{n}\\sum_{i=1}^{n}\\hat p_i \\qquad \\text{estimates } \\mu$$\n\n\n\n\n$$S^2 = \\frac{1}{n-1}\\sum_{i=1}^{n}(\\hat p_i - \\hat\\mu)^2 \\qquad \\text{estimates } \\sigma^2 + \\frac{\\tau^2}{k}$$\n\n\n\n\n$$\\widehat{\\operatorname{Var}}(\\hat\\mu) = \\frac{S^2}{n} \\qquad \\text{estimates } \\operatorname{Var}(\\hat\\mu)$$\n\n\n\n\nAnd the second way is using MLE (delta method for variances and log/exp constraint for optimization).\n\n\n\n\nHere is an R script that simulates data, and compares estimates, precision and coverage for both methods. I made it so that mean and variance can be specified in the simulation (instead of a and b from the Beta distribution) at different values of $n,k$ for some fixed true mean and variance. I discard MLE fits with invalid Hessians/variance and I specifically chose the case where there is a large true variance):\n\n\n\n\nlibrary(MASS)\n\nz <- qnorm(0.975)\n\n## Simulate \nmu_true <- 0.5\nv_true <- 0.249\nn_vals <- c(5, 10, 15, 20, 25, 50, 100, 200, 500,1000)\nk_vals <- c(1, 2, 3, 4, 5, 6,7,8,9)\nR <- 1000\n\n\nsim_data <- function(n, k, mu, v) {\n nu <- mu * (1 - mu) / v - 1\n rbinom(n, k, rbeta(n, mu * nu, (1 - mu) * nu))\n}\n\n## MLE \nbb_nll <- function(q, x, k)\n length(x) * lbeta(exp(q[1]), exp(q[2])) -\n sum(lbeta(exp(q[1]) + x, exp(q[2]) + k - x))\n\nfit_mle <- function(x, k) {\n n <- length(x)\n o <- try(optim(c(0, 0), bb_nll, x = x, k = k, method = \"BFGS\",\n hessian = TRUE), silent = TRUE)\n if (inherits(o, \"try-error\")) return(c(NA, NA))\n a <- exp(o$par[1]); b <- exp(o$par[2])\n g <- a * b / (a + b)^2 * c(1, -1)\n V <- try(drop(crossprod(g, ginv(o$hessian) %*% g)), silent = TRUE)\n ok <- !inherits(V, \"try-error\") && is.finite(V) && V > 0 &&\n V < 1 / (4 * n) && rcond(o$hessian) > 1e-10\n c(a / (a + b), if (ok) V else NA)\n}\n\n## Moments\nfit_mom <- function(x, k) {\n p <- x / k\n c(mean(p), var(p) / length(p))\n}\n\nscore <- function(m, V, mu) {\n s <- sqrt(V); ok <- is.finite(m)\n data.frame(mean_estimate = mean(m[ok]),\n bias = mean(m[ok]) - mu,\n mc_se = sd(m[ok]) / sqrt(sum(ok)),\n sd_estimate = sd(m[ok]),\n variance_estimate = mean(V, na.rm = TRUE),\n length_of_interval = mean(2 * z * s, na.rm = TRUE),\n coverage = mean(abs(m - mu) <= z * s, na.rm = TRUE))\n}\n\nrun_cell <- function(mu, v, n, k, R, i, tot, t0) {\n cat(sprintf(\"[%2d/%2d] n = %3d, k = %d ... \", i, tot, n, k))\n e <- replicate(R, { x <- sim_data(n, k, mu, v)\n rbind(fit_mom(x, k), fit_mle(x, k)) })\n cat(sprintf(\"done (%.1fs elapsed)\\n\",\n as.numeric(difftime(Sys.time(), t0, units = \"secs\"))))\n cbind(true_mean = mu, true_variance = v, n = n, k = k,\n true_var_of_mean = (v + (mu * (1 - mu) - v) / k) / n,\n method = c(\"moments\", \"mle\"),\n rbind(score(e[1, 1, ], e[1, 2, ], mu),\n score(e[2, 1, ], e[2, 2, ], mu)))\n}\n\n#Estimation\nset.seed(1)\ng <- expand.grid(n = n_vals, k = k_vals)\nres <- do.call(rbind, Map(run_cell, mu_true, v_true, g$n, g$k,\n MoreArgs = list(R = R), i = seq_len(nrow(g)),\n tot = nrow(g), t0 = t0))\n\n\n\n\n\nHere are the results:\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/kEDelnub.png] (https://i.sstatic.net/kEDelnub.png)\n[image: enter image description here; source: https://i.sstatic.net/H3ywscwO.png] (https://i.sstatic.net/H3ywscwO.png)\n\n\n\n\nPrior to running this script, I would have thought that larger $n,k$ combinations would produce less bias, tighter variances and better coverage rates. But for the MLE, it looks like this is not true. And for both Moments and MLE, it seems that sometimes coverage can sometimes decrease as $n$ increases (jagged pattern).\n\n\n\n\nWhy is this happening?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "adamkostanov", "profile_url": "https://stats.stackexchange.com/users/512554/adamkostanov", "user_type": "registered"}, "created_at": "2026-09-07T06:07:31+00:00", "raw_file": "raw/codex_api_v1/3f959895a29b33d83894e5370d82e1c0cf87f20ac57fa423ebc923738357c657_1790825253957066500_0.json", "raw_sha256": "ddd8808039e410ca99f97e2a7f12c307f046c4e5c3e184683bc12f816e6f49fc", "revision_guid": "BE06C153-8C52-4CC0-883B-294D30B035A1", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/BE06C153-8C52-4CC0-883B-294D30B035A1/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "adamkostanov", "profile_url": "https://stats.stackexchange.com/users/512554/adamkostanov", 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But the Brunner-Munzel test (https://en.wikipedia.org/wiki/Brunner_Munzel_Test) addresses this issue: so I would highly recommedn that you use it, instead of the MWU, if you have", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Brunner_Munzel_Test", "kind": "external_url", "post_id": 677307, "post_url": "https://stats.stackexchange.com/a/677307", "product": "citations", "record_id": "Scientific-Citation-Graph:67812dab910d854215fe1a88", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

To begin with, it is quite difficult to understand what you are trying to accomplish, and what led you to a MWUt.

\n

You say that you want to “compare a sample with a reference (deterministic) value”. Well, at some level, you already did, and the answer is that they are different (one is “random”, the other is not). A slightly less trivial approach is simply to compare your values from heuristics to your reference value: how many are exactly equal to the reference? Most likely, none...
\nSo (I think) what you really want to do is test if your “solutions from heuristics” are “close enough” to the reference value. For that you should first define, based on your context, what you are measuring, what you will do with the answer, etc. what would be a practically important difference between a solution from heuristics and the reference: I will call this difference $\\Delta_{PI}$. If a solution from heuristics is within $\\pm \\Delta_{PI}$ of the reference, you would consider the 2 values equivalent, because the difference is of no practical importance.

\n

The next puzzlement is why you thought that a significance test (MWU, or 1 sample t-test) would answer your question. If you run such a test, and get a statistically significant result, it would not imply that the difference is practically important: they still could be “close enough” (in your context) to be considered equivalent to your reference.
\nMore importantly, if you fail to reject the null, you would not (at all) be able to conclude that the two (heuristics and reference) are equivalent, just that you did not have enough power to “prove” a difference. Given that your sample size is small (10), you are most likely to fall in that scenario, in which case a significance test will tell you nothing...

\n

What (I think) you need is to perform an equivalence test. The most common method for this is the TOST (Two One Sided Tests) (see also here with links to some R code to perform such tests, or here).
\nYou can run a “quick and dirty” equivalence test just by looking at the CI of the mean of your sample: if it is entirely included inside the $\\pm \\Delta_{PI}$ interval around the reference, then you have established equivalence (but note that, often, that CI exceeds the bound on one side, but not on the other, and then you will need to run an actual equivalence test).

\n

The above would tell you if the mean of your heuristics is equivalent to your reference. But is that really what you need? Will you be able to use a mean of multiple runs of the heuristics, or will you want to (need to) use a single heuristic? If it is the latter case, then having established that the mean is equivalent to the reference does not help you (because any given single heuristic could be very far from the reference - all you know is that, on average, they are close enough). You will then need to look at Tolerance Intervals for your heuristics. You can still use a TOST approach, but with a different test. Tolerance intervals will ensure that a given proportion (coverage) of your heuristics are within the practically important interval, at a given confidence level: so, most of the time, a single heuristic value will be "close enough".

\n

Talking about tests, it is also unclear why you wanted to use a MWU test. Presumably because the heuristics sample did not look “normal enough”? With only 10 observations, that is hard to eyeball, even with a Q-Q plot, and tests of normality are quite unreliable with such a small sample size. More worrying, for your heuristics to be “well behaved”, they should be more or less symmetric around the reference, with a mean error to the reference of 0. But if they looked non-normal to you, it implies a skew, and thus some bias to the reference. So if you observed this, I would look at the heuristics and address this issue first, before running any statistical test.
\nFor an equivalence test of the means, unfortunately, there are no good nonparametric tests in your scenario: only the one sample t-test (permutation, or bootstrap could be used, but with a sample size of 10, I would not trust them: you do not have enough observations to claim you have a sample representative of the population). For an equivalence test of the proportion (Tolerance intervals), again the “common” method assumes normality of the distribution, but there are nonparametric methods (beside bootstrap) (see e.g. here but again, with only 10 observations, it will be challenging to achieve the desired confidence level, or coverage (proportion included in the interval).

\n

And in any case, I do not see how the MWU test will allow you to conclude that the heuristic values are “close enough” to the reference.... (because that is not what the MWU test tests - it is a test of the null of stochastic homogeneity).

\n

And just as a final comment, for scenarios outside your specific question, I see no reason why you could not use a MWU test to compare a sample, to a reference (constant vector). It may however depend on how the statistic is computed: if the software computes the W statistic (which most do, as it is more computationally efficient), then you will end up with many ties, and it would affect the power, and the computation of exact p-values. But that would not be the case if one uses the U statistic (but you should get very similar results). As an example, with a t-test, whether you compare a sample to a constant (1 sample t test), a sample to a constant vector (2 sample t test), or a sample to a constant vector (paired t test), you would obtain the exact same p-value). Another caveat is that the MWU test is subject to Type I error inflation when the variances of the 2 samples are not equal (which is seriously the case here: one variance is $0$!). But the Brunner-Munzel test addresses this issue: so I would highly recommedn that you use it, instead of the MWU, if you have reasons to continue using such a test of stochastic superiority.

\n", "answer_id": 677307, "answer_text": "To begin with, it is quite difficult to understand what you are trying to accomplish, and what led you to a MWUt.\n\n\n\n\nYou say that you want to “compare a sample with a reference (deterministic) value”. Well, at some level, you already did, and the answer is that they are different (one is “random”, the other is not). A slightly less trivial approach is simply to compare your values from heuristics to your reference value: how many are exactly equal to the reference? Most likely, none...\n\nSo (I think) what you really want to do is test if your “solutions from heuristics” are “close enough” to the reference value. For that you should first define, based on your context, what you are measuring, what you will do with the answer, etc. what would be a practically important difference between a solution from heuristics and the reference: I will call this difference $\\Delta_{PI}$. If a solution from heuristics is within $\\pm \\Delta_{PI}$ of the reference, you would consider the 2 values equivalent, because the difference is of no practical importance.\n\n\n\n\nThe next puzzlement is why you thought that a significance test (MWU, or 1 sample t-test) would answer your question. If you run such a test, and get a statistically significant result, it would not imply that the difference is practically important: they still could be “close enough” (in your context) to be considered equivalent to your reference.\n\nMore importantly, if you fail to reject the null, you would not (at all) be able to conclude that the two (heuristics and reference) are equivalent, just that you did not have enough power to “prove” a difference. Given that your sample size is small (10), you are most likely to fall in that scenario, in which case a significance test will tell you nothing...\n\n\n\n\nWhat (I think) you need is to perform an equivalence test (https://en.wikipedia.org/wiki/Equivalence_test). The most common method for this is the TOST (https://stats.stackexchange.com/tags/tost/info) (Two One Sided Tests) (see also here (https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/equival) with links to some R code to perform such tests, or here (https://pmc.ncbi.nlm.nih.gov/articles/PMC5502906/)).\n\nYou can run a “quick and dirty” equivalence test just by looking at the CI of the mean of your sample: if it is entirely included inside the $\\pm \\Delta_{PI}$ interval around the reference, then you have established equivalence (but note that, often, that CI exceeds the bound on one side, but not on the other, and then you will need to run an actual equivalence test).\n\n\n\n\nThe above would tell you if the mean of your heuristics is equivalent to your reference. But is that really what you need? Will you be able to use a mean of multiple runs of the heuristics, or will you want to (need to) use a single heuristic? If it is the latter case, then having established that the mean is equivalent to the reference does not help you (because any given single heuristic could be very far from the reference - all you know is that, on average, they are close enough). You will then need to look at Tolerance Intervals (https://en.wikipedia.org/wiki/Tolerance_interval) for your heuristics. You can still use a TOST approach, but with a different test. Tolerance intervals will ensure that a given proportion (coverage) of your heuristics are within the practically important interval, at a given confidence level: so, most of the time, a single heuristic value will be \"close enough\".\n\n\n\n\nTalking about tests, it is also unclear why you wanted to use a MWU test. Presumably because the heuristics sample did not look “normal enough”? With only 10 observations, that is hard to eyeball, even with a Q-Q plot, and tests of normality are quite unreliable with such a small sample size. More worrying, for your heuristics to be “well behaved”, they should be more or less symmetric around the reference, with a mean error to the reference of 0. But if they looked non-normal to you, it implies a skew, and thus some bias to the reference. So if you observed this, I would look at the heuristics and address this issue first, before running any statistical test.\n\nFor an equivalence test of the means, unfortunately, there are no good nonparametric tests in your scenario: only the one sample t-test (permutation, or bootstrap could be used, but with a sample size of 10, I would not trust them: you do not have enough observations to claim you have a sample representative of the population). For an equivalence test of the proportion (Tolerance intervals), again the “common” method assumes normality of the distribution, but there are nonparametric methods (beside bootstrap) (see e.g. here (https://medium.com/@animeshjoshi88/tolerance-intervals-theory-construction-and-simulation-c81a7a1367c9) but again, with only 10 observations, it will be challenging to achieve the desired confidence level, or coverage (proportion included in the interval).\n\n\n\n\nAnd in any case, I do not see how the MWU test will allow you to conclude that the heuristic values are “close enough” to the reference.... (because that is not what the MWU test tests - it is a test of the null of stochastic homogeneity).\n\n\n\n\nAnd just as a final comment, for scenarios outside your specific question, I see no reason why you could not use a MWU test to compare a sample, to a reference (constant vector). It may however depend on how the statistic is computed: if the software computes the W statistic (which most do, as it is more computationally efficient), then you will end up with many ties, and it would affect the power, and the computation of exact p-values. But that would not be the case if one uses the U statistic (but you should get very similar results). As an example, with a t-test, whether you compare a sample to a constant (1 sample t test), a sample to a constant vector (2 sample t test), or a sample to a constant vector (paired t test), you would obtain the exact same p-value). Another caveat is that the MWU test is subject to Type I error inflation when the variances of the 2 samples are not equal (which is seriously the case here: one variance is $0$!). But the Brunner-Munzel test (https://en.wikipedia.org/wiki/Brunner_Munzel_Test) addresses this issue: so I would highly recommedn that you use it, instead of the MWU, if you have reasons to continue using such a test of stochastic superiority.", "answer_url": "https://stats.stackexchange.com/a/677307", "author": "jginestet", "author_url": "https://stats.stackexchange.com/users/380096/jginestet", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-30T20:59:02+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:08.569053+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/ba8a114171cbec551f0a7f4b9f04e95c559131a62357d51e159434d4acc7183d_1790825228829630100_0.json", "raw_sha256": "a03822ca860dd0b0fb0cc402754ae4cdbaad51d18873dfd19aed56ffe1cf7ec8", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=2&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677295, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "jginestet", "profile_url": "https://stats.stackexchange.com/users/380096/jginestet", "user_type": "registered"}, "created_at": "2026-09-30T20:59:02+00:00", "raw_file": "raw/codex_api_v1/ab5f4cd7f0a10bde5970354a9b213efcc81e232042487437e8579705d4ca6a20_1790825258916612700_0.json", "raw_sha256": "4cf167c399d03b9ae013b65260fcb4e38139c42cfc70aba4807f070550c1768e", "revision_guid": "9E0FBE54-CDD3-4DDB-B1D2-6157CDED2E25", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/9E0FBE54-CDD3-4DDB-B1D2-6157CDED2E25/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "jginestet", "profile_url": "https://stats.stackexchange.com/users/380096/jginestet", "user_type": "registered"}, "created_at": "2026-10-01T03:02:57+00:00", "raw_file": "raw/codex_api_v1/ab5f4cd7f0a10bde5970354a9b213efcc81e232042487437e8579705d4ca6a20_1790825258916612700_0.json", "raw_sha256": "4cf167c399d03b9ae013b65260fcb4e38139c42cfc70aba4807f070550c1768e", "revision_guid": "D4ADF678-7BAF-486D-903C-7740CDAE23F7", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/D4ADF678-7BAF-486D-903C-7740CDAE23F7/view-source"}], "score": 0, "updated_at": "2026-10-01T03:02:57+00:00"}], "domain": "statistics", "external_links": ["https://en.wikipedia.org/wiki/Brunner_Munzel_Test", "https://en.wikipedia.org/wiki/Equivalence_test", "https://en.wikipedia.org/wiki/Tolerance_interval", "https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/equival", "https://medium.com/@animeshjoshi88/tolerance-intervals-theory-construction-and-simulation-c81a7a1367c9", "https://pmc.ncbi.nlm.nih.gov/articles/PMC5502906/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Engr. Moiz Ahmad", "question_author_url": "https://stats.stackexchange.com/users/306308/engr-moiz-ahmad", "question_author_user_type": "registered", "question_created_at": "2026-09-29T06:12:41+00:00", "question_html": "

I need to compare a sample with a reference (deterministic) value, e.g., an exact optimal solution, and I am wondering that can I use MWU test while replicating the reference value to form a set of samples (of a constant value) from a degenerate distribution (probability mass concentrated on a single value)?

\n", "question_id": 677295, "question_license": "CC BY-SA 4.0", "question_score": 0, "question_text": "I need to compare a sample with a reference (deterministic) value, e.g., an exact optimal solution, and I am wondering that can I use MWU test while replicating the reference value to form a set of samples (of a constant value) from a degenerate distribution (probability mass concentrated on a single value)?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Engr. Moiz Ahmad", "profile_url": "https://stats.stackexchange.com/users/306308/engr-moiz-ahmad", "user_type": "registered"}, "created_at": "2026-09-29T06:12:41+00:00", "raw_file": "raw/codex_api_v1/ab5f4cd7f0a10bde5970354a9b213efcc81e232042487437e8579705d4ca6a20_1790825258916612700_0.json", "raw_sha256": "4cf167c399d03b9ae013b65260fcb4e38139c42cfc70aba4807f070550c1768e", "revision_guid": "2AB4C6D5-EC2C-4411-9DCC-6EB4B533DAAB", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/2AB4C6D5-EC2C-4411-9DCC-6EB4B533DAAB/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/677295/can-the-mann-whitney-u-mwu-test-be-used-with-one-sample-set-coming-from-a-dege", "split": "test", "split_group": "c2e6ef0ec5f1aca39132b9c4a0c37afc306d5da19ac43213abc81c3e1491d02e", "tags": ["hypothesis-testing", "statistical-significance", "inference", "wilcoxon-mann-whitney-test", "method-comparison"], "thread_id": "stats:677295", "title": "Can the Mann-Whitney U (MWU) test be used with one sample set coming from a degenerate distribution in a two-sample comparison?"}} {"citation_context": "icance test will tell you nothing...\n\n\n\n\nWhat (I think) you need is to perform an equivalence test (https://en.wikipedia.org/wiki/Equivalence_test). The most common method for this is the TOST (https://stats.stackexchange.com/tags/tost/info) (Two", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Equivalence_test", "kind": "external_url", "post_id": 677307, "post_url": "https://stats.stackexchange.com/a/677307", "product": "citations", "record_id": "Scientific-Citation-Graph:4b6bff60cedd7344625170af", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

To begin with, it is quite difficult to understand what you are trying to accomplish, and what led you to a MWUt.

\n

You say that you want to “compare a sample with a reference (deterministic) value”. Well, at some level, you already did, and the answer is that they are different (one is “random”, the other is not). A slightly less trivial approach is simply to compare your values from heuristics to your reference value: how many are exactly equal to the reference? Most likely, none...
\nSo (I think) what you really want to do is test if your “solutions from heuristics” are “close enough” to the reference value. For that you should first define, based on your context, what you are measuring, what you will do with the answer, etc. what would be a practically important difference between a solution from heuristics and the reference: I will call this difference $\\Delta_{PI}$. If a solution from heuristics is within $\\pm \\Delta_{PI}$ of the reference, you would consider the 2 values equivalent, because the difference is of no practical importance.

\n

The next puzzlement is why you thought that a significance test (MWU, or 1 sample t-test) would answer your question. If you run such a test, and get a statistically significant result, it would not imply that the difference is practically important: they still could be “close enough” (in your context) to be considered equivalent to your reference.
\nMore importantly, if you fail to reject the null, you would not (at all) be able to conclude that the two (heuristics and reference) are equivalent, just that you did not have enough power to “prove” a difference. Given that your sample size is small (10), you are most likely to fall in that scenario, in which case a significance test will tell you nothing...

\n

What (I think) you need is to perform an equivalence test. The most common method for this is the TOST (Two One Sided Tests) (see also here with links to some R code to perform such tests, or here).
\nYou can run a “quick and dirty” equivalence test just by looking at the CI of the mean of your sample: if it is entirely included inside the $\\pm \\Delta_{PI}$ interval around the reference, then you have established equivalence (but note that, often, that CI exceeds the bound on one side, but not on the other, and then you will need to run an actual equivalence test).

\n

The above would tell you if the mean of your heuristics is equivalent to your reference. But is that really what you need? Will you be able to use a mean of multiple runs of the heuristics, or will you want to (need to) use a single heuristic? If it is the latter case, then having established that the mean is equivalent to the reference does not help you (because any given single heuristic could be very far from the reference - all you know is that, on average, they are close enough). You will then need to look at Tolerance Intervals for your heuristics. You can still use a TOST approach, but with a different test. Tolerance intervals will ensure that a given proportion (coverage) of your heuristics are within the practically important interval, at a given confidence level: so, most of the time, a single heuristic value will be "close enough".

\n

Talking about tests, it is also unclear why you wanted to use a MWU test. Presumably because the heuristics sample did not look “normal enough”? With only 10 observations, that is hard to eyeball, even with a Q-Q plot, and tests of normality are quite unreliable with such a small sample size. More worrying, for your heuristics to be “well behaved”, they should be more or less symmetric around the reference, with a mean error to the reference of 0. But if they looked non-normal to you, it implies a skew, and thus some bias to the reference. So if you observed this, I would look at the heuristics and address this issue first, before running any statistical test.
\nFor an equivalence test of the means, unfortunately, there are no good nonparametric tests in your scenario: only the one sample t-test (permutation, or bootstrap could be used, but with a sample size of 10, I would not trust them: you do not have enough observations to claim you have a sample representative of the population). For an equivalence test of the proportion (Tolerance intervals), again the “common” method assumes normality of the distribution, but there are nonparametric methods (beside bootstrap) (see e.g. here but again, with only 10 observations, it will be challenging to achieve the desired confidence level, or coverage (proportion included in the interval).

\n

And in any case, I do not see how the MWU test will allow you to conclude that the heuristic values are “close enough” to the reference.... (because that is not what the MWU test tests - it is a test of the null of stochastic homogeneity).

\n

And just as a final comment, for scenarios outside your specific question, I see no reason why you could not use a MWU test to compare a sample, to a reference (constant vector). It may however depend on how the statistic is computed: if the software computes the W statistic (which most do, as it is more computationally efficient), then you will end up with many ties, and it would affect the power, and the computation of exact p-values. But that would not be the case if one uses the U statistic (but you should get very similar results). As an example, with a t-test, whether you compare a sample to a constant (1 sample t test), a sample to a constant vector (2 sample t test), or a sample to a constant vector (paired t test), you would obtain the exact same p-value). Another caveat is that the MWU test is subject to Type I error inflation when the variances of the 2 samples are not equal (which is seriously the case here: one variance is $0$!). But the Brunner-Munzel test addresses this issue: so I would highly recommedn that you use it, instead of the MWU, if you have reasons to continue using such a test of stochastic superiority.

\n", "answer_id": 677307, "answer_text": "To begin with, it is quite difficult to understand what you are trying to accomplish, and what led you to a MWUt.\n\n\n\n\nYou say that you want to “compare a sample with a reference (deterministic) value”. Well, at some level, you already did, and the answer is that they are different (one is “random”, the other is not). A slightly less trivial approach is simply to compare your values from heuristics to your reference value: how many are exactly equal to the reference? Most likely, none...\n\nSo (I think) what you really want to do is test if your “solutions from heuristics” are “close enough” to the reference value. For that you should first define, based on your context, what you are measuring, what you will do with the answer, etc. what would be a practically important difference between a solution from heuristics and the reference: I will call this difference $\\Delta_{PI}$. If a solution from heuristics is within $\\pm \\Delta_{PI}$ of the reference, you would consider the 2 values equivalent, because the difference is of no practical importance.\n\n\n\n\nThe next puzzlement is why you thought that a significance test (MWU, or 1 sample t-test) would answer your question. If you run such a test, and get a statistically significant result, it would not imply that the difference is practically important: they still could be “close enough” (in your context) to be considered equivalent to your reference.\n\nMore importantly, if you fail to reject the null, you would not (at all) be able to conclude that the two (heuristics and reference) are equivalent, just that you did not have enough power to “prove” a difference. Given that your sample size is small (10), you are most likely to fall in that scenario, in which case a significance test will tell you nothing...\n\n\n\n\nWhat (I think) you need is to perform an equivalence test (https://en.wikipedia.org/wiki/Equivalence_test). The most common method for this is the TOST (https://stats.stackexchange.com/tags/tost/info) (Two One Sided Tests) (see also here (https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/equival) with links to some R code to perform such tests, or here (https://pmc.ncbi.nlm.nih.gov/articles/PMC5502906/)).\n\nYou can run a “quick and dirty” equivalence test just by looking at the CI of the mean of your sample: if it is entirely included inside the $\\pm \\Delta_{PI}$ interval around the reference, then you have established equivalence (but note that, often, that CI exceeds the bound on one side, but not on the other, and then you will need to run an actual equivalence test).\n\n\n\n\nThe above would tell you if the mean of your heuristics is equivalent to your reference. But is that really what you need? Will you be able to use a mean of multiple runs of the heuristics, or will you want to (need to) use a single heuristic? If it is the latter case, then having established that the mean is equivalent to the reference does not help you (because any given single heuristic could be very far from the reference - all you know is that, on average, they are close enough). You will then need to look at Tolerance Intervals (https://en.wikipedia.org/wiki/Tolerance_interval) for your heuristics. You can still use a TOST approach, but with a different test. Tolerance intervals will ensure that a given proportion (coverage) of your heuristics are within the practically important interval, at a given confidence level: so, most of the time, a single heuristic value will be \"close enough\".\n\n\n\n\nTalking about tests, it is also unclear why you wanted to use a MWU test. Presumably because the heuristics sample did not look “normal enough”? With only 10 observations, that is hard to eyeball, even with a Q-Q plot, and tests of normality are quite unreliable with such a small sample size. More worrying, for your heuristics to be “well behaved”, they should be more or less symmetric around the reference, with a mean error to the reference of 0. But if they looked non-normal to you, it implies a skew, and thus some bias to the reference. So if you observed this, I would look at the heuristics and address this issue first, before running any statistical test.\n\nFor an equivalence test of the means, unfortunately, there are no good nonparametric tests in your scenario: only the one sample t-test (permutation, or bootstrap could be used, but with a sample size of 10, I would not trust them: you do not have enough observations to claim you have a sample representative of the population). For an equivalence test of the proportion (Tolerance intervals), again the “common” method assumes normality of the distribution, but there are nonparametric methods (beside bootstrap) (see e.g. here (https://medium.com/@animeshjoshi88/tolerance-intervals-theory-construction-and-simulation-c81a7a1367c9) but again, with only 10 observations, it will be challenging to achieve the desired confidence level, or coverage (proportion included in the interval).\n\n\n\n\nAnd in any case, I do not see how the MWU test will allow you to conclude that the heuristic values are “close enough” to the reference.... (because that is not what the MWU test tests - it is a test of the null of stochastic homogeneity).\n\n\n\n\nAnd just as a final comment, for scenarios outside your specific question, I see no reason why you could not use a MWU test to compare a sample, to a reference (constant vector). It may however depend on how the statistic is computed: if the software computes the W statistic (which most do, as it is more computationally efficient), then you will end up with many ties, and it would affect the power, and the computation of exact p-values. But that would not be the case if one uses the U statistic (but you should get very similar results). As an example, with a t-test, whether you compare a sample to a constant (1 sample t test), a sample to a constant vector (2 sample t test), or a sample to a constant vector (paired t test), you would obtain the exact same p-value). Another caveat is that the MWU test is subject to Type I error inflation when the variances of the 2 samples are not equal (which is seriously the case here: one variance is $0$!). But the Brunner-Munzel test (https://en.wikipedia.org/wiki/Brunner_Munzel_Test) addresses this issue: so I would highly recommedn that you use it, instead of the MWU, if you have reasons to continue using such a test of stochastic superiority.", "answer_url": "https://stats.stackexchange.com/a/677307", "author": "jginestet", "author_url": "https://stats.stackexchange.com/users/380096/jginestet", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-30T20:59:02+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:08.569053+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/ba8a114171cbec551f0a7f4b9f04e95c559131a62357d51e159434d4acc7183d_1790825228829630100_0.json", "raw_sha256": "a03822ca860dd0b0fb0cc402754ae4cdbaad51d18873dfd19aed56ffe1cf7ec8", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=2&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677295, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "jginestet", "profile_url": "https://stats.stackexchange.com/users/380096/jginestet", "user_type": "registered"}, "created_at": "2026-09-30T20:59:02+00:00", "raw_file": "raw/codex_api_v1/ab5f4cd7f0a10bde5970354a9b213efcc81e232042487437e8579705d4ca6a20_1790825258916612700_0.json", "raw_sha256": "4cf167c399d03b9ae013b65260fcb4e38139c42cfc70aba4807f070550c1768e", "revision_guid": "9E0FBE54-CDD3-4DDB-B1D2-6157CDED2E25", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/9E0FBE54-CDD3-4DDB-B1D2-6157CDED2E25/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "jginestet", "profile_url": "https://stats.stackexchange.com/users/380096/jginestet", "user_type": "registered"}, "created_at": "2026-10-01T03:02:57+00:00", "raw_file": "raw/codex_api_v1/ab5f4cd7f0a10bde5970354a9b213efcc81e232042487437e8579705d4ca6a20_1790825258916612700_0.json", "raw_sha256": "4cf167c399d03b9ae013b65260fcb4e38139c42cfc70aba4807f070550c1768e", "revision_guid": "D4ADF678-7BAF-486D-903C-7740CDAE23F7", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/D4ADF678-7BAF-486D-903C-7740CDAE23F7/view-source"}], "score": 0, "updated_at": "2026-10-01T03:02:57+00:00"}], "domain": "statistics", "external_links": ["https://en.wikipedia.org/wiki/Brunner_Munzel_Test", "https://en.wikipedia.org/wiki/Equivalence_test", "https://en.wikipedia.org/wiki/Tolerance_interval", "https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/equival", "https://medium.com/@animeshjoshi88/tolerance-intervals-theory-construction-and-simulation-c81a7a1367c9", "https://pmc.ncbi.nlm.nih.gov/articles/PMC5502906/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Engr. Moiz Ahmad", "question_author_url": "https://stats.stackexchange.com/users/306308/engr-moiz-ahmad", "question_author_user_type": "registered", "question_created_at": "2026-09-29T06:12:41+00:00", "question_html": "

I need to compare a sample with a reference (deterministic) value, e.g., an exact optimal solution, and I am wondering that can I use MWU test while replicating the reference value to form a set of samples (of a constant value) from a degenerate distribution (probability mass concentrated on a single value)?

\n", "question_id": 677295, "question_license": "CC BY-SA 4.0", "question_score": 0, "question_text": "I need to compare a sample with a reference (deterministic) value, e.g., an exact optimal solution, and I am wondering that can I use MWU test while replicating the reference value to form a set of samples (of a constant value) from a degenerate distribution (probability mass concentrated on a single value)?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Engr. Moiz Ahmad", "profile_url": "https://stats.stackexchange.com/users/306308/engr-moiz-ahmad", "user_type": "registered"}, "created_at": "2026-09-29T06:12:41+00:00", "raw_file": "raw/codex_api_v1/ab5f4cd7f0a10bde5970354a9b213efcc81e232042487437e8579705d4ca6a20_1790825258916612700_0.json", "raw_sha256": "4cf167c399d03b9ae013b65260fcb4e38139c42cfc70aba4807f070550c1768e", "revision_guid": "2AB4C6D5-EC2C-4411-9DCC-6EB4B533DAAB", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/2AB4C6D5-EC2C-4411-9DCC-6EB4B533DAAB/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/677295/can-the-mann-whitney-u-mwu-test-be-used-with-one-sample-set-coming-from-a-dege", "split": "test", "split_group": "c2e6ef0ec5f1aca39132b9c4a0c37afc306d5da19ac43213abc81c3e1491d02e", "tags": ["hypothesis-testing", "statistical-significance", "inference", "wilcoxon-mann-whitney-test", "method-comparison"], "thread_id": "stats:677295", "title": "Can the Mann-Whitney U (MWU) test be used with one sample set coming from a degenerate distribution in a two-sample comparison?"}} {"citation_context": "now is that, on average, they are close enough). You will then need to look at Tolerance Intervals (https://en.wikipedia.org/wiki/Tolerance_interval) for your heuristics. You can still use a TOST approach, but with a different test. Tolerance inter", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Tolerance_interval", "kind": "external_url", "post_id": 677307, "post_url": "https://stats.stackexchange.com/a/677307", "product": "citations", "record_id": "Scientific-Citation-Graph:56dd8ebf2ccf04a0fa62c1ac", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

To begin with, it is quite difficult to understand what you are trying to accomplish, and what led you to a MWUt.

\n

You say that you want to “compare a sample with a reference (deterministic) value”. Well, at some level, you already did, and the answer is that they are different (one is “random”, the other is not). A slightly less trivial approach is simply to compare your values from heuristics to your reference value: how many are exactly equal to the reference? Most likely, none...
\nSo (I think) what you really want to do is test if your “solutions from heuristics” are “close enough” to the reference value. For that you should first define, based on your context, what you are measuring, what you will do with the answer, etc. what would be a practically important difference between a solution from heuristics and the reference: I will call this difference $\\Delta_{PI}$. If a solution from heuristics is within $\\pm \\Delta_{PI}$ of the reference, you would consider the 2 values equivalent, because the difference is of no practical importance.

\n

The next puzzlement is why you thought that a significance test (MWU, or 1 sample t-test) would answer your question. If you run such a test, and get a statistically significant result, it would not imply that the difference is practically important: they still could be “close enough” (in your context) to be considered equivalent to your reference.
\nMore importantly, if you fail to reject the null, you would not (at all) be able to conclude that the two (heuristics and reference) are equivalent, just that you did not have enough power to “prove” a difference. Given that your sample size is small (10), you are most likely to fall in that scenario, in which case a significance test will tell you nothing...

\n

What (I think) you need is to perform an equivalence test. The most common method for this is the TOST (Two One Sided Tests) (see also here with links to some R code to perform such tests, or here).
\nYou can run a “quick and dirty” equivalence test just by looking at the CI of the mean of your sample: if it is entirely included inside the $\\pm \\Delta_{PI}$ interval around the reference, then you have established equivalence (but note that, often, that CI exceeds the bound on one side, but not on the other, and then you will need to run an actual equivalence test).

\n

The above would tell you if the mean of your heuristics is equivalent to your reference. But is that really what you need? Will you be able to use a mean of multiple runs of the heuristics, or will you want to (need to) use a single heuristic? If it is the latter case, then having established that the mean is equivalent to the reference does not help you (because any given single heuristic could be very far from the reference - all you know is that, on average, they are close enough). You will then need to look at Tolerance Intervals for your heuristics. You can still use a TOST approach, but with a different test. Tolerance intervals will ensure that a given proportion (coverage) of your heuristics are within the practically important interval, at a given confidence level: so, most of the time, a single heuristic value will be "close enough".

\n

Talking about tests, it is also unclear why you wanted to use a MWU test. Presumably because the heuristics sample did not look “normal enough”? With only 10 observations, that is hard to eyeball, even with a Q-Q plot, and tests of normality are quite unreliable with such a small sample size. More worrying, for your heuristics to be “well behaved”, they should be more or less symmetric around the reference, with a mean error to the reference of 0. But if they looked non-normal to you, it implies a skew, and thus some bias to the reference. So if you observed this, I would look at the heuristics and address this issue first, before running any statistical test.
\nFor an equivalence test of the means, unfortunately, there are no good nonparametric tests in your scenario: only the one sample t-test (permutation, or bootstrap could be used, but with a sample size of 10, I would not trust them: you do not have enough observations to claim you have a sample representative of the population). For an equivalence test of the proportion (Tolerance intervals), again the “common” method assumes normality of the distribution, but there are nonparametric methods (beside bootstrap) (see e.g. here but again, with only 10 observations, it will be challenging to achieve the desired confidence level, or coverage (proportion included in the interval).

\n

And in any case, I do not see how the MWU test will allow you to conclude that the heuristic values are “close enough” to the reference.... (because that is not what the MWU test tests - it is a test of the null of stochastic homogeneity).

\n

And just as a final comment, for scenarios outside your specific question, I see no reason why you could not use a MWU test to compare a sample, to a reference (constant vector). It may however depend on how the statistic is computed: if the software computes the W statistic (which most do, as it is more computationally efficient), then you will end up with many ties, and it would affect the power, and the computation of exact p-values. But that would not be the case if one uses the U statistic (but you should get very similar results). As an example, with a t-test, whether you compare a sample to a constant (1 sample t test), a sample to a constant vector (2 sample t test), or a sample to a constant vector (paired t test), you would obtain the exact same p-value). Another caveat is that the MWU test is subject to Type I error inflation when the variances of the 2 samples are not equal (which is seriously the case here: one variance is $0$!). But the Brunner-Munzel test addresses this issue: so I would highly recommedn that you use it, instead of the MWU, if you have reasons to continue using such a test of stochastic superiority.

\n", "answer_id": 677307, "answer_text": "To begin with, it is quite difficult to understand what you are trying to accomplish, and what led you to a MWUt.\n\n\n\n\nYou say that you want to “compare a sample with a reference (deterministic) value”. Well, at some level, you already did, and the answer is that they are different (one is “random”, the other is not). A slightly less trivial approach is simply to compare your values from heuristics to your reference value: how many are exactly equal to the reference? Most likely, none...\n\nSo (I think) what you really want to do is test if your “solutions from heuristics” are “close enough” to the reference value. For that you should first define, based on your context, what you are measuring, what you will do with the answer, etc. what would be a practically important difference between a solution from heuristics and the reference: I will call this difference $\\Delta_{PI}$. If a solution from heuristics is within $\\pm \\Delta_{PI}$ of the reference, you would consider the 2 values equivalent, because the difference is of no practical importance.\n\n\n\n\nThe next puzzlement is why you thought that a significance test (MWU, or 1 sample t-test) would answer your question. If you run such a test, and get a statistically significant result, it would not imply that the difference is practically important: they still could be “close enough” (in your context) to be considered equivalent to your reference.\n\nMore importantly, if you fail to reject the null, you would not (at all) be able to conclude that the two (heuristics and reference) are equivalent, just that you did not have enough power to “prove” a difference. Given that your sample size is small (10), you are most likely to fall in that scenario, in which case a significance test will tell you nothing...\n\n\n\n\nWhat (I think) you need is to perform an equivalence test (https://en.wikipedia.org/wiki/Equivalence_test). The most common method for this is the TOST (https://stats.stackexchange.com/tags/tost/info) (Two One Sided Tests) (see also here (https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/equival) with links to some R code to perform such tests, or here (https://pmc.ncbi.nlm.nih.gov/articles/PMC5502906/)).\n\nYou can run a “quick and dirty” equivalence test just by looking at the CI of the mean of your sample: if it is entirely included inside the $\\pm \\Delta_{PI}$ interval around the reference, then you have established equivalence (but note that, often, that CI exceeds the bound on one side, but not on the other, and then you will need to run an actual equivalence test).\n\n\n\n\nThe above would tell you if the mean of your heuristics is equivalent to your reference. But is that really what you need? Will you be able to use a mean of multiple runs of the heuristics, or will you want to (need to) use a single heuristic? If it is the latter case, then having established that the mean is equivalent to the reference does not help you (because any given single heuristic could be very far from the reference - all you know is that, on average, they are close enough). You will then need to look at Tolerance Intervals (https://en.wikipedia.org/wiki/Tolerance_interval) for your heuristics. You can still use a TOST approach, but with a different test. Tolerance intervals will ensure that a given proportion (coverage) of your heuristics are within the practically important interval, at a given confidence level: so, most of the time, a single heuristic value will be \"close enough\".\n\n\n\n\nTalking about tests, it is also unclear why you wanted to use a MWU test. Presumably because the heuristics sample did not look “normal enough”? With only 10 observations, that is hard to eyeball, even with a Q-Q plot, and tests of normality are quite unreliable with such a small sample size. More worrying, for your heuristics to be “well behaved”, they should be more or less symmetric around the reference, with a mean error to the reference of 0. But if they looked non-normal to you, it implies a skew, and thus some bias to the reference. So if you observed this, I would look at the heuristics and address this issue first, before running any statistical test.\n\nFor an equivalence test of the means, unfortunately, there are no good nonparametric tests in your scenario: only the one sample t-test (permutation, or bootstrap could be used, but with a sample size of 10, I would not trust them: you do not have enough observations to claim you have a sample representative of the population). For an equivalence test of the proportion (Tolerance intervals), again the “common” method assumes normality of the distribution, but there are nonparametric methods (beside bootstrap) (see e.g. here (https://medium.com/@animeshjoshi88/tolerance-intervals-theory-construction-and-simulation-c81a7a1367c9) but again, with only 10 observations, it will be challenging to achieve the desired confidence level, or coverage (proportion included in the interval).\n\n\n\n\nAnd in any case, I do not see how the MWU test will allow you to conclude that the heuristic values are “close enough” to the reference.... (because that is not what the MWU test tests - it is a test of the null of stochastic homogeneity).\n\n\n\n\nAnd just as a final comment, for scenarios outside your specific question, I see no reason why you could not use a MWU test to compare a sample, to a reference (constant vector). It may however depend on how the statistic is computed: if the software computes the W statistic (which most do, as it is more computationally efficient), then you will end up with many ties, and it would affect the power, and the computation of exact p-values. But that would not be the case if one uses the U statistic (but you should get very similar results). As an example, with a t-test, whether you compare a sample to a constant (1 sample t test), a sample to a constant vector (2 sample t test), or a sample to a constant vector (paired t test), you would obtain the exact same p-value). Another caveat is that the MWU test is subject to Type I error inflation when the variances of the 2 samples are not equal (which is seriously the case here: one variance is $0$!). But the Brunner-Munzel test (https://en.wikipedia.org/wiki/Brunner_Munzel_Test) addresses this issue: so I would highly recommedn that you use it, instead of the MWU, if you have reasons to continue using such a test of stochastic superiority.", "answer_url": "https://stats.stackexchange.com/a/677307", "author": "jginestet", "author_url": "https://stats.stackexchange.com/users/380096/jginestet", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-30T20:59:02+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:08.569053+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/ba8a114171cbec551f0a7f4b9f04e95c559131a62357d51e159434d4acc7183d_1790825228829630100_0.json", "raw_sha256": "a03822ca860dd0b0fb0cc402754ae4cdbaad51d18873dfd19aed56ffe1cf7ec8", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=2&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677295, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "jginestet", "profile_url": "https://stats.stackexchange.com/users/380096/jginestet", "user_type": "registered"}, "created_at": "2026-09-30T20:59:02+00:00", "raw_file": "raw/codex_api_v1/ab5f4cd7f0a10bde5970354a9b213efcc81e232042487437e8579705d4ca6a20_1790825258916612700_0.json", "raw_sha256": "4cf167c399d03b9ae013b65260fcb4e38139c42cfc70aba4807f070550c1768e", "revision_guid": "9E0FBE54-CDD3-4DDB-B1D2-6157CDED2E25", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/9E0FBE54-CDD3-4DDB-B1D2-6157CDED2E25/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "jginestet", "profile_url": "https://stats.stackexchange.com/users/380096/jginestet", "user_type": "registered"}, "created_at": "2026-10-01T03:02:57+00:00", "raw_file": "raw/codex_api_v1/ab5f4cd7f0a10bde5970354a9b213efcc81e232042487437e8579705d4ca6a20_1790825258916612700_0.json", "raw_sha256": "4cf167c399d03b9ae013b65260fcb4e38139c42cfc70aba4807f070550c1768e", "revision_guid": "D4ADF678-7BAF-486D-903C-7740CDAE23F7", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/D4ADF678-7BAF-486D-903C-7740CDAE23F7/view-source"}], "score": 0, "updated_at": "2026-10-01T03:02:57+00:00"}], "domain": "statistics", "external_links": ["https://en.wikipedia.org/wiki/Brunner_Munzel_Test", "https://en.wikipedia.org/wiki/Equivalence_test", "https://en.wikipedia.org/wiki/Tolerance_interval", "https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/equival", "https://medium.com/@animeshjoshi88/tolerance-intervals-theory-construction-and-simulation-c81a7a1367c9", "https://pmc.ncbi.nlm.nih.gov/articles/PMC5502906/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Engr. Moiz Ahmad", "question_author_url": "https://stats.stackexchange.com/users/306308/engr-moiz-ahmad", "question_author_user_type": "registered", "question_created_at": "2026-09-29T06:12:41+00:00", "question_html": "

I need to compare a sample with a reference (deterministic) value, e.g., an exact optimal solution, and I am wondering that can I use MWU test while replicating the reference value to form a set of samples (of a constant value) from a degenerate distribution (probability mass concentrated on a single value)?

\n", "question_id": 677295, "question_license": "CC BY-SA 4.0", "question_score": 0, "question_text": "I need to compare a sample with a reference (deterministic) value, e.g., an exact optimal solution, and I am wondering that can I use MWU test while replicating the reference value to form a set of samples (of a constant value) from a degenerate distribution (probability mass concentrated on a single value)?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Engr. Moiz Ahmad", "profile_url": "https://stats.stackexchange.com/users/306308/engr-moiz-ahmad", "user_type": "registered"}, "created_at": "2026-09-29T06:12:41+00:00", "raw_file": "raw/codex_api_v1/ab5f4cd7f0a10bde5970354a9b213efcc81e232042487437e8579705d4ca6a20_1790825258916612700_0.json", "raw_sha256": "4cf167c399d03b9ae013b65260fcb4e38139c42cfc70aba4807f070550c1768e", "revision_guid": "2AB4C6D5-EC2C-4411-9DCC-6EB4B533DAAB", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/2AB4C6D5-EC2C-4411-9DCC-6EB4B533DAAB/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/677295/can-the-mann-whitney-u-mwu-test-be-used-with-one-sample-set-coming-from-a-dege", "split": "test", "split_group": "c2e6ef0ec5f1aca39132b9c4a0c37afc306d5da19ac43213abc81c3e1491d02e", "tags": ["hypothesis-testing", "statistical-significance", "inference", "wilcoxon-mann-whitney-test", "method-comparison"], "thread_id": "stats:677295", "title": "Can the Mann-Whitney U (MWU) test be used with one sample set coming from a degenerate distribution in a two-sample comparison?"}} {"citation_context": " is the TOST (https://stats.stackexchange.com/tags/tost/info) (Two One Sided Tests) (see also here (https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/equival) with links to some R code to perform such tests, or here (https://pmc.ncbi.nlm.nih.gov/articles/PM", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/equival", "kind": "external_url", "post_id": 677307, "post_url": "https://stats.stackexchange.com/a/677307", "product": "citations", "record_id": "Scientific-Citation-Graph:4d312861c9fb978f54c32a3e", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

To begin with, it is quite difficult to understand what you are trying to accomplish, and what led you to a MWUt.

\n

You say that you want to “compare a sample with a reference (deterministic) value”. Well, at some level, you already did, and the answer is that they are different (one is “random”, the other is not). A slightly less trivial approach is simply to compare your values from heuristics to your reference value: how many are exactly equal to the reference? Most likely, none...
\nSo (I think) what you really want to do is test if your “solutions from heuristics” are “close enough” to the reference value. For that you should first define, based on your context, what you are measuring, what you will do with the answer, etc. what would be a practically important difference between a solution from heuristics and the reference: I will call this difference $\\Delta_{PI}$. If a solution from heuristics is within $\\pm \\Delta_{PI}$ of the reference, you would consider the 2 values equivalent, because the difference is of no practical importance.

\n

The next puzzlement is why you thought that a significance test (MWU, or 1 sample t-test) would answer your question. If you run such a test, and get a statistically significant result, it would not imply that the difference is practically important: they still could be “close enough” (in your context) to be considered equivalent to your reference.
\nMore importantly, if you fail to reject the null, you would not (at all) be able to conclude that the two (heuristics and reference) are equivalent, just that you did not have enough power to “prove” a difference. Given that your sample size is small (10), you are most likely to fall in that scenario, in which case a significance test will tell you nothing...

\n

What (I think) you need is to perform an equivalence test. The most common method for this is the TOST (Two One Sided Tests) (see also here with links to some R code to perform such tests, or here).
\nYou can run a “quick and dirty” equivalence test just by looking at the CI of the mean of your sample: if it is entirely included inside the $\\pm \\Delta_{PI}$ interval around the reference, then you have established equivalence (but note that, often, that CI exceeds the bound on one side, but not on the other, and then you will need to run an actual equivalence test).

\n

The above would tell you if the mean of your heuristics is equivalent to your reference. But is that really what you need? Will you be able to use a mean of multiple runs of the heuristics, or will you want to (need to) use a single heuristic? If it is the latter case, then having established that the mean is equivalent to the reference does not help you (because any given single heuristic could be very far from the reference - all you know is that, on average, they are close enough). You will then need to look at Tolerance Intervals for your heuristics. You can still use a TOST approach, but with a different test. Tolerance intervals will ensure that a given proportion (coverage) of your heuristics are within the practically important interval, at a given confidence level: so, most of the time, a single heuristic value will be "close enough".

\n

Talking about tests, it is also unclear why you wanted to use a MWU test. Presumably because the heuristics sample did not look “normal enough”? With only 10 observations, that is hard to eyeball, even with a Q-Q plot, and tests of normality are quite unreliable with such a small sample size. More worrying, for your heuristics to be “well behaved”, they should be more or less symmetric around the reference, with a mean error to the reference of 0. But if they looked non-normal to you, it implies a skew, and thus some bias to the reference. So if you observed this, I would look at the heuristics and address this issue first, before running any statistical test.
\nFor an equivalence test of the means, unfortunately, there are no good nonparametric tests in your scenario: only the one sample t-test (permutation, or bootstrap could be used, but with a sample size of 10, I would not trust them: you do not have enough observations to claim you have a sample representative of the population). For an equivalence test of the proportion (Tolerance intervals), again the “common” method assumes normality of the distribution, but there are nonparametric methods (beside bootstrap) (see e.g. here but again, with only 10 observations, it will be challenging to achieve the desired confidence level, or coverage (proportion included in the interval).

\n

And in any case, I do not see how the MWU test will allow you to conclude that the heuristic values are “close enough” to the reference.... (because that is not what the MWU test tests - it is a test of the null of stochastic homogeneity).

\n

And just as a final comment, for scenarios outside your specific question, I see no reason why you could not use a MWU test to compare a sample, to a reference (constant vector). It may however depend on how the statistic is computed: if the software computes the W statistic (which most do, as it is more computationally efficient), then you will end up with many ties, and it would affect the power, and the computation of exact p-values. But that would not be the case if one uses the U statistic (but you should get very similar results). As an example, with a t-test, whether you compare a sample to a constant (1 sample t test), a sample to a constant vector (2 sample t test), or a sample to a constant vector (paired t test), you would obtain the exact same p-value). Another caveat is that the MWU test is subject to Type I error inflation when the variances of the 2 samples are not equal (which is seriously the case here: one variance is $0$!). But the Brunner-Munzel test addresses this issue: so I would highly recommedn that you use it, instead of the MWU, if you have reasons to continue using such a test of stochastic superiority.

\n", "answer_id": 677307, "answer_text": "To begin with, it is quite difficult to understand what you are trying to accomplish, and what led you to a MWUt.\n\n\n\n\nYou say that you want to “compare a sample with a reference (deterministic) value”. Well, at some level, you already did, and the answer is that they are different (one is “random”, the other is not). A slightly less trivial approach is simply to compare your values from heuristics to your reference value: how many are exactly equal to the reference? Most likely, none...\n\nSo (I think) what you really want to do is test if your “solutions from heuristics” are “close enough” to the reference value. For that you should first define, based on your context, what you are measuring, what you will do with the answer, etc. what would be a practically important difference between a solution from heuristics and the reference: I will call this difference $\\Delta_{PI}$. If a solution from heuristics is within $\\pm \\Delta_{PI}$ of the reference, you would consider the 2 values equivalent, because the difference is of no practical importance.\n\n\n\n\nThe next puzzlement is why you thought that a significance test (MWU, or 1 sample t-test) would answer your question. If you run such a test, and get a statistically significant result, it would not imply that the difference is practically important: they still could be “close enough” (in your context) to be considered equivalent to your reference.\n\nMore importantly, if you fail to reject the null, you would not (at all) be able to conclude that the two (heuristics and reference) are equivalent, just that you did not have enough power to “prove” a difference. Given that your sample size is small (10), you are most likely to fall in that scenario, in which case a significance test will tell you nothing...\n\n\n\n\nWhat (I think) you need is to perform an equivalence test (https://en.wikipedia.org/wiki/Equivalence_test). The most common method for this is the TOST (https://stats.stackexchange.com/tags/tost/info) (Two One Sided Tests) (see also here (https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/equival) with links to some R code to perform such tests, or here (https://pmc.ncbi.nlm.nih.gov/articles/PMC5502906/)).\n\nYou can run a “quick and dirty” equivalence test just by looking at the CI of the mean of your sample: if it is entirely included inside the $\\pm \\Delta_{PI}$ interval around the reference, then you have established equivalence (but note that, often, that CI exceeds the bound on one side, but not on the other, and then you will need to run an actual equivalence test).\n\n\n\n\nThe above would tell you if the mean of your heuristics is equivalent to your reference. But is that really what you need? Will you be able to use a mean of multiple runs of the heuristics, or will you want to (need to) use a single heuristic? If it is the latter case, then having established that the mean is equivalent to the reference does not help you (because any given single heuristic could be very far from the reference - all you know is that, on average, they are close enough). You will then need to look at Tolerance Intervals (https://en.wikipedia.org/wiki/Tolerance_interval) for your heuristics. You can still use a TOST approach, but with a different test. Tolerance intervals will ensure that a given proportion (coverage) of your heuristics are within the practically important interval, at a given confidence level: so, most of the time, a single heuristic value will be \"close enough\".\n\n\n\n\nTalking about tests, it is also unclear why you wanted to use a MWU test. Presumably because the heuristics sample did not look “normal enough”? With only 10 observations, that is hard to eyeball, even with a Q-Q plot, and tests of normality are quite unreliable with such a small sample size. More worrying, for your heuristics to be “well behaved”, they should be more or less symmetric around the reference, with a mean error to the reference of 0. But if they looked non-normal to you, it implies a skew, and thus some bias to the reference. So if you observed this, I would look at the heuristics and address this issue first, before running any statistical test.\n\nFor an equivalence test of the means, unfortunately, there are no good nonparametric tests in your scenario: only the one sample t-test (permutation, or bootstrap could be used, but with a sample size of 10, I would not trust them: you do not have enough observations to claim you have a sample representative of the population). For an equivalence test of the proportion (Tolerance intervals), again the “common” method assumes normality of the distribution, but there are nonparametric methods (beside bootstrap) (see e.g. here (https://medium.com/@animeshjoshi88/tolerance-intervals-theory-construction-and-simulation-c81a7a1367c9) but again, with only 10 observations, it will be challenging to achieve the desired confidence level, or coverage (proportion included in the interval).\n\n\n\n\nAnd in any case, I do not see how the MWU test will allow you to conclude that the heuristic values are “close enough” to the reference.... (because that is not what the MWU test tests - it is a test of the null of stochastic homogeneity).\n\n\n\n\nAnd just as a final comment, for scenarios outside your specific question, I see no reason why you could not use a MWU test to compare a sample, to a reference (constant vector). It may however depend on how the statistic is computed: if the software computes the W statistic (which most do, as it is more computationally efficient), then you will end up with many ties, and it would affect the power, and the computation of exact p-values. But that would not be the case if one uses the U statistic (but you should get very similar results). As an example, with a t-test, whether you compare a sample to a constant (1 sample t test), a sample to a constant vector (2 sample t test), or a sample to a constant vector (paired t test), you would obtain the exact same p-value). Another caveat is that the MWU test is subject to Type I error inflation when the variances of the 2 samples are not equal (which is seriously the case here: one variance is $0$!). But the Brunner-Munzel test (https://en.wikipedia.org/wiki/Brunner_Munzel_Test) addresses this issue: so I would highly recommedn that you use it, instead of the MWU, if you have reasons to continue using such a test of stochastic superiority.", "answer_url": "https://stats.stackexchange.com/a/677307", "author": "jginestet", "author_url": "https://stats.stackexchange.com/users/380096/jginestet", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-30T20:59:02+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:08.569053+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/ba8a114171cbec551f0a7f4b9f04e95c559131a62357d51e159434d4acc7183d_1790825228829630100_0.json", "raw_sha256": "a03822ca860dd0b0fb0cc402754ae4cdbaad51d18873dfd19aed56ffe1cf7ec8", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=2&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677295, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "jginestet", "profile_url": "https://stats.stackexchange.com/users/380096/jginestet", "user_type": "registered"}, "created_at": "2026-09-30T20:59:02+00:00", "raw_file": "raw/codex_api_v1/ab5f4cd7f0a10bde5970354a9b213efcc81e232042487437e8579705d4ca6a20_1790825258916612700_0.json", "raw_sha256": "4cf167c399d03b9ae013b65260fcb4e38139c42cfc70aba4807f070550c1768e", "revision_guid": "9E0FBE54-CDD3-4DDB-B1D2-6157CDED2E25", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/9E0FBE54-CDD3-4DDB-B1D2-6157CDED2E25/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "jginestet", "profile_url": "https://stats.stackexchange.com/users/380096/jginestet", "user_type": "registered"}, "created_at": "2026-10-01T03:02:57+00:00", "raw_file": "raw/codex_api_v1/ab5f4cd7f0a10bde5970354a9b213efcc81e232042487437e8579705d4ca6a20_1790825258916612700_0.json", "raw_sha256": "4cf167c399d03b9ae013b65260fcb4e38139c42cfc70aba4807f070550c1768e", "revision_guid": "D4ADF678-7BAF-486D-903C-7740CDAE23F7", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/D4ADF678-7BAF-486D-903C-7740CDAE23F7/view-source"}], "score": 0, "updated_at": "2026-10-01T03:02:57+00:00"}], "domain": "statistics", "external_links": ["https://en.wikipedia.org/wiki/Brunner_Munzel_Test", "https://en.wikipedia.org/wiki/Equivalence_test", "https://en.wikipedia.org/wiki/Tolerance_interval", "https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/equival", "https://medium.com/@animeshjoshi88/tolerance-intervals-theory-construction-and-simulation-c81a7a1367c9", "https://pmc.ncbi.nlm.nih.gov/articles/PMC5502906/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Engr. Moiz Ahmad", "question_author_url": "https://stats.stackexchange.com/users/306308/engr-moiz-ahmad", "question_author_user_type": "registered", "question_created_at": "2026-09-29T06:12:41+00:00", "question_html": "

I need to compare a sample with a reference (deterministic) value, e.g., an exact optimal solution, and I am wondering that can I use MWU test while replicating the reference value to form a set of samples (of a constant value) from a degenerate distribution (probability mass concentrated on a single value)?

\n", "question_id": 677295, "question_license": "CC BY-SA 4.0", "question_score": 0, "question_text": "I need to compare a sample with a reference (deterministic) value, e.g., an exact optimal solution, and I am wondering that can I use MWU test while replicating the reference value to form a set of samples (of a constant value) from a degenerate distribution (probability mass concentrated on a single value)?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Engr. Moiz Ahmad", "profile_url": "https://stats.stackexchange.com/users/306308/engr-moiz-ahmad", "user_type": "registered"}, "created_at": "2026-09-29T06:12:41+00:00", "raw_file": "raw/codex_api_v1/ab5f4cd7f0a10bde5970354a9b213efcc81e232042487437e8579705d4ca6a20_1790825258916612700_0.json", "raw_sha256": "4cf167c399d03b9ae013b65260fcb4e38139c42cfc70aba4807f070550c1768e", "revision_guid": "2AB4C6D5-EC2C-4411-9DCC-6EB4B533DAAB", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/2AB4C6D5-EC2C-4411-9DCC-6EB4B533DAAB/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/677295/can-the-mann-whitney-u-mwu-test-be-used-with-one-sample-set-coming-from-a-dege", "split": "test", "split_group": "c2e6ef0ec5f1aca39132b9c4a0c37afc306d5da19ac43213abc81c3e1491d02e", "tags": ["hypothesis-testing", "statistical-significance", "inference", "wilcoxon-mann-whitney-test", "method-comparison"], "thread_id": "stats:677295", "title": "Can the Mann-Whitney U (MWU) test be used with one sample set coming from a degenerate distribution in a two-sample comparison?"}} {"citation_context": "rmality of the distribution, but there are nonparametric methods (beside bootstrap) (see e.g. here (https://medium.com/@animeshjoshi88/tolerance-intervals-theory-construction-and-simulation-c81a7a1367c9) but again, with only 10 observations, it will be challenging to achieve the desired confidence lev", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://medium.com/@animeshjoshi88/tolerance-intervals-theory-construction-and-simulation-c81a7a1367c9", "kind": "external_url", "post_id": 677307, "post_url": "https://stats.stackexchange.com/a/677307", "product": "citations", "record_id": "Scientific-Citation-Graph:2fc2d99820eca151a3ec3bf0", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

To begin with, it is quite difficult to understand what you are trying to accomplish, and what led you to a MWUt.

\n

You say that you want to “compare a sample with a reference (deterministic) value”. Well, at some level, you already did, and the answer is that they are different (one is “random”, the other is not). A slightly less trivial approach is simply to compare your values from heuristics to your reference value: how many are exactly equal to the reference? Most likely, none...
\nSo (I think) what you really want to do is test if your “solutions from heuristics” are “close enough” to the reference value. For that you should first define, based on your context, what you are measuring, what you will do with the answer, etc. what would be a practically important difference between a solution from heuristics and the reference: I will call this difference $\\Delta_{PI}$. If a solution from heuristics is within $\\pm \\Delta_{PI}$ of the reference, you would consider the 2 values equivalent, because the difference is of no practical importance.

\n

The next puzzlement is why you thought that a significance test (MWU, or 1 sample t-test) would answer your question. If you run such a test, and get a statistically significant result, it would not imply that the difference is practically important: they still could be “close enough” (in your context) to be considered equivalent to your reference.
\nMore importantly, if you fail to reject the null, you would not (at all) be able to conclude that the two (heuristics and reference) are equivalent, just that you did not have enough power to “prove” a difference. Given that your sample size is small (10), you are most likely to fall in that scenario, in which case a significance test will tell you nothing...

\n

What (I think) you need is to perform an equivalence test. The most common method for this is the TOST (Two One Sided Tests) (see also here with links to some R code to perform such tests, or here).
\nYou can run a “quick and dirty” equivalence test just by looking at the CI of the mean of your sample: if it is entirely included inside the $\\pm \\Delta_{PI}$ interval around the reference, then you have established equivalence (but note that, often, that CI exceeds the bound on one side, but not on the other, and then you will need to run an actual equivalence test).

\n

The above would tell you if the mean of your heuristics is equivalent to your reference. But is that really what you need? Will you be able to use a mean of multiple runs of the heuristics, or will you want to (need to) use a single heuristic? If it is the latter case, then having established that the mean is equivalent to the reference does not help you (because any given single heuristic could be very far from the reference - all you know is that, on average, they are close enough). You will then need to look at Tolerance Intervals for your heuristics. You can still use a TOST approach, but with a different test. Tolerance intervals will ensure that a given proportion (coverage) of your heuristics are within the practically important interval, at a given confidence level: so, most of the time, a single heuristic value will be "close enough".

\n

Talking about tests, it is also unclear why you wanted to use a MWU test. Presumably because the heuristics sample did not look “normal enough”? With only 10 observations, that is hard to eyeball, even with a Q-Q plot, and tests of normality are quite unreliable with such a small sample size. More worrying, for your heuristics to be “well behaved”, they should be more or less symmetric around the reference, with a mean error to the reference of 0. But if they looked non-normal to you, it implies a skew, and thus some bias to the reference. So if you observed this, I would look at the heuristics and address this issue first, before running any statistical test.
\nFor an equivalence test of the means, unfortunately, there are no good nonparametric tests in your scenario: only the one sample t-test (permutation, or bootstrap could be used, but with a sample size of 10, I would not trust them: you do not have enough observations to claim you have a sample representative of the population). For an equivalence test of the proportion (Tolerance intervals), again the “common” method assumes normality of the distribution, but there are nonparametric methods (beside bootstrap) (see e.g. here but again, with only 10 observations, it will be challenging to achieve the desired confidence level, or coverage (proportion included in the interval).

\n

And in any case, I do not see how the MWU test will allow you to conclude that the heuristic values are “close enough” to the reference.... (because that is not what the MWU test tests - it is a test of the null of stochastic homogeneity).

\n

And just as a final comment, for scenarios outside your specific question, I see no reason why you could not use a MWU test to compare a sample, to a reference (constant vector). It may however depend on how the statistic is computed: if the software computes the W statistic (which most do, as it is more computationally efficient), then you will end up with many ties, and it would affect the power, and the computation of exact p-values. But that would not be the case if one uses the U statistic (but you should get very similar results). As an example, with a t-test, whether you compare a sample to a constant (1 sample t test), a sample to a constant vector (2 sample t test), or a sample to a constant vector (paired t test), you would obtain the exact same p-value). Another caveat is that the MWU test is subject to Type I error inflation when the variances of the 2 samples are not equal (which is seriously the case here: one variance is $0$!). But the Brunner-Munzel test addresses this issue: so I would highly recommedn that you use it, instead of the MWU, if you have reasons to continue using such a test of stochastic superiority.

\n", "answer_id": 677307, "answer_text": "To begin with, it is quite difficult to understand what you are trying to accomplish, and what led you to a MWUt.\n\n\n\n\nYou say that you want to “compare a sample with a reference (deterministic) value”. Well, at some level, you already did, and the answer is that they are different (one is “random”, the other is not). A slightly less trivial approach is simply to compare your values from heuristics to your reference value: how many are exactly equal to the reference? Most likely, none...\n\nSo (I think) what you really want to do is test if your “solutions from heuristics” are “close enough” to the reference value. For that you should first define, based on your context, what you are measuring, what you will do with the answer, etc. what would be a practically important difference between a solution from heuristics and the reference: I will call this difference $\\Delta_{PI}$. If a solution from heuristics is within $\\pm \\Delta_{PI}$ of the reference, you would consider the 2 values equivalent, because the difference is of no practical importance.\n\n\n\n\nThe next puzzlement is why you thought that a significance test (MWU, or 1 sample t-test) would answer your question. If you run such a test, and get a statistically significant result, it would not imply that the difference is practically important: they still could be “close enough” (in your context) to be considered equivalent to your reference.\n\nMore importantly, if you fail to reject the null, you would not (at all) be able to conclude that the two (heuristics and reference) are equivalent, just that you did not have enough power to “prove” a difference. Given that your sample size is small (10), you are most likely to fall in that scenario, in which case a significance test will tell you nothing...\n\n\n\n\nWhat (I think) you need is to perform an equivalence test (https://en.wikipedia.org/wiki/Equivalence_test). The most common method for this is the TOST (https://stats.stackexchange.com/tags/tost/info) (Two One Sided Tests) (see also here (https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/equival) with links to some R code to perform such tests, or here (https://pmc.ncbi.nlm.nih.gov/articles/PMC5502906/)).\n\nYou can run a “quick and dirty” equivalence test just by looking at the CI of the mean of your sample: if it is entirely included inside the $\\pm \\Delta_{PI}$ interval around the reference, then you have established equivalence (but note that, often, that CI exceeds the bound on one side, but not on the other, and then you will need to run an actual equivalence test).\n\n\n\n\nThe above would tell you if the mean of your heuristics is equivalent to your reference. But is that really what you need? Will you be able to use a mean of multiple runs of the heuristics, or will you want to (need to) use a single heuristic? If it is the latter case, then having established that the mean is equivalent to the reference does not help you (because any given single heuristic could be very far from the reference - all you know is that, on average, they are close enough). You will then need to look at Tolerance Intervals (https://en.wikipedia.org/wiki/Tolerance_interval) for your heuristics. You can still use a TOST approach, but with a different test. Tolerance intervals will ensure that a given proportion (coverage) of your heuristics are within the practically important interval, at a given confidence level: so, most of the time, a single heuristic value will be \"close enough\".\n\n\n\n\nTalking about tests, it is also unclear why you wanted to use a MWU test. Presumably because the heuristics sample did not look “normal enough”? With only 10 observations, that is hard to eyeball, even with a Q-Q plot, and tests of normality are quite unreliable with such a small sample size. More worrying, for your heuristics to be “well behaved”, they should be more or less symmetric around the reference, with a mean error to the reference of 0. But if they looked non-normal to you, it implies a skew, and thus some bias to the reference. So if you observed this, I would look at the heuristics and address this issue first, before running any statistical test.\n\nFor an equivalence test of the means, unfortunately, there are no good nonparametric tests in your scenario: only the one sample t-test (permutation, or bootstrap could be used, but with a sample size of 10, I would not trust them: you do not have enough observations to claim you have a sample representative of the population). For an equivalence test of the proportion (Tolerance intervals), again the “common” method assumes normality of the distribution, but there are nonparametric methods (beside bootstrap) (see e.g. here (https://medium.com/@animeshjoshi88/tolerance-intervals-theory-construction-and-simulation-c81a7a1367c9) but again, with only 10 observations, it will be challenging to achieve the desired confidence level, or coverage (proportion included in the interval).\n\n\n\n\nAnd in any case, I do not see how the MWU test will allow you to conclude that the heuristic values are “close enough” to the reference.... (because that is not what the MWU test tests - it is a test of the null of stochastic homogeneity).\n\n\n\n\nAnd just as a final comment, for scenarios outside your specific question, I see no reason why you could not use a MWU test to compare a sample, to a reference (constant vector). It may however depend on how the statistic is computed: if the software computes the W statistic (which most do, as it is more computationally efficient), then you will end up with many ties, and it would affect the power, and the computation of exact p-values. But that would not be the case if one uses the U statistic (but you should get very similar results). As an example, with a t-test, whether you compare a sample to a constant (1 sample t test), a sample to a constant vector (2 sample t test), or a sample to a constant vector (paired t test), you would obtain the exact same p-value). Another caveat is that the MWU test is subject to Type I error inflation when the variances of the 2 samples are not equal (which is seriously the case here: one variance is $0$!). But the Brunner-Munzel test (https://en.wikipedia.org/wiki/Brunner_Munzel_Test) addresses this issue: so I would highly recommedn that you use it, instead of the MWU, if you have reasons to continue using such a test of stochastic superiority.", "answer_url": "https://stats.stackexchange.com/a/677307", "author": "jginestet", "author_url": "https://stats.stackexchange.com/users/380096/jginestet", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-30T20:59:02+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:08.569053+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/ba8a114171cbec551f0a7f4b9f04e95c559131a62357d51e159434d4acc7183d_1790825228829630100_0.json", "raw_sha256": "a03822ca860dd0b0fb0cc402754ae4cdbaad51d18873dfd19aed56ffe1cf7ec8", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=2&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677295, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "jginestet", "profile_url": "https://stats.stackexchange.com/users/380096/jginestet", "user_type": "registered"}, "created_at": "2026-09-30T20:59:02+00:00", "raw_file": "raw/codex_api_v1/ab5f4cd7f0a10bde5970354a9b213efcc81e232042487437e8579705d4ca6a20_1790825258916612700_0.json", "raw_sha256": "4cf167c399d03b9ae013b65260fcb4e38139c42cfc70aba4807f070550c1768e", "revision_guid": "9E0FBE54-CDD3-4DDB-B1D2-6157CDED2E25", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/9E0FBE54-CDD3-4DDB-B1D2-6157CDED2E25/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "jginestet", "profile_url": "https://stats.stackexchange.com/users/380096/jginestet", "user_type": "registered"}, "created_at": "2026-10-01T03:02:57+00:00", "raw_file": "raw/codex_api_v1/ab5f4cd7f0a10bde5970354a9b213efcc81e232042487437e8579705d4ca6a20_1790825258916612700_0.json", "raw_sha256": "4cf167c399d03b9ae013b65260fcb4e38139c42cfc70aba4807f070550c1768e", "revision_guid": "D4ADF678-7BAF-486D-903C-7740CDAE23F7", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/D4ADF678-7BAF-486D-903C-7740CDAE23F7/view-source"}], "score": 0, "updated_at": "2026-10-01T03:02:57+00:00"}], "domain": "statistics", "external_links": ["https://en.wikipedia.org/wiki/Brunner_Munzel_Test", "https://en.wikipedia.org/wiki/Equivalence_test", "https://en.wikipedia.org/wiki/Tolerance_interval", "https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/equival", "https://medium.com/@animeshjoshi88/tolerance-intervals-theory-construction-and-simulation-c81a7a1367c9", "https://pmc.ncbi.nlm.nih.gov/articles/PMC5502906/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Engr. Moiz Ahmad", "question_author_url": "https://stats.stackexchange.com/users/306308/engr-moiz-ahmad", "question_author_user_type": "registered", "question_created_at": "2026-09-29T06:12:41+00:00", "question_html": "

I need to compare a sample with a reference (deterministic) value, e.g., an exact optimal solution, and I am wondering that can I use MWU test while replicating the reference value to form a set of samples (of a constant value) from a degenerate distribution (probability mass concentrated on a single value)?

\n", "question_id": 677295, "question_license": "CC BY-SA 4.0", "question_score": 0, "question_text": "I need to compare a sample with a reference (deterministic) value, e.g., an exact optimal solution, and I am wondering that can I use MWU test while replicating the reference value to form a set of samples (of a constant value) from a degenerate distribution (probability mass concentrated on a single value)?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Engr. Moiz Ahmad", "profile_url": "https://stats.stackexchange.com/users/306308/engr-moiz-ahmad", "user_type": "registered"}, "created_at": "2026-09-29T06:12:41+00:00", "raw_file": "raw/codex_api_v1/ab5f4cd7f0a10bde5970354a9b213efcc81e232042487437e8579705d4ca6a20_1790825258916612700_0.json", "raw_sha256": "4cf167c399d03b9ae013b65260fcb4e38139c42cfc70aba4807f070550c1768e", "revision_guid": "2AB4C6D5-EC2C-4411-9DCC-6EB4B533DAAB", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/2AB4C6D5-EC2C-4411-9DCC-6EB4B533DAAB/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/677295/can-the-mann-whitney-u-mwu-test-be-used-with-one-sample-set-coming-from-a-dege", "split": "test", "split_group": "c2e6ef0ec5f1aca39132b9c4a0c37afc306d5da19ac43213abc81c3e1491d02e", "tags": ["hypothesis-testing", "statistical-significance", "inference", "wilcoxon-mann-whitney-test", "method-comparison"], "thread_id": "stats:677295", "title": "Can the Mann-Whitney U (MWU) test be used with one sample set coming from a degenerate distribution in a two-sample comparison?"}} {"citation_context": ".mrc-cbu.cam.ac.uk/statswiki/FAQ/equival) with links to some R code to perform such tests, or here (https://pmc.ncbi.nlm.nih.gov/articles/PMC5502906/)).\n\nYou can run a “quick and dirty” equivalence test just by looking at the CI of the mean of your ", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC5502906/", "kind": "external_url", "post_id": 677307, "post_url": "https://stats.stackexchange.com/a/677307", "product": "citations", "record_id": "Scientific-Citation-Graph:36a4364d35e9b17899c50f91", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

To begin with, it is quite difficult to understand what you are trying to accomplish, and what led you to a MWUt.

\n

You say that you want to “compare a sample with a reference (deterministic) value”. Well, at some level, you already did, and the answer is that they are different (one is “random”, the other is not). A slightly less trivial approach is simply to compare your values from heuristics to your reference value: how many are exactly equal to the reference? Most likely, none...
\nSo (I think) what you really want to do is test if your “solutions from heuristics” are “close enough” to the reference value. For that you should first define, based on your context, what you are measuring, what you will do with the answer, etc. what would be a practically important difference between a solution from heuristics and the reference: I will call this difference $\\Delta_{PI}$. If a solution from heuristics is within $\\pm \\Delta_{PI}$ of the reference, you would consider the 2 values equivalent, because the difference is of no practical importance.

\n

The next puzzlement is why you thought that a significance test (MWU, or 1 sample t-test) would answer your question. If you run such a test, and get a statistically significant result, it would not imply that the difference is practically important: they still could be “close enough” (in your context) to be considered equivalent to your reference.
\nMore importantly, if you fail to reject the null, you would not (at all) be able to conclude that the two (heuristics and reference) are equivalent, just that you did not have enough power to “prove” a difference. Given that your sample size is small (10), you are most likely to fall in that scenario, in which case a significance test will tell you nothing...

\n

What (I think) you need is to perform an equivalence test. The most common method for this is the TOST (Two One Sided Tests) (see also here with links to some R code to perform such tests, or here).
\nYou can run a “quick and dirty” equivalence test just by looking at the CI of the mean of your sample: if it is entirely included inside the $\\pm \\Delta_{PI}$ interval around the reference, then you have established equivalence (but note that, often, that CI exceeds the bound on one side, but not on the other, and then you will need to run an actual equivalence test).

\n

The above would tell you if the mean of your heuristics is equivalent to your reference. But is that really what you need? Will you be able to use a mean of multiple runs of the heuristics, or will you want to (need to) use a single heuristic? If it is the latter case, then having established that the mean is equivalent to the reference does not help you (because any given single heuristic could be very far from the reference - all you know is that, on average, they are close enough). You will then need to look at Tolerance Intervals for your heuristics. You can still use a TOST approach, but with a different test. Tolerance intervals will ensure that a given proportion (coverage) of your heuristics are within the practically important interval, at a given confidence level: so, most of the time, a single heuristic value will be "close enough".

\n

Talking about tests, it is also unclear why you wanted to use a MWU test. Presumably because the heuristics sample did not look “normal enough”? With only 10 observations, that is hard to eyeball, even with a Q-Q plot, and tests of normality are quite unreliable with such a small sample size. More worrying, for your heuristics to be “well behaved”, they should be more or less symmetric around the reference, with a mean error to the reference of 0. But if they looked non-normal to you, it implies a skew, and thus some bias to the reference. So if you observed this, I would look at the heuristics and address this issue first, before running any statistical test.
\nFor an equivalence test of the means, unfortunately, there are no good nonparametric tests in your scenario: only the one sample t-test (permutation, or bootstrap could be used, but with a sample size of 10, I would not trust them: you do not have enough observations to claim you have a sample representative of the population). For an equivalence test of the proportion (Tolerance intervals), again the “common” method assumes normality of the distribution, but there are nonparametric methods (beside bootstrap) (see e.g. here but again, with only 10 observations, it will be challenging to achieve the desired confidence level, or coverage (proportion included in the interval).

\n

And in any case, I do not see how the MWU test will allow you to conclude that the heuristic values are “close enough” to the reference.... (because that is not what the MWU test tests - it is a test of the null of stochastic homogeneity).

\n

And just as a final comment, for scenarios outside your specific question, I see no reason why you could not use a MWU test to compare a sample, to a reference (constant vector). It may however depend on how the statistic is computed: if the software computes the W statistic (which most do, as it is more computationally efficient), then you will end up with many ties, and it would affect the power, and the computation of exact p-values. But that would not be the case if one uses the U statistic (but you should get very similar results). As an example, with a t-test, whether you compare a sample to a constant (1 sample t test), a sample to a constant vector (2 sample t test), or a sample to a constant vector (paired t test), you would obtain the exact same p-value). Another caveat is that the MWU test is subject to Type I error inflation when the variances of the 2 samples are not equal (which is seriously the case here: one variance is $0$!). But the Brunner-Munzel test addresses this issue: so I would highly recommedn that you use it, instead of the MWU, if you have reasons to continue using such a test of stochastic superiority.

\n", "answer_id": 677307, "answer_text": "To begin with, it is quite difficult to understand what you are trying to accomplish, and what led you to a MWUt.\n\n\n\n\nYou say that you want to “compare a sample with a reference (deterministic) value”. Well, at some level, you already did, and the answer is that they are different (one is “random”, the other is not). A slightly less trivial approach is simply to compare your values from heuristics to your reference value: how many are exactly equal to the reference? Most likely, none...\n\nSo (I think) what you really want to do is test if your “solutions from heuristics” are “close enough” to the reference value. For that you should first define, based on your context, what you are measuring, what you will do with the answer, etc. what would be a practically important difference between a solution from heuristics and the reference: I will call this difference $\\Delta_{PI}$. If a solution from heuristics is within $\\pm \\Delta_{PI}$ of the reference, you would consider the 2 values equivalent, because the difference is of no practical importance.\n\n\n\n\nThe next puzzlement is why you thought that a significance test (MWU, or 1 sample t-test) would answer your question. If you run such a test, and get a statistically significant result, it would not imply that the difference is practically important: they still could be “close enough” (in your context) to be considered equivalent to your reference.\n\nMore importantly, if you fail to reject the null, you would not (at all) be able to conclude that the two (heuristics and reference) are equivalent, just that you did not have enough power to “prove” a difference. Given that your sample size is small (10), you are most likely to fall in that scenario, in which case a significance test will tell you nothing...\n\n\n\n\nWhat (I think) you need is to perform an equivalence test (https://en.wikipedia.org/wiki/Equivalence_test). The most common method for this is the TOST (https://stats.stackexchange.com/tags/tost/info) (Two One Sided Tests) (see also here (https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/equival) with links to some R code to perform such tests, or here (https://pmc.ncbi.nlm.nih.gov/articles/PMC5502906/)).\n\nYou can run a “quick and dirty” equivalence test just by looking at the CI of the mean of your sample: if it is entirely included inside the $\\pm \\Delta_{PI}$ interval around the reference, then you have established equivalence (but note that, often, that CI exceeds the bound on one side, but not on the other, and then you will need to run an actual equivalence test).\n\n\n\n\nThe above would tell you if the mean of your heuristics is equivalent to your reference. But is that really what you need? Will you be able to use a mean of multiple runs of the heuristics, or will you want to (need to) use a single heuristic? If it is the latter case, then having established that the mean is equivalent to the reference does not help you (because any given single heuristic could be very far from the reference - all you know is that, on average, they are close enough). You will then need to look at Tolerance Intervals (https://en.wikipedia.org/wiki/Tolerance_interval) for your heuristics. You can still use a TOST approach, but with a different test. Tolerance intervals will ensure that a given proportion (coverage) of your heuristics are within the practically important interval, at a given confidence level: so, most of the time, a single heuristic value will be \"close enough\".\n\n\n\n\nTalking about tests, it is also unclear why you wanted to use a MWU test. Presumably because the heuristics sample did not look “normal enough”? With only 10 observations, that is hard to eyeball, even with a Q-Q plot, and tests of normality are quite unreliable with such a small sample size. More worrying, for your heuristics to be “well behaved”, they should be more or less symmetric around the reference, with a mean error to the reference of 0. But if they looked non-normal to you, it implies a skew, and thus some bias to the reference. So if you observed this, I would look at the heuristics and address this issue first, before running any statistical test.\n\nFor an equivalence test of the means, unfortunately, there are no good nonparametric tests in your scenario: only the one sample t-test (permutation, or bootstrap could be used, but with a sample size of 10, I would not trust them: you do not have enough observations to claim you have a sample representative of the population). For an equivalence test of the proportion (Tolerance intervals), again the “common” method assumes normality of the distribution, but there are nonparametric methods (beside bootstrap) (see e.g. here (https://medium.com/@animeshjoshi88/tolerance-intervals-theory-construction-and-simulation-c81a7a1367c9) but again, with only 10 observations, it will be challenging to achieve the desired confidence level, or coverage (proportion included in the interval).\n\n\n\n\nAnd in any case, I do not see how the MWU test will allow you to conclude that the heuristic values are “close enough” to the reference.... (because that is not what the MWU test tests - it is a test of the null of stochastic homogeneity).\n\n\n\n\nAnd just as a final comment, for scenarios outside your specific question, I see no reason why you could not use a MWU test to compare a sample, to a reference (constant vector). It may however depend on how the statistic is computed: if the software computes the W statistic (which most do, as it is more computationally efficient), then you will end up with many ties, and it would affect the power, and the computation of exact p-values. But that would not be the case if one uses the U statistic (but you should get very similar results). As an example, with a t-test, whether you compare a sample to a constant (1 sample t test), a sample to a constant vector (2 sample t test), or a sample to a constant vector (paired t test), you would obtain the exact same p-value). Another caveat is that the MWU test is subject to Type I error inflation when the variances of the 2 samples are not equal (which is seriously the case here: one variance is $0$!). But the Brunner-Munzel test (https://en.wikipedia.org/wiki/Brunner_Munzel_Test) addresses this issue: so I would highly recommedn that you use it, instead of the MWU, if you have reasons to continue using such a test of stochastic superiority.", "answer_url": "https://stats.stackexchange.com/a/677307", "author": "jginestet", "author_url": "https://stats.stackexchange.com/users/380096/jginestet", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-09-30T20:59:02+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:08.569053+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/ba8a114171cbec551f0a7f4b9f04e95c559131a62357d51e159434d4acc7183d_1790825228829630100_0.json", "raw_sha256": "a03822ca860dd0b0fb0cc402754ae4cdbaad51d18873dfd19aed56ffe1cf7ec8", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/677298;677295;677280;677279;677278;677275;677269;677266;677262;677256;677245;677243;677242;677226;677225;677217;677211;677201;677194;677193;677186;677183;677179;677177;677171;677169;677168;677151;677149;677147;677137;677135;677131;677129;677115;677110;677109;677101;677099;677098;677096;677095;677094;677085;677083;677079;677078;677075;677071;677066;677065;677062;677058;677045;677041;677035;677033;677023;677021;676999;676997;676991;676982;676981;676979;676977;676975;676971;676966;676961;676958;676956;676952;676947;676945;676937;676935;676933;676924;676922;676899;676898;676893;676889;676888;676879;676874;676873;676870;676867;676865;676858;676855;676850;676842;676832;676830;676824;676823;676821/answers?filter=withbody&order=asc&page=2&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 677295, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "jginestet", "profile_url": "https://stats.stackexchange.com/users/380096/jginestet", "user_type": "registered"}, "created_at": "2026-09-30T20:59:02+00:00", "raw_file": "raw/codex_api_v1/ab5f4cd7f0a10bde5970354a9b213efcc81e232042487437e8579705d4ca6a20_1790825258916612700_0.json", "raw_sha256": "4cf167c399d03b9ae013b65260fcb4e38139c42cfc70aba4807f070550c1768e", "revision_guid": "9E0FBE54-CDD3-4DDB-B1D2-6157CDED2E25", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/9E0FBE54-CDD3-4DDB-B1D2-6157CDED2E25/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "jginestet", "profile_url": "https://stats.stackexchange.com/users/380096/jginestet", "user_type": "registered"}, "created_at": "2026-10-01T03:02:57+00:00", "raw_file": "raw/codex_api_v1/ab5f4cd7f0a10bde5970354a9b213efcc81e232042487437e8579705d4ca6a20_1790825258916612700_0.json", "raw_sha256": "4cf167c399d03b9ae013b65260fcb4e38139c42cfc70aba4807f070550c1768e", "revision_guid": "D4ADF678-7BAF-486D-903C-7740CDAE23F7", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/D4ADF678-7BAF-486D-903C-7740CDAE23F7/view-source"}], "score": 0, "updated_at": "2026-10-01T03:02:57+00:00"}], "domain": "statistics", "external_links": ["https://en.wikipedia.org/wiki/Brunner_Munzel_Test", "https://en.wikipedia.org/wiki/Equivalence_test", "https://en.wikipedia.org/wiki/Tolerance_interval", "https://imaging.mrc-cbu.cam.ac.uk/statswiki/FAQ/equival", "https://medium.com/@animeshjoshi88/tolerance-intervals-theory-construction-and-simulation-c81a7a1367c9", "https://pmc.ncbi.nlm.nih.gov/articles/PMC5502906/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:27:03.428408+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/774052c18cd9e8fa951e893347bfa3c1a85e743fc46ec4667572002cadb10cbf_1790825224163423600_0.json", "raw_sha256": "fe4dd06d3de6c0b1bb33ba88aee0ed4284118e01f76a58dcdce220a4946329b2", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=stats&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Engr. Moiz Ahmad", "question_author_url": "https://stats.stackexchange.com/users/306308/engr-moiz-ahmad", "question_author_user_type": "registered", "question_created_at": "2026-09-29T06:12:41+00:00", "question_html": "

I need to compare a sample with a reference (deterministic) value, e.g., an exact optimal solution, and I am wondering that can I use MWU test while replicating the reference value to form a set of samples (of a constant value) from a degenerate distribution (probability mass concentrated on a single value)?

\n", "question_id": 677295, "question_license": "CC BY-SA 4.0", "question_score": 0, "question_text": "I need to compare a sample with a reference (deterministic) value, e.g., an exact optimal solution, and I am wondering that can I use MWU test while replicating the reference value to form a set of samples (of a constant value) from a degenerate distribution (probability mass concentrated on a single value)?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Engr. Moiz Ahmad", "profile_url": "https://stats.stackexchange.com/users/306308/engr-moiz-ahmad", "user_type": "registered"}, "created_at": "2026-09-29T06:12:41+00:00", "raw_file": "raw/codex_api_v1/ab5f4cd7f0a10bde5970354a9b213efcc81e232042487437e8579705d4ca6a20_1790825258916612700_0.json", "raw_sha256": "4cf167c399d03b9ae013b65260fcb4e38139c42cfc70aba4807f070550c1768e", "revision_guid": "2AB4C6D5-EC2C-4411-9DCC-6EB4B533DAAB", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://stats.stackexchange.com/revisions/2AB4C6D5-EC2C-4411-9DCC-6EB4B533DAAB/view-source"}], "source_site": "stats", "source_url": "https://stats.stackexchange.com/questions/677295/can-the-mann-whitney-u-mwu-test-be-used-with-one-sample-set-coming-from-a-dege", "split": "test", "split_group": "c2e6ef0ec5f1aca39132b9c4a0c37afc306d5da19ac43213abc81c3e1491d02e", "tags": ["hypothesis-testing", "statistical-significance", "inference", "wilcoxon-mann-whitney-test", "method-comparison"], "thread_id": "stats:677295", "title": "Can the Mann-Whitney U (MWU) test be used with one sample set coming from a degenerate distribution in a two-sample comparison?"}} {"citation_context": "The Wikipedia entry on Gauss-Legendre (https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_quadrature) says that there is a tri-diagonal matrix whose eigenvalues yield good approximations for the nodes", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_quadrature", "kind": "external_url", "post_id": 45134, "post_url": "https://scicomp.stackexchange.com/questions/45134/generating-the-quadrature-points-for-gauss-legendre", "product": "citations", "record_id": "Scientific-Citation-Graph:478b256e231443ca8c257d41", "split": "test", "thread": {"accepted_answer_id": 45135, "answers": [{"answer_html": "

As others mentioned in the comments, calculating the quadrature rule ahead of time is usually the fastest approach. However, you do not want to do that, you have a few options:

\n\n

Some libraries/packages might use a mixture of these approaches. For instance, the Julia package FastGaussQuadrature uses tabulated values for $n\\le 5$, Newton's iteration for $5<n\\le 60$ and the asymptotic formulas for $n> 60$.

\n", "answer_id": 45135, "answer_text": "As others mentioned in the comments, calculating the quadrature rule ahead of time is usually the fastest approach. However, you do not want to do that, you have a few options:\n\n\n\n\n\n\n\nGolub-Welsch algorithm (https://www.ams.org/journals/mcom/1969-23-106/S0025-5718-69-99647-1/S0025-5718-69-99647-1.pdf): Basically, you create a triadigonal matrix and calculate its eigendecomposition. The eigenvalues are the nodes and the weights are obtained from the first row of eigenvectors. For a matlab implementation, see this code (https://github.com/tcew/nodal-dg/blob/master/Codes1.1/Codes1D/JacobiGQ.m) where the coefficients alpha and beta correspond to the Jacobi polynomial associated with the quadrature (For Legendre quadrature use alpha=beta=0)\n\n\n\n\n\n\n\n\n\nCalculate the roots of the n-th Legendre polynomial (or other orthogonal polynomial) using Newton's method. You need a good initial guess, and you should use the derivative formulas to obtain the derivatives of the polynomial from its values as well as the recurrence relation. Here's a Matlab implementation (https://www.mathworks.com/matlabcentral/fileexchange/4540-legendre-gauss-quadrature-weights-and-nodes) as an example.\n\n\n\n\n\n\n\n\n\nFor very high order quadrature rules, you can consider using an asymptotic formula for the roots and weights like the ones discussed in this recent paper (https://doi.org/10.1137/140954969).\n\n\n\n\n\n\n\n\nSome libraries/packages might use a mixture of these approaches. For instance, the Julia package FastGaussQuadrature (https://github.com/JuliaApproximation/FastGaussQuadrature.jl) uses tabulated values for $n\\le 5$, Newton's iteration for $5 60$.", "answer_url": "https://scicomp.stackexchange.com/a/45135", "author": "HMe", "author_url": "https://scicomp.stackexchange.com/users/52227/hme", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-06-23T02:23:34+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; 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mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Makogan", "question_author_url": "https://scicomp.stackexchange.com/users/38908/makogan", "question_author_user_type": "registered", "question_created_at": "2025-06-22T15:37:39+00:00", "question_html": "

The Wikipedia entry on Gauss-Legendre says that there is a tri-diagonal matrix whose eigenvalues yield good approximations for the nodes of the Legendre polynomials.

\n

There are a couple of papers I have found that talk about iteration-less methods as well.

\n

If I care about computation speed much more than I do robustness, what would a good method to approximate the 0's be?

\n", "question_id": 45134, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "The Wikipedia entry on Gauss-Legendre (https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_quadrature) says that there is a tri-diagonal matrix whose eigenvalues yield good approximations for the nodes of the Legendre polynomials.\n\n\n\n\nThere are a couple of papers I have found that talk about iteration-less methods as well.\n\n\n\n\nIf I care about computation speed much more than I do robustness, what would a good method to approximate the 0's be?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Makogan", "profile_url": "https://scicomp.stackexchange.com/users/38908/makogan", "user_type": "registered"}, "created_at": "2025-06-22T15:37:39+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "07553FF8-9272-42C5-A2B7-1B148A7B7192", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/07553FF8-9272-42C5-A2B7-1B148A7B7192/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2025-06-23T15:58:46+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "D9C93E64-BD3E-4570-AC26-631D0D18E64C", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://scicomp.stackexchange.com/revisions/D9C93E64-BD3E-4570-AC26-631D0D18E64C/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Anton Menshov", "profile_url": "https://scicomp.stackexchange.com/users/20688/anton-menshov", "user_type": "moderator"}, "created_at": "2025-06-24T22:14:07+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "5EA1A740-F16C-4BC6-BEC6-176E698E39EB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/5EA1A740-F16C-4BC6-BEC6-176E698E39EB/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45134/generating-the-quadrature-points-for-gauss-legendre", "split": "test", "split_group": "33c5482fd4ae22f5fa06393523263229d384085484a92366eb6dbf9a38687f94", "tags": ["numerics", "quadrature", "approximation", "polynomials", "numerical-integration"], "thread_id": "scicomp:45134", "title": "Generating the quadrature points for Gauss Legendre?"}} {"citation_context": "using an asymptotic formula for the roots and weights like the ones discussed in this recent paper (https://doi.org/10.1137/140954969).\n\n\n\n\n\n\n\n\nSome libraries/packages might use a mixture of these approaches. For instance, the Julia ", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": "10.1137/140954969", "external_url": "https://doi.org/10.1137/140954969", "kind": "doi_url", "post_id": 45135, "post_url": "https://scicomp.stackexchange.com/a/45135", "product": "citations", "record_id": "Scientific-Citation-Graph:f21027907e525b3b1562182c", "split": "test", "thread": {"accepted_answer_id": 45135, "answers": [{"answer_html": "

As others mentioned in the comments, calculating the quadrature rule ahead of time is usually the fastest approach. However, you do not want to do that, you have a few options:

\n\n

Some libraries/packages might use a mixture of these approaches. For instance, the Julia package FastGaussQuadrature uses tabulated values for $n\\le 5$, Newton's iteration for $5<n\\le 60$ and the asymptotic formulas for $n> 60$.

\n", "answer_id": 45135, "answer_text": "As others mentioned in the comments, calculating the quadrature rule ahead of time is usually the fastest approach. However, you do not want to do that, you have a few options:\n\n\n\n\n\n\n\nGolub-Welsch algorithm (https://www.ams.org/journals/mcom/1969-23-106/S0025-5718-69-99647-1/S0025-5718-69-99647-1.pdf): Basically, you create a triadigonal matrix and calculate its eigendecomposition. The eigenvalues are the nodes and the weights are obtained from the first row of eigenvectors. For a matlab implementation, see this code (https://github.com/tcew/nodal-dg/blob/master/Codes1.1/Codes1D/JacobiGQ.m) where the coefficients alpha and beta correspond to the Jacobi polynomial associated with the quadrature (For Legendre quadrature use alpha=beta=0)\n\n\n\n\n\n\n\n\n\nCalculate the roots of the n-th Legendre polynomial (or other orthogonal polynomial) using Newton's method. You need a good initial guess, and you should use the derivative formulas to obtain the derivatives of the polynomial from its values as well as the recurrence relation. Here's a Matlab implementation (https://www.mathworks.com/matlabcentral/fileexchange/4540-legendre-gauss-quadrature-weights-and-nodes) as an example.\n\n\n\n\n\n\n\n\n\nFor very high order quadrature rules, you can consider using an asymptotic formula for the roots and weights like the ones discussed in this recent paper (https://doi.org/10.1137/140954969).\n\n\n\n\n\n\n\n\nSome libraries/packages might use a mixture of these approaches. 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The Wikipedia entry on Gauss-Legendre says that there is a tri-diagonal matrix whose eigenvalues yield good approximations for the nodes of the Legendre polynomials.

\n

There are a couple of papers I have found that talk about iteration-less methods as well.

\n

If I care about computation speed much more than I do robustness, what would a good method to approximate the 0's be?

\n", "question_id": 45134, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "The Wikipedia entry on Gauss-Legendre (https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_quadrature) says that there is a tri-diagonal matrix whose eigenvalues yield good approximations for the nodes of the Legendre polynomials.\n\n\n\n\nThere are a couple of papers I have found that talk about iteration-less methods as well.\n\n\n\n\nIf I care about computation speed much more than I do robustness, what would a good method to approximate the 0's be?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Makogan", "profile_url": "https://scicomp.stackexchange.com/users/38908/makogan", "user_type": "registered"}, "created_at": "2025-06-22T15:37:39+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "07553FF8-9272-42C5-A2B7-1B148A7B7192", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/07553FF8-9272-42C5-A2B7-1B148A7B7192/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2025-06-23T15:58:46+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "D9C93E64-BD3E-4570-AC26-631D0D18E64C", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://scicomp.stackexchange.com/revisions/D9C93E64-BD3E-4570-AC26-631D0D18E64C/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Anton Menshov", "profile_url": "https://scicomp.stackexchange.com/users/20688/anton-menshov", "user_type": "moderator"}, "created_at": "2025-06-24T22:14:07+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "5EA1A740-F16C-4BC6-BEC6-176E698E39EB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/5EA1A740-F16C-4BC6-BEC6-176E698E39EB/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45134/generating-the-quadrature-points-for-gauss-legendre", "split": "test", "split_group": "33c5482fd4ae22f5fa06393523263229d384085484a92366eb6dbf9a38687f94", "tags": ["numerics", "quadrature", "approximation", "polynomials", "numerical-integration"], "thread_id": "scicomp:45134", "title": "Generating the quadrature points for Gauss Legendre?"}} {"citation_context": "kages might use a mixture of these approaches. For instance, the Julia package FastGaussQuadrature (https://github.com/JuliaApproximation/FastGaussQuadrature.jl) uses tabulated values for $n\\le 5$, Newton's iteration for $5As others mentioned in the comments, calculating the quadrature rule ahead of time is usually the fastest approach. However, you do not want to do that, you have a few options:

\n
    \n

  • Golub-Welsch algorithm: Basically, you create a triadigonal matrix and calculate its eigendecomposition. The eigenvalues are the nodes and the weights are obtained from the first row of eigenvectors. For a matlab implementation, see this code where the coefficients alpha and beta correspond to the Jacobi polynomial associated with the quadrature (For Legendre quadrature use alpha=beta=0)

    \n
    • \n

  • Calculate the roots of the n-th Legendre polynomial (or other orthogonal polynomial) using Newton's method. You need a good initial guess, and you should use the derivative formulas to obtain the derivatives of the polynomial from its values as well as the recurrence relation. Here's a Matlab implementation as an example.

    \n
    • \n

  • For very high order quadrature rules, you can consider using an asymptotic formula for the roots and weights like the ones discussed in this recent paper.

    \n
    • \n
\n

Some libraries/packages might use a mixture of these approaches. For instance, the Julia package FastGaussQuadrature uses tabulated values for $n\\le 5$, Newton's iteration for $5<n\\le 60$ and the asymptotic formulas for $n> 60$.

\n", "answer_id": 45135, "answer_text": "As others mentioned in the comments, calculating the quadrature rule ahead of time is usually the fastest approach. However, you do not want to do that, you have a few options:\n\n\n\n\n\n\n\nGolub-Welsch algorithm (https://www.ams.org/journals/mcom/1969-23-106/S0025-5718-69-99647-1/S0025-5718-69-99647-1.pdf): Basically, you create a triadigonal matrix and calculate its eigendecomposition. The eigenvalues are the nodes and the weights are obtained from the first row of eigenvectors. For a matlab implementation, see this code (https://github.com/tcew/nodal-dg/blob/master/Codes1.1/Codes1D/JacobiGQ.m) where the coefficients alpha and beta correspond to the Jacobi polynomial associated with the quadrature (For Legendre quadrature use alpha=beta=0)\n\n\n\n\n\n\n\n\n\nCalculate the roots of the n-th Legendre polynomial (or other orthogonal polynomial) using Newton's method. You need a good initial guess, and you should use the derivative formulas to obtain the derivatives of the polynomial from its values as well as the recurrence relation. Here's a Matlab implementation (https://www.mathworks.com/matlabcentral/fileexchange/4540-legendre-gauss-quadrature-weights-and-nodes) as an example.\n\n\n\n\n\n\n\n\n\nFor very high order quadrature rules, you can consider using an asymptotic formula for the roots and weights like the ones discussed in this recent paper (https://doi.org/10.1137/140954969).\n\n\n\n\n\n\n\n\nSome libraries/packages might use a mixture of these approaches. 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mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Makogan", "question_author_url": "https://scicomp.stackexchange.com/users/38908/makogan", "question_author_user_type": "registered", "question_created_at": "2025-06-22T15:37:39+00:00", "question_html": "

The Wikipedia entry on Gauss-Legendre says that there is a tri-diagonal matrix whose eigenvalues yield good approximations for the nodes of the Legendre polynomials.

\n

There are a couple of papers I have found that talk about iteration-less methods as well.

\n

If I care about computation speed much more than I do robustness, what would a good method to approximate the 0's be?

\n", "question_id": 45134, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "The Wikipedia entry on Gauss-Legendre (https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_quadrature) says that there is a tri-diagonal matrix whose eigenvalues yield good approximations for the nodes of the Legendre polynomials.\n\n\n\n\nThere are a couple of papers I have found that talk about iteration-less methods as well.\n\n\n\n\nIf I care about computation speed much more than I do robustness, what would a good method to approximate the 0's be?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Makogan", "profile_url": "https://scicomp.stackexchange.com/users/38908/makogan", "user_type": "registered"}, "created_at": "2025-06-22T15:37:39+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "07553FF8-9272-42C5-A2B7-1B148A7B7192", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/07553FF8-9272-42C5-A2B7-1B148A7B7192/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2025-06-23T15:58:46+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "D9C93E64-BD3E-4570-AC26-631D0D18E64C", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://scicomp.stackexchange.com/revisions/D9C93E64-BD3E-4570-AC26-631D0D18E64C/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Anton Menshov", "profile_url": "https://scicomp.stackexchange.com/users/20688/anton-menshov", "user_type": "moderator"}, "created_at": "2025-06-24T22:14:07+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "5EA1A740-F16C-4BC6-BEC6-176E698E39EB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/5EA1A740-F16C-4BC6-BEC6-176E698E39EB/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45134/generating-the-quadrature-points-for-gauss-legendre", "split": "test", "split_group": "33c5482fd4ae22f5fa06393523263229d384085484a92366eb6dbf9a38687f94", "tags": ["numerics", "quadrature", "approximation", "polynomials", "numerical-integration"], "thread_id": "scicomp:45134", "title": "Generating the quadrature points for Gauss Legendre?"}} {"citation_context": "eights are obtained from the first row of eigenvectors. For a matlab implementation, see this code (https://github.com/tcew/nodal-dg/blob/master/Codes1.1/Codes1D/JacobiGQ.m) where the coefficients alpha and beta correspond to the Jacobi polynomial associated with the quad", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://github.com/tcew/nodal-dg/blob/master/Codes1.1/Codes1D/JacobiGQ.m", "kind": "external_url", "post_id": 45135, "post_url": "https://scicomp.stackexchange.com/a/45135", "product": "citations", "record_id": "Scientific-Citation-Graph:6408e357b755598d075d09b0", "split": "test", "thread": {"accepted_answer_id": 45135, "answers": [{"answer_html": "

As others mentioned in the comments, calculating the quadrature rule ahead of time is usually the fastest approach. However, you do not want to do that, you have a few options:

\n
    \n

  • Golub-Welsch algorithm: Basically, you create a triadigonal matrix and calculate its eigendecomposition. The eigenvalues are the nodes and the weights are obtained from the first row of eigenvectors. For a matlab implementation, see this code where the coefficients alpha and beta correspond to the Jacobi polynomial associated with the quadrature (For Legendre quadrature use alpha=beta=0)

    \n
    • \n

  • Calculate the roots of the n-th Legendre polynomial (or other orthogonal polynomial) using Newton's method. You need a good initial guess, and you should use the derivative formulas to obtain the derivatives of the polynomial from its values as well as the recurrence relation. Here's a Matlab implementation as an example.

    \n
    • \n

  • For very high order quadrature rules, you can consider using an asymptotic formula for the roots and weights like the ones discussed in this recent paper.

    \n
    • \n
\n

Some libraries/packages might use a mixture of these approaches. For instance, the Julia package FastGaussQuadrature uses tabulated values for $n\\le 5$, Newton's iteration for $5<n\\le 60$ and the asymptotic formulas for $n> 60$.

\n", "answer_id": 45135, "answer_text": "As others mentioned in the comments, calculating the quadrature rule ahead of time is usually the fastest approach. However, you do not want to do that, you have a few options:\n\n\n\n\n\n\n\nGolub-Welsch algorithm (https://www.ams.org/journals/mcom/1969-23-106/S0025-5718-69-99647-1/S0025-5718-69-99647-1.pdf): Basically, you create a triadigonal matrix and calculate its eigendecomposition. The eigenvalues are the nodes and the weights are obtained from the first row of eigenvectors. For a matlab implementation, see this code (https://github.com/tcew/nodal-dg/blob/master/Codes1.1/Codes1D/JacobiGQ.m) where the coefficients alpha and beta correspond to the Jacobi polynomial associated with the quadrature (For Legendre quadrature use alpha=beta=0)\n\n\n\n\n\n\n\n\n\nCalculate the roots of the n-th Legendre polynomial (or other orthogonal polynomial) using Newton's method. You need a good initial guess, and you should use the derivative formulas to obtain the derivatives of the polynomial from its values as well as the recurrence relation. Here's a Matlab implementation (https://www.mathworks.com/matlabcentral/fileexchange/4540-legendre-gauss-quadrature-weights-and-nodes) as an example.\n\n\n\n\n\n\n\n\n\nFor very high order quadrature rules, you can consider using an asymptotic formula for the roots and weights like the ones discussed in this recent paper (https://doi.org/10.1137/140954969).\n\n\n\n\n\n\n\n\nSome libraries/packages might use a mixture of these approaches. For instance, the Julia package FastGaussQuadrature (https://github.com/JuliaApproximation/FastGaussQuadrature.jl) uses tabulated values for $n\\le 5$, Newton's iteration for $5 60$.", "answer_url": "https://scicomp.stackexchange.com/a/45135", "author": "HMe", "author_url": "https://scicomp.stackexchange.com/users/52227/hme", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-06-23T02:23:34+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; 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The Wikipedia entry on Gauss-Legendre says that there is a tri-diagonal matrix whose eigenvalues yield good approximations for the nodes of the Legendre polynomials.

\n

There are a couple of papers I have found that talk about iteration-less methods as well.

\n

If I care about computation speed much more than I do robustness, what would a good method to approximate the 0's be?

\n", "question_id": 45134, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "The Wikipedia entry on Gauss-Legendre (https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_quadrature) says that there is a tri-diagonal matrix whose eigenvalues yield good approximations for the nodes of the Legendre polynomials.\n\n\n\n\nThere are a couple of papers I have found that talk about iteration-less methods as well.\n\n\n\n\nIf I care about computation speed much more than I do robustness, what would a good method to approximate the 0's be?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Makogan", "profile_url": "https://scicomp.stackexchange.com/users/38908/makogan", "user_type": "registered"}, "created_at": "2025-06-22T15:37:39+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "07553FF8-9272-42C5-A2B7-1B148A7B7192", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/07553FF8-9272-42C5-A2B7-1B148A7B7192/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2025-06-23T15:58:46+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "D9C93E64-BD3E-4570-AC26-631D0D18E64C", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://scicomp.stackexchange.com/revisions/D9C93E64-BD3E-4570-AC26-631D0D18E64C/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Anton Menshov", "profile_url": "https://scicomp.stackexchange.com/users/20688/anton-menshov", "user_type": "moderator"}, "created_at": "2025-06-24T22:14:07+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "5EA1A740-F16C-4BC6-BEC6-176E698E39EB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/5EA1A740-F16C-4BC6-BEC6-176E698E39EB/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45134/generating-the-quadrature-points-for-gauss-legendre", "split": "test", "split_group": "33c5482fd4ae22f5fa06393523263229d384085484a92366eb6dbf9a38687f94", "tags": ["numerics", "quadrature", "approximation", "polynomials", "numerical-integration"], "thread_id": "scicomp:45134", "title": "Generating the quadrature points for Gauss Legendre?"}} {"citation_context": "proach. However, you do not want to do that, you have a few options:\n\n\n\n\n\n\n\nGolub-Welsch algorithm (https://www.ams.org/journals/mcom/1969-23-106/S0025-5718-69-99647-1/S0025-5718-69-99647-1.pdf): Basically, you create a triadigonal matrix and calculate its eigendecomposition. The eigenvalues ", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.ams.org/journals/mcom/1969-23-106/S0025-5718-69-99647-1/S0025-5718-69-99647-1.pdf", "kind": "external_url", "post_id": 45135, "post_url": "https://scicomp.stackexchange.com/a/45135", "product": "citations", "record_id": "Scientific-Citation-Graph:8ac45f456ea7232e54017715", "split": "test", "thread": {"accepted_answer_id": 45135, "answers": [{"answer_html": "

As others mentioned in the comments, calculating the quadrature rule ahead of time is usually the fastest approach. However, you do not want to do that, you have a few options:

\n
    \n

  • Golub-Welsch algorithm: Basically, you create a triadigonal matrix and calculate its eigendecomposition. The eigenvalues are the nodes and the weights are obtained from the first row of eigenvectors. For a matlab implementation, see this code where the coefficients alpha and beta correspond to the Jacobi polynomial associated with the quadrature (For Legendre quadrature use alpha=beta=0)

    \n
    • \n

  • Calculate the roots of the n-th Legendre polynomial (or other orthogonal polynomial) using Newton's method. You need a good initial guess, and you should use the derivative formulas to obtain the derivatives of the polynomial from its values as well as the recurrence relation. Here's a Matlab implementation as an example.

    \n
    • \n

  • For very high order quadrature rules, you can consider using an asymptotic formula for the roots and weights like the ones discussed in this recent paper.

    \n
    • \n
\n

Some libraries/packages might use a mixture of these approaches. For instance, the Julia package FastGaussQuadrature uses tabulated values for $n\\le 5$, Newton's iteration for $5<n\\le 60$ and the asymptotic formulas for $n> 60$.

\n", "answer_id": 45135, "answer_text": "As others mentioned in the comments, calculating the quadrature rule ahead of time is usually the fastest approach. However, you do not want to do that, you have a few options:\n\n\n\n\n\n\n\nGolub-Welsch algorithm (https://www.ams.org/journals/mcom/1969-23-106/S0025-5718-69-99647-1/S0025-5718-69-99647-1.pdf): Basically, you create a triadigonal matrix and calculate its eigendecomposition. The eigenvalues are the nodes and the weights are obtained from the first row of eigenvectors. For a matlab implementation, see this code (https://github.com/tcew/nodal-dg/blob/master/Codes1.1/Codes1D/JacobiGQ.m) where the coefficients alpha and beta correspond to the Jacobi polynomial associated with the quadrature (For Legendre quadrature use alpha=beta=0)\n\n\n\n\n\n\n\n\n\nCalculate the roots of the n-th Legendre polynomial (or other orthogonal polynomial) using Newton's method. You need a good initial guess, and you should use the derivative formulas to obtain the derivatives of the polynomial from its values as well as the recurrence relation. Here's a Matlab implementation (https://www.mathworks.com/matlabcentral/fileexchange/4540-legendre-gauss-quadrature-weights-and-nodes) as an example.\n\n\n\n\n\n\n\n\n\nFor very high order quadrature rules, you can consider using an asymptotic formula for the roots and weights like the ones discussed in this recent paper (https://doi.org/10.1137/140954969).\n\n\n\n\n\n\n\n\nSome libraries/packages might use a mixture of these approaches. For instance, the Julia package FastGaussQuadrature (https://github.com/JuliaApproximation/FastGaussQuadrature.jl) uses tabulated values for $n\\le 5$, Newton's iteration for $5 60$.", "answer_url": "https://scicomp.stackexchange.com/a/45135", "author": "HMe", "author_url": "https://scicomp.stackexchange.com/users/52227/hme", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-06-23T02:23:34+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; 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mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Makogan", "question_author_url": "https://scicomp.stackexchange.com/users/38908/makogan", "question_author_user_type": "registered", "question_created_at": "2025-06-22T15:37:39+00:00", "question_html": "

The Wikipedia entry on Gauss-Legendre says that there is a tri-diagonal matrix whose eigenvalues yield good approximations for the nodes of the Legendre polynomials.

\n

There are a couple of papers I have found that talk about iteration-less methods as well.

\n

If I care about computation speed much more than I do robustness, what would a good method to approximate the 0's be?

\n", "question_id": 45134, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "The Wikipedia entry on Gauss-Legendre (https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_quadrature) says that there is a tri-diagonal matrix whose eigenvalues yield good approximations for the nodes of the Legendre polynomials.\n\n\n\n\nThere are a couple of papers I have found that talk about iteration-less methods as well.\n\n\n\n\nIf I care about computation speed much more than I do robustness, what would a good method to approximate the 0's be?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Makogan", "profile_url": "https://scicomp.stackexchange.com/users/38908/makogan", "user_type": "registered"}, "created_at": "2025-06-22T15:37:39+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "07553FF8-9272-42C5-A2B7-1B148A7B7192", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/07553FF8-9272-42C5-A2B7-1B148A7B7192/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2025-06-23T15:58:46+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "D9C93E64-BD3E-4570-AC26-631D0D18E64C", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://scicomp.stackexchange.com/revisions/D9C93E64-BD3E-4570-AC26-631D0D18E64C/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Anton Menshov", "profile_url": "https://scicomp.stackexchange.com/users/20688/anton-menshov", "user_type": "moderator"}, "created_at": "2025-06-24T22:14:07+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "5EA1A740-F16C-4BC6-BEC6-176E698E39EB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/5EA1A740-F16C-4BC6-BEC6-176E698E39EB/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45134/generating-the-quadrature-points-for-gauss-legendre", "split": "test", "split_group": "33c5482fd4ae22f5fa06393523263229d384085484a92366eb6dbf9a38687f94", "tags": ["numerics", "quadrature", "approximation", "polynomials", "numerical-integration"], "thread_id": "scicomp:45134", "title": "Generating the quadrature points for Gauss Legendre?"}} {"citation_context": " the polynomial from its values as well as the recurrence relation. Here's a Matlab implementation (https://www.mathworks.com/matlabcentral/fileexchange/4540-legendre-gauss-quadrature-weights-and-nodes) as an example.\n\n\n\n\n\n\n\n\n\nFor very high order quadrature rules, you can consider using an asymptotic", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.mathworks.com/matlabcentral/fileexchange/4540-legendre-gauss-quadrature-weights-and-nodes", "kind": "external_url", "post_id": 45135, "post_url": "https://scicomp.stackexchange.com/a/45135", "product": "citations", "record_id": "Scientific-Citation-Graph:3198b8b0a6f9bf845ae27235", "split": "test", "thread": {"accepted_answer_id": 45135, "answers": [{"answer_html": "

As others mentioned in the comments, calculating the quadrature rule ahead of time is usually the fastest approach. However, you do not want to do that, you have a few options:

\n
    \n

  • Golub-Welsch algorithm: Basically, you create a triadigonal matrix and calculate its eigendecomposition. The eigenvalues are the nodes and the weights are obtained from the first row of eigenvectors. For a matlab implementation, see this code where the coefficients alpha and beta correspond to the Jacobi polynomial associated with the quadrature (For Legendre quadrature use alpha=beta=0)

    \n
    • \n

  • Calculate the roots of the n-th Legendre polynomial (or other orthogonal polynomial) using Newton's method. You need a good initial guess, and you should use the derivative formulas to obtain the derivatives of the polynomial from its values as well as the recurrence relation. Here's a Matlab implementation as an example.

    \n
    • \n

  • For very high order quadrature rules, you can consider using an asymptotic formula for the roots and weights like the ones discussed in this recent paper.

    \n
    • \n
\n

Some libraries/packages might use a mixture of these approaches. For instance, the Julia package FastGaussQuadrature uses tabulated values for $n\\le 5$, Newton's iteration for $5<n\\le 60$ and the asymptotic formulas for $n> 60$.

\n", "answer_id": 45135, "answer_text": "As others mentioned in the comments, calculating the quadrature rule ahead of time is usually the fastest approach. However, you do not want to do that, you have a few options:\n\n\n\n\n\n\n\nGolub-Welsch algorithm (https://www.ams.org/journals/mcom/1969-23-106/S0025-5718-69-99647-1/S0025-5718-69-99647-1.pdf): Basically, you create a triadigonal matrix and calculate its eigendecomposition. The eigenvalues are the nodes and the weights are obtained from the first row of eigenvectors. For a matlab implementation, see this code (https://github.com/tcew/nodal-dg/blob/master/Codes1.1/Codes1D/JacobiGQ.m) where the coefficients alpha and beta correspond to the Jacobi polynomial associated with the quadrature (For Legendre quadrature use alpha=beta=0)\n\n\n\n\n\n\n\n\n\nCalculate the roots of the n-th Legendre polynomial (or other orthogonal polynomial) using Newton's method. You need a good initial guess, and you should use the derivative formulas to obtain the derivatives of the polynomial from its values as well as the recurrence relation. Here's a Matlab implementation (https://www.mathworks.com/matlabcentral/fileexchange/4540-legendre-gauss-quadrature-weights-and-nodes) as an example.\n\n\n\n\n\n\n\n\n\nFor very high order quadrature rules, you can consider using an asymptotic formula for the roots and weights like the ones discussed in this recent paper (https://doi.org/10.1137/140954969).\n\n\n\n\n\n\n\n\nSome libraries/packages might use a mixture of these approaches. For instance, the Julia package FastGaussQuadrature (https://github.com/JuliaApproximation/FastGaussQuadrature.jl) uses tabulated values for $n\\le 5$, Newton's iteration for $5 60$.", "answer_url": "https://scicomp.stackexchange.com/a/45135", "author": "HMe", "author_url": "https://scicomp.stackexchange.com/users/52227/hme", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-06-23T02:23:34+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45134, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "HMe", "profile_url": "https://scicomp.stackexchange.com/users/52227/hme", "user_type": "registered"}, "created_at": "2025-06-23T02:23:34+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "17767E1C-AF5C-411F-89D2-28DD34C67512", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/17767E1C-AF5C-411F-89D2-28DD34C67512/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "HMe", "profile_url": "https://scicomp.stackexchange.com/users/52227/hme", "user_type": "registered"}, "created_at": "2025-06-23T04:06:45+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "178A6446-7EB2-4C17-845C-7E820E13E2BF", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/178A6446-7EB2-4C17-845C-7E820E13E2BF/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "HMe", "profile_url": "https://scicomp.stackexchange.com/users/52227/hme", "user_type": "registered"}, "created_at": "2025-06-24T03:02:15+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "0AF827CC-EA76-4824-885A-7F8BF1496A5A", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/0AF827CC-EA76-4824-885A-7F8BF1496A5A/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "HMe", "profile_url": "https://scicomp.stackexchange.com/users/52227/hme", "user_type": "registered"}, "created_at": "2025-07-01T18:15:05+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "96D706EA-8EFC-472F-8503-5634732C3B41", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/96D706EA-8EFC-472F-8503-5634732C3B41/view-source"}], "score": 7, "updated_at": "2025-07-01T18:15:05+00:00"}], "domain": "computational_science", "external_links": ["https://doi.org/10.1137/140954969", "https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_quadrature", "https://github.com/JuliaApproximation/FastGaussQuadrature.jl", "https://github.com/tcew/nodal-dg/blob/master/Codes1.1/Codes1D/JacobiGQ.m", "https://www.ams.org/journals/mcom/1969-23-106/S0025-5718-69-99647-1/S0025-5718-69-99647-1.pdf", "https://www.mathworks.com/matlabcentral/fileexchange/4540-legendre-gauss-quadrature-weights-and-nodes"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:44.584971+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/272744bcc95b58699f7df6e6979b288bb8b00a80ab9c7982dbe170a6d0b63584_1790825325025901700_0.json", "raw_sha256": "27a81850a40920682c29ada76a2b55e80340a5c82764a3e9dde8a9c2ba23db4e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Makogan", "question_author_url": "https://scicomp.stackexchange.com/users/38908/makogan", "question_author_user_type": "registered", "question_created_at": "2025-06-22T15:37:39+00:00", "question_html": "

The Wikipedia entry on Gauss-Legendre says that there is a tri-diagonal matrix whose eigenvalues yield good approximations for the nodes of the Legendre polynomials.

\n

There are a couple of papers I have found that talk about iteration-less methods as well.

\n

If I care about computation speed much more than I do robustness, what would a good method to approximate the 0's be?

\n", "question_id": 45134, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "The Wikipedia entry on Gauss-Legendre (https://en.wikipedia.org/wiki/Gauss%E2%80%93Legendre_quadrature) says that there is a tri-diagonal matrix whose eigenvalues yield good approximations for the nodes of the Legendre polynomials.\n\n\n\n\nThere are a couple of papers I have found that talk about iteration-less methods as well.\n\n\n\n\nIf I care about computation speed much more than I do robustness, what would a good method to approximate the 0's be?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Makogan", "profile_url": "https://scicomp.stackexchange.com/users/38908/makogan", "user_type": "registered"}, "created_at": "2025-06-22T15:37:39+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "07553FF8-9272-42C5-A2B7-1B148A7B7192", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/07553FF8-9272-42C5-A2B7-1B148A7B7192/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2025-06-23T15:58:46+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "D9C93E64-BD3E-4570-AC26-631D0D18E64C", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://scicomp.stackexchange.com/revisions/D9C93E64-BD3E-4570-AC26-631D0D18E64C/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Anton Menshov", "profile_url": "https://scicomp.stackexchange.com/users/20688/anton-menshov", "user_type": "moderator"}, "created_at": "2025-06-24T22:14:07+00:00", "raw_file": "raw/codex_api_v1/8b02bbba3a1a1a633af4866e7fea0bd6789190b52c4b8380b0538b5c670e7131_1790825346551636200_0.json", "raw_sha256": "33050439b68e1f78cef06bf4c2ce07c0ec45a5fdf656fa1a9efd04691108f5e0", "revision_guid": "5EA1A740-F16C-4BC6-BEC6-176E698E39EB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/5EA1A740-F16C-4BC6-BEC6-176E698E39EB/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45134/generating-the-quadrature-points-for-gauss-legendre", "split": "test", "split_group": "33c5482fd4ae22f5fa06393523263229d384085484a92366eb6dbf9a38687f94", "tags": ["numerics", "quadrature", "approximation", "polynomials", "numerical-integration"], "thread_id": "scicomp:45134", "title": "Generating the quadrature points for Gauss Legendre?"}} {"citation_context": " cell, then maybe the cosine transform is the way to go and not the fourier base. cosine transform (https://en.wikipedia.org/wiki/Discrete_cosine_transform)\n\n\n\n\nedit:\nI think I was wrong on this. It might be possible although i am not sure about the conti", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Discrete_cosine_transform", "kind": "external_url", "post_id": 45286, "post_url": "https://scicomp.stackexchange.com/a/45286", "product": "citations", "record_id": "Scientific-Citation-Graph:650ddbafbada9296ef61623b", "split": "test", "thread": {"accepted_answer_id": 45287, "answers": [{"answer_html": "

The fourier transform assumes that the domain is infinite. In a finite domain the periodicity is only given for the symmetric cosine part of the base. The cosine function is symmetric around 0. The sine function is only for certain frequencies!

\n

If you want to create a usefull base in a finite cell, then maybe the cosine transform is the way to go and not the fourier base. cosine transform

\n

edit:\nI think I was wrong on this. It might be possible although i am not sure about the continuities at the borders of the cell.

\n", "answer_id": 45286, "answer_text": "The fourier transform assumes that the domain is infinite. In a finite domain the periodicity is only given for the symmetric cosine part of the base. The cosine function is symmetric around 0. The sine function is only for certain frequencies!\n\n\n\n\nIf you want to create a usefull base in a finite cell, then maybe the cosine transform is the way to go and not the fourier base. cosine transform (https://en.wikipedia.org/wiki/Discrete_cosine_transform)\n\n\n\n\nedit:\nI think I was wrong on this. It might be possible although i am not sure about the continuities at the borders of the cell.", "answer_url": "https://scicomp.stackexchange.com/a/45286", "author": "MPIchael", "author_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-11-21T06:31:22+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45285, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MPIchael", "profile_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "user_type": "registered"}, "created_at": "2025-11-21T06:31:22+00:00", "raw_file": "raw/codex_api_v1/932c57dde4e92dfe2af05c19643e98b6494a44cb31534e6703e92349c4e07eb4_1790825333093747000_0.json", "raw_sha256": "646e25c86dbb0c4df1ebe365442e733a253ac993340d2ed18168bbf783f75cac", "revision_guid": "CBEFF318-897B-4078-914B-16A6943BCDC5", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/CBEFF318-897B-4078-914B-16A6943BCDC5/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MPIchael", "profile_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "user_type": "registered"}, "created_at": "2025-11-21T10:25:12+00:00", "raw_file": "raw/codex_api_v1/932c57dde4e92dfe2af05c19643e98b6494a44cb31534e6703e92349c4e07eb4_1790825333093747000_0.json", "raw_sha256": "646e25c86dbb0c4df1ebe365442e733a253ac993340d2ed18168bbf783f75cac", "revision_guid": "64E18437-B71C-4033-8D9E-EBECF3C94E96", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/64E18437-B71C-4033-8D9E-EBECF3C94E96/view-source"}], "score": 1, "updated_at": "2025-11-21T10:25:12+00:00"}, {"answer_html": "

The integral is incorrect. It should be:

\n

$$\\int^1_{-1}\\int^1_{-1}\\int^1_{-1} \\frac{\\cos^2(\\pi x)}{2} dx dy dz = 2$$

\n

The reason is that $[2, 0, 0]$ maps to two level 0 cosines each with norm $\\sqrt{2}$

\n", "answer_id": 45287, "answer_text": "The integral is incorrect. It should be:\n\n\n\n\n$$\\int^1_{-1}\\int^1_{-1}\\int^1_{-1} \\frac{\\cos^2(\\pi x)}{2} dx dy dz = 2$$\n\n\n\n\nThe reason is that $[2, 0, 0]$ maps to two level 0 cosines each with norm $\\sqrt{2}$", "answer_url": "https://scicomp.stackexchange.com/a/45287", "author": "Makogan", "author_url": "https://scicomp.stackexchange.com/users/38908/makogan", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-11-21T06:39:36+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45285, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Makogan", "profile_url": "https://scicomp.stackexchange.com/users/38908/makogan", "user_type": "registered"}, "created_at": "2025-11-21T06:39:36+00:00", "raw_file": "raw/codex_api_v1/932c57dde4e92dfe2af05c19643e98b6494a44cb31534e6703e92349c4e07eb4_1790825333093747000_0.json", "raw_sha256": "646e25c86dbb0c4df1ebe365442e733a253ac993340d2ed18168bbf783f75cac", "revision_guid": "BFA52975-239F-441C-8A99-5359D4A5D377", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/BFA52975-239F-441C-8A99-5359D4A5D377/view-source"}], "score": 2, "updated_at": "2025-11-21T06:39:36+00:00"}], "domain": "computational_science", "external_links": ["https://en.wikipedia.org/wiki/Discrete_cosine_transform"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:44.584971+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/272744bcc95b58699f7df6e6979b288bb8b00a80ab9c7982dbe170a6d0b63584_1790825325025901700_0.json", "raw_sha256": "27a81850a40920682c29ada76a2b55e80340a5c82764a3e9dde8a9c2ba23db4e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Makogan", "question_author_url": "https://scicomp.stackexchange.com/users/38908/makogan", "question_author_user_type": "registered", "question_created_at": "2025-11-21T02:24:58+00:00", "question_html": "

Math preamble

\n

I am trying to create a functional basis for $[-1, 1]^3$ in $\\mathbb{R}^3$. To this effect I take the real expression of the fourier basis and index it with an integer such that

\n

$$\\phi_i(x) = \\cos(\\pi n/2 x)$$

\n

if $i$ is even and

\n

$$\\phi_i(x) = \\sin(\\pi [(n/2) + 1] x)$$

\n

if $i$ is odd.

\n

Then I normalize them, so for simplicity of writing, assume $\\phi_i$ is the normalized version of the function.

\n

With that definition I create the basis through the tensor product.

\n

$$\\Phi_{i,j,k}(x, y, z) = \\phi_i(x) \\phi_j(y) \\phi_k(z)$$

\n

Algorithm

\n

Now to render the above basis computable I am only dealing with triplets such that $i + j + k \\leq N$ for some integer $N$.

\n

I am using the trapezoidal rule (also extended through the tensor product) in order to compute integrals, so

\n

$$\\int_\\Omega f(X) \\Phi_{i, j, k}(X) dV \\approx \\sum w_l w_m w_n f(X_{l, m, n})) \\Phi_{i, j, k}(X_{l, m, n}) \\Delta x \\Delta y \\Delta z$$

\n

where $w_i$ refer to the weights from the trapezoidal rule. 0.5 at the margins and 1 in the interior.

\n

Using the above I am projecting different functions onto the discretized basis and then reconstructing them to see the accuracy.

\n

Experiments

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I am testing my code and I am noticing discrepancies, for example. I am trying to project $f(x, y, z) = \\cos(\\pi x)$ onto $\\Phi_{2, 0, 0}$

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From the original definition you will notice that $\\Phi_{2, 0, 0}$ should be $\\cos(\\pi x) / \\sqrt{2}$

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So my expectation is that I am computing:

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$$\\int^1_{-1}\\int^1_{-1}\\int^1_{-1} \\frac{\\cos^2(\\pi x)}{\\sqrt{2}} dx dy dz \\approx 2.83$$

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However, what I am getting is

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1.9999999999967393\n
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This is my code (written in rust):

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fn fourier_projection<F, S: RealField, const DIM: usize>(\n    mut function: F,\n    interval: [[S; 2]; DIM],\n    basis_index: [usize; DIM],\n    resolution: usize,\n) -> S\nwhere\n    F: FnMut([S; DIM]) -> S,\n{\n    let trapezoidal_weight = |i: usize| {\n        if i == 0 || i == resolution - 1\n        {\n            S::from(0.5).unwrap()\n        }\n        else\n        {\n            S::from(1).unwrap()\n        }\n    };\n\n    let mut res = S::default();\n\n    for xi in IterDimensions::new([resolution; DIM])\n    {\n        let mut point = [S::default(); DIM];\n        for d in 0..DIM\n        {\n            let range = interval[d][1] - interval[d][0];\n            let t = S::from(xi[d]).unwrap() / S::from(resolution - 1).unwrap();\n            let x = t * range + interval[d][0];\n\n            point[d] = x;\n        }\n\n        let mut val = function(point);\n        for d in 0..DIM\n        {\n            let range = interval[d][1] - interval[d][0];\n            let dx = range / S::from(resolution - 1).unwrap();\n            let t = S::from(xi[d]).unwrap() / S::from(resolution - 1).unwrap();\n            let xp = t * S::from(2).unwrap() - S::from(1).unwrap();\n\n            val *= fourier_basis(xp, basis_index[d]) * trapezoidal_weight(xi[d]) * dx\n                / fourier_norm_on_standard_interval(basis_index[d]);\n        }\n\n        res += val\n    }\n\n    res\n}\n\npub fn fourier_norm_on_standard_interval<S: RealField>(basis_index: usize) -> S\n{\n    // Only for the very first function (constant) is the norm different.\n    if basis_index == 0\n    {\n        S::from(f64::sqrt(2.)).unwrap()\n    }\n    else\n    {\n        S::from(1).unwrap()\n    }\n}\n\npub fn fourier_basis<S: RealField>(t: S, basis_index: usize) -> S\n{\n    let pi = S::from(PI).unwrap();\n\n    let n = basis_index / 2;\n    if basis_index % 2 == 0\n    {\n        ((t * pi) * S::from(n).unwrap()).cos()\n    }\n    else\n    {\n        ((t * pi) * S::from(n + 1).unwrap()).sin()\n    }\n}\n\n// test\n let test = fourier_projection(\n            |[x, y, z]| (PI * x).cos(),\n            [[-1., 1.]; 3],\n            [2, 0, 0],\n            100,\n        );\n
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I was hoping someone could point out where I made a mistake.

\n", "question_id": 45285, "question_license": "CC BY-SA 4.0", "question_score": 0, "question_text": "Math preamble\n\n\n\n\nI am trying to create a functional basis for $[-1, 1]^3$ in $\\mathbb{R}^3$. To this effect I take the real expression of the fourier basis and index it with an integer such that\n\n\n\n\n$$\\phi_i(x) = \\cos(\\pi n/2 x)$$\n\n\n\n\nif $i$ is even and\n\n\n\n\n$$\\phi_i(x) = \\sin(\\pi [(n/2) + 1] x)$$\n\n\n\n\nif $i$ is odd.\n\n\n\n\nThen I normalize them, so for simplicity of writing, assume $\\phi_i$ is the normalized version of the function.\n\n\n\n\nWith that definition I create the basis through the tensor product.\n\n\n\n\n$$\\Phi_{i,j,k}(x, y, z) = \\phi_i(x) \\phi_j(y) \\phi_k(z)$$\n\n\n\n\nAlgorithm\n\n\n\n\nNow to render the above basis computable I am only dealing with triplets such that $i + j + k \\leq N$ for some integer $N$.\n\n\n\n\nI am using the trapezoidal rule (also extended through the tensor product) in order to compute integrals, so\n\n\n\n\n$$\\int_\\Omega f(X) \\Phi_{i, j, k}(X) dV \\approx \\sum w_l w_m w_n f(X_{l, m, n})) \\Phi_{i, j, k}(X_{l, m, n}) \\Delta x \\Delta y \\Delta z$$\n\n\n\n\nwhere $w_i$ refer to the weights from the trapezoidal rule. 0.5 at the margins and 1 in the interior.\n\n\n\n\nUsing the above I am projecting different functions onto the discretized basis and then reconstructing them to see the accuracy.\n\n\n\n\nExperiments\n\n\n\n\nI am testing my code and I am noticing discrepancies, for example. I am trying to project $f(x, y, z) = \\cos(\\pi x)$ onto $\\Phi_{2, 0, 0}$\n\n\n\n\nFrom the original definition you will notice that $\\Phi_{2, 0, 0}$ should be $\\cos(\\pi x) / \\sqrt{2}$\n\n\n\n\nSo my expectation is that I am computing:\n\n\n\n\n$$\\int^1_{-1}\\int^1_{-1}\\int^1_{-1} \\frac{\\cos^2(\\pi x)}{\\sqrt{2}} dx dy dz \\approx 2.83$$\n\n\n\n\nHowever, what I am getting is\n\n\n\n\n1.9999999999967393\n\n\n\n\n\nThis is my code (written in rust):\n\n\n\n\nfn fourier_projection(\n mut function: F,\n interval: [[S; 2]; DIM],\n basis_index: [usize; DIM],\n resolution: usize,\n) -> S\nwhere\n F: FnMut([S; DIM]) -> S,\n{\n let trapezoidal_weight = |i: usize| {\n if i == 0 || i == resolution - 1\n {\n S::from(0.5).unwrap()\n }\n else\n {\n S::from(1).unwrap()\n }\n };\n\n let mut res = S::default();\n\n for xi in IterDimensions::new([resolution; DIM])\n {\n let mut point = [S::default(); DIM];\n for d in 0..DIM\n {\n let range = interval[d][1] - interval[d][0];\n let t = S::from(xi[d]).unwrap() / S::from(resolution - 1).unwrap();\n let x = t * range + interval[d][0];\n\n point[d] = x;\n }\n\n let mut val = function(point);\n for d in 0..DIM\n {\n let range = interval[d][1] - interval[d][0];\n let dx = range / S::from(resolution - 1).unwrap();\n let t = S::from(xi[d]).unwrap() / S::from(resolution - 1).unwrap();\n let xp = t * S::from(2).unwrap() - S::from(1).unwrap();\n\n val *= fourier_basis(xp, basis_index[d]) * trapezoidal_weight(xi[d]) * dx\n / fourier_norm_on_standard_interval(basis_index[d]);\n }\n\n res += val\n }\n\n res\n}\n\npub fn fourier_norm_on_standard_interval(basis_index: usize) -> S\n{\n // Only for the very first function (constant) is the norm different.\n if basis_index == 0\n {\n S::from(f64::sqrt(2.)).unwrap()\n }\n else\n {\n S::from(1).unwrap()\n }\n}\n\npub fn fourier_basis(t: S, basis_index: usize) -> S\n{\n let pi = S::from(PI).unwrap();\n\n let n = basis_index / 2;\n if basis_index % 2 == 0\n {\n ((t * pi) * S::from(n).unwrap()).cos()\n }\n else\n {\n ((t * pi) * S::from(n + 1).unwrap()).sin()\n }\n}\n\n// test\n let test = fourier_projection(\n |[x, y, z]| (PI * x).cos(),\n [[-1., 1.]; 3],\n [2, 0, 0],\n 100,\n );\n\n\n\n\n\nI was hoping someone could point out where I made a mistake.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Makogan", "profile_url": "https://scicomp.stackexchange.com/users/38908/makogan", "user_type": "registered"}, "created_at": "2025-11-21T02:24:58+00:00", "raw_file": "raw/codex_api_v1/932c57dde4e92dfe2af05c19643e98b6494a44cb31534e6703e92349c4e07eb4_1790825333093747000_0.json", "raw_sha256": "646e25c86dbb0c4df1ebe365442e733a253ac993340d2ed18168bbf783f75cac", "revision_guid": "B9CFB5A4-3B47-4382-BEF6-D74DBB33E85A", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/B9CFB5A4-3B47-4382-BEF6-D74DBB33E85A/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45285/issues-deriving-a-periodic-basis-in-r3", "split": "test", "split_group": "96bd03d5e1726730a642e946c45093801632d13b9c66e58b80e7027e3583e631", "tags": ["numerics", "algorithms", "fourier-analysis"], "thread_id": "scicomp:45285", "title": "Issues deriving a periodic basis in r^3"}} {"citation_context": "stack{j=1 \\\\ j \\ne k}}^{m}\n\\frac{j^{2}}{k^{2} - j^{2}}.\n$$\n\n\n\n\nWe can use the Chebyshev polynomial (https://en.wikipedia.org/wiki/Chebyshev_polynomials) of the second kind:\n$$\nU_n(\\cos x) = \\frac{\\sin\\bigl((n+1)x\\bigr)}{\\sin x}.\n$$\n\n\n\n\nPlugging $n = k", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Chebyshev_polynomials", "kind": "external_url", "post_id": 45295, "post_url": "https://scicomp.stackexchange.com/a/45295", "product": "citations", "record_id": "Scientific-Citation-Graph:9764bac79e77efd3727fb031", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

An efficient way to compute $\\sin(kx)$ in the context of iteration over $k$ is to make use of the recursive formula $\\sin(kx) = 2 \\cos x \\sin((k-1)x) - \\sin((k-2)x)$.

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However, when performing this computation in fixed-precision floating-point arithmetic there is a caveat, in that accuracy can be lost due to subtractive cancellation. Some quick experiments indicate that this would be the case here.

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The issue of subtractive cancellation can be largely mitigated by the use of a fused multiply-add operation, or FMA. This operation first computes the full, unrounded, product $ab$ before applying the addition of $c$, finally returning the final result $ab+c$ with a single rounding. This operation is supported in many programming environments as a function fma() for precisions defined by IEEE-754, and as such is supported in hardware for most modern processor architectures such as x86-64 and ARM64.

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However, I am not personally aware of an arbitrary-precision library with support for FMA. One could try to approximately emulate it by computing $ab+c$ at twice the current working precision and then rounding to working precision. This would still leave an issue of double rounding, which could likely be tolerated in the given context.

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With FMA support, one computes $\\sin(kx)=\\mathrm{fma}(2\\cos x,\\sin((k-1)x),-\\sin((k-2)x))$.

\n", "answer_id": 45293, "answer_text": "An efficient way to compute $\\sin(kx)$ in the context of iteration over $k$ is to make use of the recursive formula $\\sin(kx) = 2 \\cos x \\sin((k-1)x) - \\sin((k-2)x)$.\n\n\n\n\nHowever, when performing this computation in fixed-precision floating-point arithmetic there is a caveat, in that accuracy can be lost due to subtractive cancellation. Some quick experiments indicate that this would be the case here.\n\n\n\n\nThe issue of subtractive cancellation can be largely mitigated by the use of a fused multiply-add operation, or FMA. This operation first computes the full, unrounded, product $ab$ before applying the addition of $c$, finally returning the final result $ab+c$ with a single rounding. This operation is supported in many programming environments as a function fma() for precisions defined by IEEE-754, and as such is supported in hardware for most modern processor architectures such as x86-64 and ARM64.\n\n\n\n\nHowever, I am not personally aware of an arbitrary-precision library with support for FMA. One could try to approximately emulate it by computing $ab+c$ at twice the current working precision and then rounding to working precision. This would still leave an issue of double rounding, which could likely be tolerated in the given context.\n\n\n\n\nWith FMA support, one computes $\\sin(kx)=\\mathrm{fma}(2\\cos x,\\sin((k-1)x),-\\sin((k-2)x))$.", "answer_url": "https://scicomp.stackexchange.com/a/45293", "author": "njuffa", "author_url": "https://scicomp.stackexchange.com/users/20458/njuffa", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-11-26T23:33:21+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45291, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "njuffa", "profile_url": "https://scicomp.stackexchange.com/users/20458/njuffa", "user_type": "registered"}, "created_at": "2025-11-26T23:33:21+00:00", "raw_file": "raw/codex_api_v1/932c57dde4e92dfe2af05c19643e98b6494a44cb31534e6703e92349c4e07eb4_1790825333093747000_0.json", "raw_sha256": "646e25c86dbb0c4df1ebe365442e733a253ac993340d2ed18168bbf783f75cac", "revision_guid": "B6ACA9A9-61E5-4827-8876-77505A1EE621", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/B6ACA9A9-61E5-4827-8876-77505A1EE621/view-source"}], "score": 4, "updated_at": "2025-11-26T23:33:21+00:00"}, {"answer_html": "

One idea would be to use part of the series expansion of $sin(x)$ for the first couple of iterations. That is what the computer does internally anyway, but there you can control the order of approximation (how many terms of the expansion you consider and therefore how much compute you use). In iterative methods the first iterations often only have to put your solution in the general vicinity of the solution, being refined in the later stages.

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That way you spent less compute on the rough parts, and only when you are close to convergence you use the costly full-precision approximation of $sin(x)$ as before.

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\\begin{align}\n\\sin(x) &= x - \\frac{x^3}{3!} + \\frac{x^5}{5!} - \\frac{x^7}{7!} + \\cdots \\\\\n &= \\sum_{n=0}^\\infty \\frac{(-1)^n}{(2n+1)!}x^{2n+1}\n\\end{align}

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Note that the expansion looses precision the further away you are from 0.

\n", "answer_id": 45294, "answer_text": "One idea would be to use part of the series expansion of $sin(x)$ for the first couple of iterations. That is what the computer does internally anyway, but there you can control the order of approximation (how many terms of the expansion you consider and therefore how much compute you use). In iterative methods the first iterations often only have to put your solution in the general vicinity of the solution, being refined in the later stages.\n\n\n\n\nThat way you spent less compute on the rough parts, and only when you are close to convergence you use the costly full-precision approximation of $sin(x)$ as before.\n\n\n\n\n\\begin{align}\n\\sin(x) &= x - \\frac{x^3}{3!} + \\frac{x^5}{5!} - \\frac{x^7}{7!} + \\cdots \\\\\n &= \\sum_{n=0}^\\infty \\frac{(-1)^n}{(2n+1)!}x^{2n+1}\n\\end{align}\n\n\n\n\nNote that the expansion looses precision the further away you are from 0.", "answer_url": "https://scicomp.stackexchange.com/a/45294", "author": "MPIchael", "author_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-11-27T07:31:18+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45291, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MPIchael", "profile_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "user_type": "registered"}, "created_at": "2025-11-27T07:31:18+00:00", "raw_file": "raw/codex_api_v1/932c57dde4e92dfe2af05c19643e98b6494a44cb31534e6703e92349c4e07eb4_1790825333093747000_0.json", "raw_sha256": "646e25c86dbb0c4df1ebe365442e733a253ac993340d2ed18168bbf783f75cac", "revision_guid": "968C67F8-16E6-40D8-80A4-8E5335D3FC2C", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/968C67F8-16E6-40D8-80A4-8E5335D3FC2C/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MPIchael", "profile_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "user_type": "registered"}, "created_at": "2025-11-27T07:36:23+00:00", "raw_file": "raw/codex_api_v1/932c57dde4e92dfe2af05c19643e98b6494a44cb31534e6703e92349c4e07eb4_1790825333093747000_0.json", "raw_sha256": "646e25c86dbb0c4df1ebe365442e733a253ac993340d2ed18168bbf783f75cac", "revision_guid": "1885B799-B6E4-4653-BEFB-37E50B86F7E6", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/1885B799-B6E4-4653-BEFB-37E50B86F7E6/view-source"}], "score": 2, "updated_at": "2025-11-27T07:36:23+00:00"}, {"answer_html": "

Given the recurrence\n$$\nx_{n+1}\n= x_n + \\sum_{k=1}^{m} a_k \\,\\sin(k x_n),\n\\qquad\na_k := (-1)^{m+k}\\,\\frac{1}{k}\\prod_{\\substack{j=1 \\\\ j \\ne k}}^{m}\n\\frac{j^{2}}{k^{2} - j^{2}}.\n$$

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We can use the Chebyshev polynomial of the second kind:\n$$\nU_n(\\cos x) = \\frac{\\sin\\bigl((n+1)x\\bigr)}{\\sin x}.\n$$

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Plugging $n = k-1$ into this definition gives\n$$\nU_{k-1}(\\cos x)= \\frac{\\sin(kx)}{\\sin x}\\;\\Longrightarrow\\;\n\\sin(kx) = \\sin x \\, U_{k-1}(\\cos x).\n$$

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Therefore, the iteration can be written equivalently as\n$$\n\\sum_{k=1}^{m} a_k \\sin(kx)\n= \\sin x \\sum_{k=1}^{m} a_k U_{k-1}(\\cos x)\n= \\sin x \\, P_m(\\cos x),\n$$\nwith\n$$\nP_m(c) := \\sum_{k=1}^{m} a_k \\, U_{k-1}(c),\n$$

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and

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$$\nU_{k-1}(c)\n= \\sum_{r=0}^{\\left\\lfloor (k-1)/2 \\right\\rfloor}\n (-1)^r\n \\binom{k-1-r}{r}\\,\n (2c)^{\\,k-1-2r}.\n$$

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Therefore, the new iteration can be written as\n$$\nx_{n+1}\n= x_n + \\sin(x_n)\\,P_m\\big(\\cos(x_n)\\big),\n$$

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where $P_m$ is the polynomial\n$$\nP_m(c)\n := \\sum_{k=1}^{m} a_k\n \\sum_{r=0}^{\\left\\lfloor (k-1)/2 \\right\\rfloor}\n (-1)^r\n \\binom{k-1-r}{r}\\,\n (2c)^{\\,k-1-2r}.\n$$

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So instead of computing $\\sin(k x_n)$ for every $k$, we can:

\n
    \n
  • Compute $s = \\sin(x_n)$ once,
    • \n
  • Compute $c = \\cos(x_n)$ once,
    • \n
  • Evaluate the polynomial $P_m(c)$.
    • \n
\n

Example

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We start from the Chebyshev representation for $m=5$:\n$$\nP_5(t) = \\sum_{k=1}^5 a_k\\,U_{k-1}(t),\n$$\nwith\n$$\na_1 = \\frac{5}{3},\\quad\na_2 = \\frac{10}{21},\\quad\na_3 = \\frac{5}{42},\\quad\na_4 = \\frac{5}{252},\\quad\na_5 = \\frac{1}{630},\n$$\nand\n$$\n\\begin{aligned}\nU_0(t) &= 1,\\\\\nU_1(t) &= 2t,\\\\\nU_2(t) &= 4t^2 - 1,\\\\\nU_3(t) &= 8t^3 - 4t,\\\\\nU_4(t) &= 16t^4 - 12t^2 + 1.\n\\end{aligned}\n$$

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Thus\n$$\n\\begin{aligned}\nP_5(t)\n&= a_1 U_0(t) + a_2 U_1(t) + a_3 U_2(t) + a_4 U_3(t) + a_5 U_4(t)\\\\[4pt]\n&= \\frac{5}{3}\\cdot 1\n + \\frac{10}{21}\\cdot (2t)\n + \\frac{5}{42}\\cdot (4t^2 - 1)\n + \\frac{5}{252}\\cdot (8t^3 - 4t)\n + \\frac{1}{630}\\cdot (16t^4 - 12t^2 + 1).\n\\end{aligned}\n$$

\n

Simplifying each term:\n$$\n\\begin{aligned}\nP_5(t)\n&= \\frac{5}{3}\n + \\frac{20}{21}t\n + \\left(\\frac{20}{42}t^2 - \\frac{5}{42}\\right)\n + \\left(\\frac{40}{252}t^3 - \\frac{20}{252}t\\right)\n + \\left(\\frac{16}{630}t^4 - \\frac{12}{630}t^2 + \\frac{1}{630}\\right)\\\\[4pt]\n&= \\frac{5}{3}\n + \\frac{20}{21}t\n + \\left(\\frac{10}{21}t^2 - \\frac{5}{42}\\right)\n + \\left(\\frac{10}{63}t^3 - \\frac{5}{63}t\\right)\n + \\left(\\frac{8}{315}t^4 - \\frac{2}{105}t^2 + \\frac{1}{630}\\right).\n\\end{aligned}\n$$

\n

Now collect like powers of $t$.

\n

$t^4$ term:\n$$\n\\frac{8}{315}t^4.\n$$

\n

$t^3$ term:\n$$\n\\frac{10}{63}t^3.\n$$

\n

$t^2$ term:\n$$\n\\frac{10}{21}t^2 - \\frac{2}{105}t^2\n= \\left(\\frac{10}{21} - \\frac{2}{105}\\right)t^2\n= \\left(\\frac{50}{105} - \\frac{2}{105}\\right)t^2\n= \\frac{48}{105}t^2\n= \\frac{16}{35}t^2.\n$$

\n

$t^1$ term:\n$$\n\\frac{20}{21}t - \\frac{5}{63}t\n= \\left(\\frac{20}{21} - \\frac{5}{63}\\right)t\n= \\left(\\frac{60}{63} - \\frac{5}{63}\\right)t\n= \\frac{55}{63}t.\n$$

\n

Constant term:\n$$\n\\frac{5}{3} - \\frac{5}{42} + \\frac{1}{630}\n= \\frac{1050}{630} - \\frac{75}{630} + \\frac{1}{630}\n= \\frac{976}{630}\n= \\frac{488}{315}.\n$$

\n

So we obtain\n$$\nP_5(t)\n= \\frac{8}{315}t^4\n+ \\frac{10}{63}t^3\n+ \\frac{16}{35}t^2\n+ \\frac{55}{63}t\n+ \\frac{488}{315}.\n$$

\n

Factoring out $\\frac{1}{315}$ gives the compact form\n$$\nP_5(t)\n= \\frac{1}{315}\\bigl(8t^4 + 50t^3 + 144t^2 + 275t + 488\\bigr).\n$$

\n

Test Case

\n

For $m = 5$ we have\n$$\nP_5(t) = \\frac{1}{315}\\bigl(8t^4 + 50t^3 + 144t^2 + 275t + 488\\bigr),\n$$\nand the iteration\n$$\nx_{n+1} = x_n + \\sin(x_n)\\,P_5(\\cos x_n).\n$$

\n
from mpmath import mp\nimport time\n\nmp.dps = 1000  # 1000 digits of precision\n\n# m = 5 polynomial:\n# P5(t) = (1/315) * (8 t^4 + 50 t^3 + 144 t^2 + 275 t + 488)\n\ndef step_m5(x):\n    """\n    m = 5 iteration:\n        x_{n+1} = x_n + sin(x_n) * P5(cos(x_n))\n\n    where\n        P5(t) = (1/315) * (8 t^4 + 50 t^3 + 144 t^2 + 275 t + 488).\n    """\n    s = mp.sin(x)\n    c = mp.cos(x)\n    P5 = (mp.mpf(1) / 315) * (8*c**4 + 50*c**3 + 144*c**2 + 275*c + 488)\n    return x + s * P5\n\n# initial value x0 = 3\nx = mp.mpf(3)\n\nstart = time.perf_counter()\nfor n in range(1, 4):  # a few iterations are enough because order = 11\n    x = step_m5(x)\nend = time.perf_counter()\n\nprint("Approximate pi (m=5):")\nprint(mp.nstr(x, 1000))\nprint(f"\\nTime Taken: {end - start:.6f} seconds")\n\n# Show how close we are to the true mp.pi\nerr = x - mp.pi\nprint("\\nError x - pi:")\nprint(mp.nstr(err, 5))\n
\n
\n

Approximate pi (m=5):\n3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420199

\n

Time Taken: 0.001180 seconds

\n

Error x - pi:\n0.0

\n", "answer_id": 45295, "answer_text": "Given the recurrence\n$$\nx_{n+1}\n= x_n + \\sum_{k=1}^{m} a_k \\,\\sin(k x_n),\n\\qquad\na_k := (-1)^{m+k}\\,\\frac{1}{k}\\prod_{\\substack{j=1 \\\\ j \\ne k}}^{m}\n\\frac{j^{2}}{k^{2} - j^{2}}.\n$$\n\n\n\n\nWe can use the Chebyshev polynomial (https://en.wikipedia.org/wiki/Chebyshev_polynomials) of the second kind:\n$$\nU_n(\\cos x) = \\frac{\\sin\\bigl((n+1)x\\bigr)}{\\sin x}.\n$$\n\n\n\n\nPlugging $n = k-1$ into this definition gives\n$$\nU_{k-1}(\\cos x)= \\frac{\\sin(kx)}{\\sin x}\\;\\Longrightarrow\\;\n\\sin(kx) = \\sin x \\, U_{k-1}(\\cos x).\n$$\n\n\n\n\nTherefore, the iteration can be written equivalently as\n$$\n\\sum_{k=1}^{m} a_k \\sin(kx)\n= \\sin x \\sum_{k=1}^{m} a_k U_{k-1}(\\cos x)\n= \\sin x \\, P_m(\\cos x),\n$$\nwith\n$$\nP_m(c) := \\sum_{k=1}^{m} a_k \\, U_{k-1}(c),\n$$\n\n\n\n\nand\n\n\n\n\n$$\nU_{k-1}(c)\n= \\sum_{r=0}^{\\left\\lfloor (k-1)/2 \\right\\rfloor}\n (-1)^r\n \\binom{k-1-r}{r}\\,\n (2c)^{\\,k-1-2r}.\n$$\n\n\n\n\nTherefore, the new iteration can be written as\n$$\nx_{n+1}\n= x_n + \\sin(x_n)\\,P_m\\big(\\cos(x_n)\\big),\n$$\n\n\n\n\nwhere $P_m$ is the polynomial\n$$\nP_m(c)\n := \\sum_{k=1}^{m} a_k\n \\sum_{r=0}^{\\left\\lfloor (k-1)/2 \\right\\rfloor}\n (-1)^r\n \\binom{k-1-r}{r}\\,\n (2c)^{\\,k-1-2r}.\n$$\n\n\n\n\nSo instead of computing $\\sin(k x_n)$ for every $k$, we can:\n\n\n\n\n\nCompute $s = \\sin(x_n)$ once,\n\n\n\n\nCompute $c = \\cos(x_n)$ once,\n\n\n\n\nEvaluate the polynomial $P_m(c)$.\n\n\n\n\n\nExample\n\n\n\n\nWe start from the Chebyshev representation for $m=5$:\n$$\nP_5(t) = \\sum_{k=1}^5 a_k\\,U_{k-1}(t),\n$$\nwith\n$$\na_1 = \\frac{5}{3},\\quad\na_2 = \\frac{10}{21},\\quad\na_3 = \\frac{5}{42},\\quad\na_4 = \\frac{5}{252},\\quad\na_5 = \\frac{1}{630},\n$$\nand\n$$\n\\begin{aligned}\nU_0(t) &= 1,\\\\\nU_1(t) &= 2t,\\\\\nU_2(t) &= 4t^2 - 1,\\\\\nU_3(t) &= 8t^3 - 4t,\\\\\nU_4(t) &= 16t^4 - 12t^2 + 1.\n\\end{aligned}\n$$\n\n\n\n\nThus\n$$\n\\begin{aligned}\nP_5(t)\n&= a_1 U_0(t) + a_2 U_1(t) + a_3 U_2(t) + a_4 U_3(t) + a_5 U_4(t)\\\\[4pt]\n&= \\frac{5}{3}\\cdot 1\n + \\frac{10}{21}\\cdot (2t)\n + \\frac{5}{42}\\cdot (4t^2 - 1)\n + \\frac{5}{252}\\cdot (8t^3 - 4t)\n + \\frac{1}{630}\\cdot (16t^4 - 12t^2 + 1).\n\\end{aligned}\n$$\n\n\n\n\nSimplifying each term:\n$$\n\\begin{aligned}\nP_5(t)\n&= \\frac{5}{3}\n + \\frac{20}{21}t\n + \\left(\\frac{20}{42}t^2 - \\frac{5}{42}\\right)\n + \\left(\\frac{40}{252}t^3 - \\frac{20}{252}t\\right)\n + \\left(\\frac{16}{630}t^4 - \\frac{12}{630}t^2 + \\frac{1}{630}\\right)\\\\[4pt]\n&= \\frac{5}{3}\n + \\frac{20}{21}t\n + \\left(\\frac{10}{21}t^2 - \\frac{5}{42}\\right)\n + \\left(\\frac{10}{63}t^3 - \\frac{5}{63}t\\right)\n + \\left(\\frac{8}{315}t^4 - \\frac{2}{105}t^2 + \\frac{1}{630}\\right).\n\\end{aligned}\n$$\n\n\n\n\nNow collect like powers of $t$.\n\n\n\n\n$t^4$ term:\n$$\n\\frac{8}{315}t^4.\n$$\n\n\n\n\n$t^3$ term:\n$$\n\\frac{10}{63}t^3.\n$$\n\n\n\n\n$t^2$ term:\n$$\n\\frac{10}{21}t^2 - \\frac{2}{105}t^2\n= \\left(\\frac{10}{21} - \\frac{2}{105}\\right)t^2\n= \\left(\\frac{50}{105} - \\frac{2}{105}\\right)t^2\n= \\frac{48}{105}t^2\n= \\frac{16}{35}t^2.\n$$\n\n\n\n\n$t^1$ term:\n$$\n\\frac{20}{21}t - \\frac{5}{63}t\n= \\left(\\frac{20}{21} - \\frac{5}{63}\\right)t\n= \\left(\\frac{60}{63} - \\frac{5}{63}\\right)t\n= \\frac{55}{63}t.\n$$\n\n\n\n\nConstant term:\n$$\n\\frac{5}{3} - \\frac{5}{42} + \\frac{1}{630}\n= \\frac{1050}{630} - \\frac{75}{630} + \\frac{1}{630}\n= \\frac{976}{630}\n= \\frac{488}{315}.\n$$\n\n\n\n\nSo we obtain\n$$\nP_5(t)\n= \\frac{8}{315}t^4\n+ \\frac{10}{63}t^3\n+ \\frac{16}{35}t^2\n+ \\frac{55}{63}t\n+ \\frac{488}{315}.\n$$\n\n\n\n\nFactoring out $\\frac{1}{315}$ gives the compact form\n$$\nP_5(t)\n= \\frac{1}{315}\\bigl(8t^4 + 50t^3 + 144t^2 + 275t + 488\\bigr).\n$$\n\n\n\n\nTest Case\n\n\n\n\nFor $m = 5$ we have\n$$\nP_5(t) = \\frac{1}{315}\\bigl(8t^4 + 50t^3 + 144t^2 + 275t + 488\\bigr),\n$$\nand the iteration\n$$\nx_{n+1} = x_n + \\sin(x_n)\\,P_5(\\cos x_n).\n$$\n\n\n\n\nfrom mpmath import mp\nimport time\n\nmp.dps = 1000 # 1000 digits of precision\n\n# m = 5 polynomial:\n# P5(t) = (1/315) * (8 t^4 + 50 t^3 + 144 t^2 + 275 t + 488)\n\ndef step_m5(x):\n \"\"\"\n m = 5 iteration:\n x_{n+1} = x_n + sin(x_n) * P5(cos(x_n))\n\n where\n P5(t) = (1/315) * (8 t^4 + 50 t^3 + 144 t^2 + 275 t + 488).\n \"\"\"\n s = mp.sin(x)\n c = mp.cos(x)\n P5 = (mp.mpf(1) / 315) * (8*c**4 + 50*c**3 + 144*c**2 + 275*c + 488)\n return x + s * P5\n\n# initial value x0 = 3\nx = mp.mpf(3)\n\nstart = time.perf_counter()\nfor n in range(1, 4): # a few iterations are enough because order = 11\n x = step_m5(x)\nend = time.perf_counter()\n\nprint(\"Approximate pi (m=5):\")\nprint(mp.nstr(x, 1000))\nprint(f\"\\nTime Taken: {end - start:.6f} seconds\")\n\n# Show how close we are to the true mp.pi\nerr = x - mp.pi\nprint(\"\\nError x - pi:\")\nprint(mp.nstr(err, 5))\n\n\n\n\n\n\n\n\nApproximate pi (m=5):\n3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420199\n\n\n\n\nTime Taken: 0.001180 seconds\n\n\n\n\nError x - pi:\n0.0", "answer_url": "https://scicomp.stackexchange.com/a/45295", "author": "vengy", "author_url": "https://scicomp.stackexchange.com/users/56070/vengy", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-11-27T16:01:03+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45291, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "vengy", "profile_url": "https://scicomp.stackexchange.com/users/56070/vengy", "user_type": "registered"}, "created_at": "2025-11-27T16:01:03+00:00", "raw_file": "raw/codex_api_v1/932c57dde4e92dfe2af05c19643e98b6494a44cb31534e6703e92349c4e07eb4_1790825333093747000_0.json", "raw_sha256": "646e25c86dbb0c4df1ebe365442e733a253ac993340d2ed18168bbf783f75cac", "revision_guid": "12F528C5-3339-4BD9-82C4-1F98C0E30ABD", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/12F528C5-3339-4BD9-82C4-1F98C0E30ABD/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "vengy", "profile_url": "https://scicomp.stackexchange.com/users/56070/vengy", "user_type": "registered"}, "created_at": "2025-11-27T16:46:02+00:00", "raw_file": "raw/codex_api_v1/932c57dde4e92dfe2af05c19643e98b6494a44cb31534e6703e92349c4e07eb4_1790825333093747000_0.json", "raw_sha256": "646e25c86dbb0c4df1ebe365442e733a253ac993340d2ed18168bbf783f75cac", "revision_guid": "94F6BA8F-8639-48FE-844B-374EC8092EC7", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/94F6BA8F-8639-48FE-844B-374EC8092EC7/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "vengy", "profile_url": "https://scicomp.stackexchange.com/users/56070/vengy", "user_type": "registered"}, "created_at": "2025-11-27T17:19:25+00:00", "raw_file": "raw/codex_api_v1/932c57dde4e92dfe2af05c19643e98b6494a44cb31534e6703e92349c4e07eb4_1790825333093747000_0.json", "raw_sha256": "646e25c86dbb0c4df1ebe365442e733a253ac993340d2ed18168bbf783f75cac", "revision_guid": "C72508F8-E2C5-4479-B135-70BE30A2F07C", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/C72508F8-E2C5-4479-B135-70BE30A2F07C/view-source"}], "score": 7, "updated_at": "2025-11-27T17:19:25+00:00"}], "domain": "computational_science", "external_links": ["https://en.wikipedia.org/wiki/Chebyshev_polynomials"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:44.584971+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/272744bcc95b58699f7df6e6979b288bb8b00a80ab9c7982dbe170a6d0b63584_1790825325025901700_0.json", "raw_sha256": "27a81850a40920682c29ada76a2b55e80340a5c82764a3e9dde8a9c2ba23db4e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "vengy", "question_author_url": "https://scicomp.stackexchange.com/users/56070/vengy", "question_author_user_type": "registered", "question_created_at": "2025-11-26T20:12:50+00:00", "question_html": "

I have this recurrence formula for $\\pi$ with convergence order $2m+1$:

\n

$$\nx_{n+1} = x_n + \\sum_{k=1}^{m} \\left[ (-1)^{m+k} \\cdot \\frac{1}{k} \\prod_{\\substack{j=1 \\\\ j \\ne k}}^{m} \\frac{j^{2}}{k^{2} - j^{2}} \\right] \\sin(k x_n).\n$$

\n

For example, let $m=2$. The recurrence is:\n$$\nx_{n+1}=x_n+ \\frac{4}{3}\\,\\sin(x_n)+ \\frac{1}{6}\\,\\sin(2x_n).\n$$

\n

After four iterations, $\\pi$ is accurate to $761$ digits:

\n

3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211343082259728864581849972469526130405086109419964771039095301381998678247215175696280484782896433126351623817501296615376345723979560286352234586232286130523901015245593954685898250839054728621411070507501722658851574741380974002315574736131

\n
from mpmath import mp\nimport time\n\nmp.dps = 1000\n\nc21 = mp.mpf(4) / 3\nc22 = mp.mpf(1) / 6\n\ndef step_m2(x):\n    return x + c21 * mp.sin(x) + c22 * mp.sin(2*x)\n\n# initial value x0 = 3\nx = mp.mpf(3)\n\nstart = time.perf_counter()\nfor n in range(1, 5):\n    x = step_m2(x)\nend = time.perf_counter()\n\nprint("Approximate pi:", mp.nstr(x, 1000))\nprint(f"Time Taken: {end - start:.6f} seconds")\n
\n

However, evaluating $\\sin(k x_n)$ at high precision becomes very slow, especially for large $m$.

\n

Question

\n

Are there efficient approximations or methods for computing $\\sin(k x_n)$ in iterative algorithms?

\n

Update

\n

Based on the answers, the iteration has been optimized so that each step\nrequires only one evaluation of $\\sin$, one of $\\cos$, and a polynomial\nevaluation:

\n

$$\nx_{n+1}\n= x_n\n+ \\sin(x_n)\\,\n \\sum_{r=0}^{m-1} \\frac{r!}{(2r+1)!!}\\,(\\cos x_n + 1)^r.\n$$

\n

Thanks!

\n", "question_id": 45291, "question_license": "CC BY-SA 4.0", "question_score": 6, "question_text": "I have this recurrence formula for $\\pi$ with convergence order $2m+1$:\n\n\n\n\n$$\nx_{n+1} = x_n + \\sum_{k=1}^{m} \\left[ (-1)^{m+k} \\cdot \\frac{1}{k} \\prod_{\\substack{j=1 \\\\ j \\ne k}}^{m} \\frac{j^{2}}{k^{2} - j^{2}} \\right] \\sin(k x_n).\n$$\n\n\n\n\nFor example, let $m=2$. The recurrence is:\n$$\nx_{n+1}=x_n+ \\frac{4}{3}\\,\\sin(x_n)+ \\frac{1}{6}\\,\\sin(2x_n).\n$$\n\n\n\n\nAfter four iterations, $\\pi$ is accurate to $761$ digits:\n\n\n\n\n3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211343082259728864581849972469526130405086109419964771039095301381998678247215175696280484782896433126351623817501296615376345723979560286352234586232286130523901015245593954685898250839054728621411070507501722658851574741380974002315574736131\n\n\n\n\nfrom mpmath import mp\nimport time\n\nmp.dps = 1000\n\nc21 = mp.mpf(4) / 3\nc22 = mp.mpf(1) / 6\n\ndef step_m2(x):\n return x + c21 * mp.sin(x) + c22 * mp.sin(2*x)\n\n# initial value x0 = 3\nx = mp.mpf(3)\n\nstart = time.perf_counter()\nfor n in range(1, 5):\n x = step_m2(x)\nend = time.perf_counter()\n\nprint(\"Approximate pi:\", mp.nstr(x, 1000))\nprint(f\"Time Taken: {end - start:.6f} seconds\")\n\n\n\n\n\nHowever, evaluating $\\sin(k x_n)$ at high precision becomes very slow, especially for large $m$.\n\n\n\n\nQuestion\n\n\n\n\nAre there efficient approximations or methods for computing $\\sin(k x_n)$ in iterative algorithms?\n\n\n\n\nUpdate\n\n\n\n\nBased on the answers, the iteration has been optimized so that each step\nrequires only one evaluation of $\\sin$, one of $\\cos$, and a polynomial\nevaluation:\n\n\n\n\n$$\nx_{n+1}\n= x_n\n+ \\sin(x_n)\\,\n \\sum_{r=0}^{m-1} \\frac{r!}{(2r+1)!!}\\,(\\cos x_n + 1)^r.\n$$\n\n\n\n\nThanks!", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "vengy", "profile_url": "https://scicomp.stackexchange.com/users/56070/vengy", "user_type": "registered"}, "created_at": "2025-11-26T20:12:50+00:00", "raw_file": "raw/codex_api_v1/932c57dde4e92dfe2af05c19643e98b6494a44cb31534e6703e92349c4e07eb4_1790825333093747000_0.json", "raw_sha256": "646e25c86dbb0c4df1ebe365442e733a253ac993340d2ed18168bbf783f75cac", "revision_guid": "E62E0A8C-8E01-4C14-B7C2-285A89EF1CC1", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/E62E0A8C-8E01-4C14-B7C2-285A89EF1CC1/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "vengy", "profile_url": "https://scicomp.stackexchange.com/users/56070/vengy", "user_type": "registered"}, "created_at": "2025-11-28T14:23:44+00:00", "raw_file": "raw/codex_api_v1/932c57dde4e92dfe2af05c19643e98b6494a44cb31534e6703e92349c4e07eb4_1790825333093747000_0.json", "raw_sha256": "646e25c86dbb0c4df1ebe365442e733a253ac993340d2ed18168bbf783f75cac", "revision_guid": "38B727A1-9571-4258-B34C-572EA2A4CA69", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/38B727A1-9571-4258-B34C-572EA2A4CA69/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Reinderien", "profile_url": "https://scicomp.stackexchange.com/users/41212/reinderien", "user_type": "registered"}, "created_at": "2025-12-27T13:30:00+00:00", "raw_file": "raw/codex_api_v1/932c57dde4e92dfe2af05c19643e98b6494a44cb31534e6703e92349c4e07eb4_1790825333093747000_0.json", "raw_sha256": "646e25c86dbb0c4df1ebe365442e733a253ac993340d2ed18168bbf783f75cac", "revision_guid": "26017B5A-7A85-4984-8B51-2083CED200D4", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/26017B5A-7A85-4984-8B51-2083CED200D4/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45291/efficient-computation-of-sink-x-n-in-iterative-algorithms", "split": "test", "split_group": "1bfd52fa7b070e0b5559d8e3ecd78760d9854e9302a5ee1988f94d4b3224295f", "tags": ["optimization", "numerics"], "thread_id": "scicomp:45291", "title": "Efficient computation of $\\sin(k x_n)$ in iterative algorithms"}} {"citation_context": "used and the diagram that it produced. My code closely mirrors the example from MPSKit.jl's github (https://github.com/QuantumKitHub/MPSKit.jl):\n\n\n\n\nusing MPSKit, MPSKitModels, TensorKit \nusing Plots, ProgressMeter\n\nD = 6\ninit_state = Infinit", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://github.com/QuantumKitHub/MPSKit.jl", "kind": "external_url", "post_id": 45344, "post_url": "https://scicomp.stackexchange.com/questions/45344/dmrg-returns-weird-results-for-the-tfim-ground-state-magnetization", "product": "citations", "record_id": "Scientific-Citation-Graph:781f3ee84a876215ed1461c1", "split": "test", "thread": {"accepted_answer_id": 45345, "answers": [{"answer_html": "

Ok, I figured it out after all, it was just a silly misunderstanding. The problem is that I misunderstood the way the Hamiltonian is defined. What I had in mind was the Hamiltonian:\n$$\nH = -J \\sum_i Z_i Z_{i+1} - h \\sum_i X_i\n$$\nwhich is correct, but I thought that the parameter $g$ was the same as the parameter $h$, because the documentation said it was the transverse field. What I failed to notice is that the Hamiltonian they use is\n$$\nH = -J (\\sum_i Z_i Z_{i+1} + g \\sum_i X_i)\n$$\nso, $g$ is not $h$, it is $g=h/J$. So the phase diagram I was getting was actually correct, it just didn't have the parameters that I expected. If I used $h$ as a parameter by correctly passing $g \\to g=h/J$, then I would get the diagram I expected:\n\"Expected

\n", "answer_id": 45345, "answer_text": "Ok, I figured it out after all, it was just a silly misunderstanding. The problem is that I misunderstood the way the Hamiltonian is defined. What I had in mind was the Hamiltonian:\n$$\nH = -J \\sum_i Z_i Z_{i+1} - h \\sum_i X_i\n$$\nwhich is correct, but I thought that the parameter $g$ was the same as the parameter $h$, because the documentation said it was the transverse field. What I failed to notice is that the Hamiltonian they use is\n$$\nH = -J (\\sum_i Z_i Z_{i+1} + g \\sum_i X_i)\n$$\nso, $g$ is not $h$, it is $g=h/J$. So the phase diagram I was getting was actually correct, it just didn't have the parameters that I expected. If I used $h$ as a parameter by correctly passing $g \\to g=h/J$, then I would get the diagram I expected:\n[image: Expected phase diagram for magnetization; source: https://i.sstatic.net/BHts2usz.png] (https://i.sstatic.net/BHts2usz.png)", "answer_url": "https://scicomp.stackexchange.com/a/45345", "author": "Andreas Christophilopoulos", "author_url": "https://scicomp.stackexchange.com/users/56337/andreas-christophilopoulos", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-20T08:42:22+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45344, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Andreas Christophilopoulos", "profile_url": "https://scicomp.stackexchange.com/users/56337/andreas-christophilopoulos", "user_type": "registered"}, "created_at": "2026-01-20T08:42:22+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "48A405D5-BF35-4435-851C-8D73362C5805", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/48A405D5-BF35-4435-851C-8D73362C5805/view-source"}], "score": 3, "updated_at": "2026-01-20T08:42:22+00:00"}], "domain": "computational_science", "external_links": ["https://github.com/QuantumKitHub/MPSKit.jl", "https://i.sstatic.net/82wynbiT.png", "https://i.sstatic.net/BHts2usz.png"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:44.584971+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/272744bcc95b58699f7df6e6979b288bb8b00a80ab9c7982dbe170a6d0b63584_1790825325025901700_0.json", "raw_sha256": "27a81850a40920682c29ada76a2b55e80340a5c82764a3e9dde8a9c2ba23db4e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Andreas Christophilopoulos", "question_author_url": "https://scicomp.stackexchange.com/users/56337/andreas-christophilopoulos", "question_author_user_type": "registered", "question_created_at": "2026-01-19T13:26:44+00:00", "question_html": "

If I am not mistaken, the transverse field Ising model should have a ground state which displays ferromagnetic order for $|J/g|>1$ with positive $J$ (here $J$ is the coupling and $g$ the transverse field) and disorder or Neel order otherwise. In the first case the magnetization should be 1, and in the second it should be 0.

\n

I tried to run a DMRG simulation, and instead of this behavior, the $M=1$ phase appears for $J>0$ and $-0.5<g<0.5$. In other words, it doesn't matter how strong or weak $J$ is (as long as it is positive), there is always ferromagnetic order as long as $|g|$ is smaller than $0.5$, and $M=0$ everywhere else.

\n

This is a very odd result that doesn't make sense to me, so I am inclined to believe there is something wrong with my computational methods. I attach the code I used and the diagram that it produced. My code closely mirrors the example from MPSKit.jl's github:

\n
using MPSKit, MPSKitModels, TensorKit \nusing Plots, ProgressMeter\n\nD = 6\ninit_state = InfiniteMPS(ℂ^2, ℂ^D)\n\ng_values = 0.0:0.2:2.0\nJ_values = -2.01:0.5:2.01\n\nM = @showprogress map(Iterators.product(g_values, J_values)) do (g,J)\n    H = transverse_field_ising(; J=J, g=g)\n    groundstate, environment, δ = find_groundstate(init_state, H, VUMPS(; verbosity=0))\n    return abs(expectation_value(groundstate, 1 => σᶻ()))\nend\n\nheatmap(J_values, g_values, M, \n        xlabel="J", ylabel="g", title="Magnetization M(g, J)")\n
\n

And here is the resulting heatmap:

\n

\"heatmap\"

\n

I tried increasing the bond dimension $D$, but it did nothing. Now, this is VUMPS, but I got the same result more or less with finite $L$ DMRG. I'm at my wit's end! Any help would be appreciated.

\n", "question_id": 45344, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "If I am not mistaken, the transverse field Ising model should have a ground state which displays ferromagnetic order for $|J/g|>1$ with positive $J$ (here $J$ is the coupling and $g$ the transverse field) and disorder or Neel order otherwise. In the first case the magnetization should be 1, and in the second it should be 0.\n\n\n\n\nI tried to run a DMRG simulation, and instead of this behavior, the $M=1$ phase appears for $J>0$ and $-0.5 σᶻ()))\nend\n\nheatmap(J_values, g_values, M, \n xlabel=\"J\", ylabel=\"g\", title=\"Magnetization M(g, J)\")\n\n\n\n\n\nAnd here is the resulting heatmap:\n\n\n\n\n[image: heatmap; source: https://i.sstatic.net/82wynbiT.png] (https://i.sstatic.net/82wynbiT.png)\n\n\n\n\nI tried increasing the bond dimension $D$, but it did nothing. Now, this is VUMPS, but I got the same result more or less with finite $L$ DMRG. I'm at my wit's end! Any help would be appreciated.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Andreas Christophilopoulos", "profile_url": "https://scicomp.stackexchange.com/users/56337/andreas-christophilopoulos", "user_type": "registered"}, "created_at": "2026-01-19T13:26:44+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "9A79D116-A5E8-4995-9CDC-86061D8C4F49", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/9A79D116-A5E8-4995-9CDC-86061D8C4F49/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Andreas Christophilopoulos", "profile_url": "https://scicomp.stackexchange.com/users/56337/andreas-christophilopoulos", "user_type": "registered"}, "created_at": "2026-01-19T14:39:59+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "17008AF4-25DE-4356-9CA5-A73B1EB6B8C6", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/17008AF4-25DE-4356-9CA5-A73B1EB6B8C6/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Reinderien", "profile_url": "https://scicomp.stackexchange.com/users/41212/reinderien", "user_type": "registered"}, "created_at": "2026-01-21T20:16:26+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "D0303D22-34B4-4CE9-B587-04FCADC6EBF4", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/D0303D22-34B4-4CE9-B587-04FCADC6EBF4/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45344/dmrg-returns-weird-results-for-the-tfim-ground-state-magnetization", "split": "test", "split_group": "66f5c7bb70e6d18950c8f6dfdfb104814d80069b9f3004b754c7ecddd2ef175d", "tags": ["quantum-mechanics", "julia"], "thread_id": "scicomp:45344", "title": "DMRG returns weird results for the TFIM ground state magnetization"}} {"citation_context": "title=\"Magnetization M(g, J)\")\n\n\n\n\n\nAnd here is the resulting heatmap:\n\n\n\n\n[image: heatmap; source: https://i.sstatic.net/82wynbiT.png] (https://i.sstatic.net/82wynbiT.png)\n\n\n\n\nI tried increasing the bond dimension $D$, but it did not", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://i.sstatic.net/82wynbiT.png", "kind": "external_url", "post_id": 45344, "post_url": "https://scicomp.stackexchange.com/questions/45344/dmrg-returns-weird-results-for-the-tfim-ground-state-magnetization", "product": "citations", "record_id": "Scientific-Citation-Graph:51a97f082eea66e0a0c9c6ff", "split": "test", "thread": {"accepted_answer_id": 45345, "answers": [{"answer_html": "

Ok, I figured it out after all, it was just a silly misunderstanding. The problem is that I misunderstood the way the Hamiltonian is defined. What I had in mind was the Hamiltonian:\n$$\nH = -J \\sum_i Z_i Z_{i+1} - h \\sum_i X_i\n$$\nwhich is correct, but I thought that the parameter $g$ was the same as the parameter $h$, because the documentation said it was the transverse field. What I failed to notice is that the Hamiltonian they use is\n$$\nH = -J (\\sum_i Z_i Z_{i+1} + g \\sum_i X_i)\n$$\nso, $g$ is not $h$, it is $g=h/J$. So the phase diagram I was getting was actually correct, it just didn't have the parameters that I expected. If I used $h$ as a parameter by correctly passing $g \\to g=h/J$, then I would get the diagram I expected:\n\"Expected

\n", "answer_id": 45345, "answer_text": "Ok, I figured it out after all, it was just a silly misunderstanding. The problem is that I misunderstood the way the Hamiltonian is defined. What I had in mind was the Hamiltonian:\n$$\nH = -J \\sum_i Z_i Z_{i+1} - h \\sum_i X_i\n$$\nwhich is correct, but I thought that the parameter $g$ was the same as the parameter $h$, because the documentation said it was the transverse field. What I failed to notice is that the Hamiltonian they use is\n$$\nH = -J (\\sum_i Z_i Z_{i+1} + g \\sum_i X_i)\n$$\nso, $g$ is not $h$, it is $g=h/J$. So the phase diagram I was getting was actually correct, it just didn't have the parameters that I expected. If I used $h$ as a parameter by correctly passing $g \\to g=h/J$, then I would get the diagram I expected:\n[image: Expected phase diagram for magnetization; source: https://i.sstatic.net/BHts2usz.png] (https://i.sstatic.net/BHts2usz.png)", "answer_url": "https://scicomp.stackexchange.com/a/45345", "author": "Andreas Christophilopoulos", "author_url": "https://scicomp.stackexchange.com/users/56337/andreas-christophilopoulos", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-20T08:42:22+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45344, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Andreas Christophilopoulos", "profile_url": "https://scicomp.stackexchange.com/users/56337/andreas-christophilopoulos", "user_type": "registered"}, "created_at": "2026-01-20T08:42:22+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "48A405D5-BF35-4435-851C-8D73362C5805", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/48A405D5-BF35-4435-851C-8D73362C5805/view-source"}], "score": 3, "updated_at": "2026-01-20T08:42:22+00:00"}], "domain": "computational_science", "external_links": ["https://github.com/QuantumKitHub/MPSKit.jl", "https://i.sstatic.net/82wynbiT.png", "https://i.sstatic.net/BHts2usz.png"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:44.584971+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/272744bcc95b58699f7df6e6979b288bb8b00a80ab9c7982dbe170a6d0b63584_1790825325025901700_0.json", "raw_sha256": "27a81850a40920682c29ada76a2b55e80340a5c82764a3e9dde8a9c2ba23db4e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Andreas Christophilopoulos", "question_author_url": "https://scicomp.stackexchange.com/users/56337/andreas-christophilopoulos", "question_author_user_type": "registered", "question_created_at": "2026-01-19T13:26:44+00:00", "question_html": "

If I am not mistaken, the transverse field Ising model should have a ground state which displays ferromagnetic order for $|J/g|>1$ with positive $J$ (here $J$ is the coupling and $g$ the transverse field) and disorder or Neel order otherwise. In the first case the magnetization should be 1, and in the second it should be 0.

\n

I tried to run a DMRG simulation, and instead of this behavior, the $M=1$ phase appears for $J>0$ and $-0.5<g<0.5$. In other words, it doesn't matter how strong or weak $J$ is (as long as it is positive), there is always ferromagnetic order as long as $|g|$ is smaller than $0.5$, and $M=0$ everywhere else.

\n

This is a very odd result that doesn't make sense to me, so I am inclined to believe there is something wrong with my computational methods. I attach the code I used and the diagram that it produced. My code closely mirrors the example from MPSKit.jl's github:

\n
using MPSKit, MPSKitModels, TensorKit \nusing Plots, ProgressMeter\n\nD = 6\ninit_state = InfiniteMPS(ℂ^2, ℂ^D)\n\ng_values = 0.0:0.2:2.0\nJ_values = -2.01:0.5:2.01\n\nM = @showprogress map(Iterators.product(g_values, J_values)) do (g,J)\n    H = transverse_field_ising(; J=J, g=g)\n    groundstate, environment, δ = find_groundstate(init_state, H, VUMPS(; verbosity=0))\n    return abs(expectation_value(groundstate, 1 => σᶻ()))\nend\n\nheatmap(J_values, g_values, M, \n        xlabel="J", ylabel="g", title="Magnetization M(g, J)")\n
\n

And here is the resulting heatmap:

\n

\"heatmap\"

\n

I tried increasing the bond dimension $D$, but it did nothing. Now, this is VUMPS, but I got the same result more or less with finite $L$ DMRG. I'm at my wit's end! Any help would be appreciated.

\n", "question_id": 45344, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "If I am not mistaken, the transverse field Ising model should have a ground state which displays ferromagnetic order for $|J/g|>1$ with positive $J$ (here $J$ is the coupling and $g$ the transverse field) and disorder or Neel order otherwise. In the first case the magnetization should be 1, and in the second it should be 0.\n\n\n\n\nI tried to run a DMRG simulation, and instead of this behavior, the $M=1$ phase appears for $J>0$ and $-0.5 σᶻ()))\nend\n\nheatmap(J_values, g_values, M, \n xlabel=\"J\", ylabel=\"g\", title=\"Magnetization M(g, J)\")\n\n\n\n\n\nAnd here is the resulting heatmap:\n\n\n\n\n[image: heatmap; source: https://i.sstatic.net/82wynbiT.png] (https://i.sstatic.net/82wynbiT.png)\n\n\n\n\nI tried increasing the bond dimension $D$, but it did nothing. Now, this is VUMPS, but I got the same result more or less with finite $L$ DMRG. I'm at my wit's end! Any help would be appreciated.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Andreas Christophilopoulos", "profile_url": "https://scicomp.stackexchange.com/users/56337/andreas-christophilopoulos", "user_type": "registered"}, "created_at": "2026-01-19T13:26:44+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "9A79D116-A5E8-4995-9CDC-86061D8C4F49", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/9A79D116-A5E8-4995-9CDC-86061D8C4F49/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Andreas Christophilopoulos", "profile_url": "https://scicomp.stackexchange.com/users/56337/andreas-christophilopoulos", "user_type": "registered"}, "created_at": "2026-01-19T14:39:59+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "17008AF4-25DE-4356-9CA5-A73B1EB6B8C6", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/17008AF4-25DE-4356-9CA5-A73B1EB6B8C6/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Reinderien", "profile_url": "https://scicomp.stackexchange.com/users/41212/reinderien", "user_type": "registered"}, "created_at": "2026-01-21T20:16:26+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "D0303D22-34B4-4CE9-B587-04FCADC6EBF4", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/D0303D22-34B4-4CE9-B587-04FCADC6EBF4/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45344/dmrg-returns-weird-results-for-the-tfim-ground-state-magnetization", "split": "test", "split_group": "66f5c7bb70e6d18950c8f6dfdfb104814d80069b9f3004b754c7ecddd2ef175d", "tags": ["quantum-mechanics", "julia"], "thread_id": "scicomp:45344", "title": "DMRG returns weird results for the TFIM ground state magnetization"}} {"citation_context": " then I would get the diagram I expected:\n[image: Expected phase diagram for magnetization; source: https://i.sstatic.net/BHts2usz.png] (https://i.sstatic.net/BHts2usz.png)", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://i.sstatic.net/BHts2usz.png", "kind": "external_url", "post_id": 45345, "post_url": "https://scicomp.stackexchange.com/a/45345", "product": "citations", "record_id": "Scientific-Citation-Graph:ca599c0ad807263b9e569117", "split": "test", "thread": {"accepted_answer_id": 45345, "answers": [{"answer_html": "

Ok, I figured it out after all, it was just a silly misunderstanding. The problem is that I misunderstood the way the Hamiltonian is defined. What I had in mind was the Hamiltonian:\n$$\nH = -J \\sum_i Z_i Z_{i+1} - h \\sum_i X_i\n$$\nwhich is correct, but I thought that the parameter $g$ was the same as the parameter $h$, because the documentation said it was the transverse field. What I failed to notice is that the Hamiltonian they use is\n$$\nH = -J (\\sum_i Z_i Z_{i+1} + g \\sum_i X_i)\n$$\nso, $g$ is not $h$, it is $g=h/J$. So the phase diagram I was getting was actually correct, it just didn't have the parameters that I expected. If I used $h$ as a parameter by correctly passing $g \\to g=h/J$, then I would get the diagram I expected:\n\"Expected

\n", "answer_id": 45345, "answer_text": "Ok, I figured it out after all, it was just a silly misunderstanding. The problem is that I misunderstood the way the Hamiltonian is defined. What I had in mind was the Hamiltonian:\n$$\nH = -J \\sum_i Z_i Z_{i+1} - h \\sum_i X_i\n$$\nwhich is correct, but I thought that the parameter $g$ was the same as the parameter $h$, because the documentation said it was the transverse field. What I failed to notice is that the Hamiltonian they use is\n$$\nH = -J (\\sum_i Z_i Z_{i+1} + g \\sum_i X_i)\n$$\nso, $g$ is not $h$, it is $g=h/J$. So the phase diagram I was getting was actually correct, it just didn't have the parameters that I expected. If I used $h$ as a parameter by correctly passing $g \\to g=h/J$, then I would get the diagram I expected:\n[image: Expected phase diagram for magnetization; source: https://i.sstatic.net/BHts2usz.png] (https://i.sstatic.net/BHts2usz.png)", "answer_url": "https://scicomp.stackexchange.com/a/45345", "author": "Andreas Christophilopoulos", "author_url": "https://scicomp.stackexchange.com/users/56337/andreas-christophilopoulos", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-20T08:42:22+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45344, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Andreas Christophilopoulos", "profile_url": "https://scicomp.stackexchange.com/users/56337/andreas-christophilopoulos", "user_type": "registered"}, "created_at": "2026-01-20T08:42:22+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "48A405D5-BF35-4435-851C-8D73362C5805", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/48A405D5-BF35-4435-851C-8D73362C5805/view-source"}], "score": 3, "updated_at": "2026-01-20T08:42:22+00:00"}], "domain": "computational_science", "external_links": ["https://github.com/QuantumKitHub/MPSKit.jl", "https://i.sstatic.net/82wynbiT.png", "https://i.sstatic.net/BHts2usz.png"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:44.584971+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/272744bcc95b58699f7df6e6979b288bb8b00a80ab9c7982dbe170a6d0b63584_1790825325025901700_0.json", "raw_sha256": "27a81850a40920682c29ada76a2b55e80340a5c82764a3e9dde8a9c2ba23db4e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Andreas Christophilopoulos", "question_author_url": "https://scicomp.stackexchange.com/users/56337/andreas-christophilopoulos", "question_author_user_type": "registered", "question_created_at": "2026-01-19T13:26:44+00:00", "question_html": "

If I am not mistaken, the transverse field Ising model should have a ground state which displays ferromagnetic order for $|J/g|>1$ with positive $J$ (here $J$ is the coupling and $g$ the transverse field) and disorder or Neel order otherwise. In the first case the magnetization should be 1, and in the second it should be 0.

\n

I tried to run a DMRG simulation, and instead of this behavior, the $M=1$ phase appears for $J>0$ and $-0.5<g<0.5$. In other words, it doesn't matter how strong or weak $J$ is (as long as it is positive), there is always ferromagnetic order as long as $|g|$ is smaller than $0.5$, and $M=0$ everywhere else.

\n

This is a very odd result that doesn't make sense to me, so I am inclined to believe there is something wrong with my computational methods. I attach the code I used and the diagram that it produced. My code closely mirrors the example from MPSKit.jl's github:

\n
using MPSKit, MPSKitModels, TensorKit \nusing Plots, ProgressMeter\n\nD = 6\ninit_state = InfiniteMPS(ℂ^2, ℂ^D)\n\ng_values = 0.0:0.2:2.0\nJ_values = -2.01:0.5:2.01\n\nM = @showprogress map(Iterators.product(g_values, J_values)) do (g,J)\n    H = transverse_field_ising(; J=J, g=g)\n    groundstate, environment, δ = find_groundstate(init_state, H, VUMPS(; verbosity=0))\n    return abs(expectation_value(groundstate, 1 => σᶻ()))\nend\n\nheatmap(J_values, g_values, M, \n        xlabel="J", ylabel="g", title="Magnetization M(g, J)")\n
\n

And here is the resulting heatmap:

\n

\"heatmap\"

\n

I tried increasing the bond dimension $D$, but it did nothing. Now, this is VUMPS, but I got the same result more or less with finite $L$ DMRG. I'm at my wit's end! Any help would be appreciated.

\n", "question_id": 45344, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "If I am not mistaken, the transverse field Ising model should have a ground state which displays ferromagnetic order for $|J/g|>1$ with positive $J$ (here $J$ is the coupling and $g$ the transverse field) and disorder or Neel order otherwise. In the first case the magnetization should be 1, and in the second it should be 0.\n\n\n\n\nI tried to run a DMRG simulation, and instead of this behavior, the $M=1$ phase appears for $J>0$ and $-0.5 σᶻ()))\nend\n\nheatmap(J_values, g_values, M, \n xlabel=\"J\", ylabel=\"g\", title=\"Magnetization M(g, J)\")\n\n\n\n\n\nAnd here is the resulting heatmap:\n\n\n\n\n[image: heatmap; source: https://i.sstatic.net/82wynbiT.png] (https://i.sstatic.net/82wynbiT.png)\n\n\n\n\nI tried increasing the bond dimension $D$, but it did nothing. Now, this is VUMPS, but I got the same result more or less with finite $L$ DMRG. I'm at my wit's end! Any help would be appreciated.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Andreas Christophilopoulos", "profile_url": "https://scicomp.stackexchange.com/users/56337/andreas-christophilopoulos", "user_type": "registered"}, "created_at": "2026-01-19T13:26:44+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "9A79D116-A5E8-4995-9CDC-86061D8C4F49", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/9A79D116-A5E8-4995-9CDC-86061D8C4F49/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Andreas Christophilopoulos", "profile_url": "https://scicomp.stackexchange.com/users/56337/andreas-christophilopoulos", "user_type": "registered"}, "created_at": "2026-01-19T14:39:59+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "17008AF4-25DE-4356-9CA5-A73B1EB6B8C6", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/17008AF4-25DE-4356-9CA5-A73B1EB6B8C6/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Reinderien", "profile_url": "https://scicomp.stackexchange.com/users/41212/reinderien", "user_type": "registered"}, "created_at": "2026-01-21T20:16:26+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "D0303D22-34B4-4CE9-B587-04FCADC6EBF4", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/D0303D22-34B4-4CE9-B587-04FCADC6EBF4/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45344/dmrg-returns-weird-results-for-the-tfim-ground-state-magnetization", "split": "test", "split_group": "66f5c7bb70e6d18950c8f6dfdfb104814d80069b9f3004b754c7ecddd2ef175d", "tags": ["quantum-mechanics", "julia"], "thread_id": "scicomp:45344", "title": "DMRG returns weird results for the TFIM ground state magnetization"}} {"citation_context": "eness): Game of life (https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life),card games, Minecraft (https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html) and you can safely add humans to the list.\n\n\n\n\nIf you approach it from the perspective of trying t", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html", "kind": "external_url", "post_id": 45349, "post_url": "https://scicomp.stackexchange.com/a/45349", "product": "citations", "record_id": "Scientific-Citation-Graph:f98cccbeccf3388a8ef62126", "split": "test", "thread": {"accepted_answer_id": 45458, "answers": [{"answer_html": "

Great Question!

\n

One thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.

\n

Maybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine.

\n

One thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete: Game of life,card games, Minecraft and you can safely add humans to the list.

\n

If you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)

\n

Coming back to your first question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

I would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.

\n

\"The

\n

Whether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells, and whatever this is). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.

\n

Also, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)

\n

There has been recent progress in actually writing code snippets into existing cells DNA via CRISPR. Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs or glowing petunias.

\n

(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)

\n", "answer_id": 45349, "answer_text": "Great Question!\n\n\n\n\nOne thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.\n\n\n\n\nMaybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine (https://en.wikipedia.org/wiki/Quine_(computing)).\n\n\n\n\nOne thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete (https://en.wikipedia.org/wiki/Turing_completeness): Game of life (https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life),card games, Minecraft (https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html) and you can safely add humans to the list.\n\n\n\n\nIf you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)\n\n\n\n\nComing back to your first question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\nI would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.\n\n\n\n\n[image: The four base pairs forming the 'instruction set' (wiki); source: https://i.sstatic.net/yiV9XU0w.png] (https://i.sstatic.net/yiV9XU0w.png)\n\n\n\n\nWhether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells (https://en.wikipedia.org/wiki/Non-cellular_life), and whatever this is (https://en.wikipedia.org/wiki/Obelisk_(biology))). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.\n\n\n\n\nAlso, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)\n\n\n\n\nThere has been recent progress in actually writing code snippets into existing cells DNA via CRISPR (https://en.wikipedia.org/wiki/CRISPR_gene_editing). Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs (https://www.nature.com/articles/nature.2015.18448) or glowing petunias (https://light.bio/).\n\n\n\n\n(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)", "answer_url": "https://scicomp.stackexchange.com/a/45349", "author": "MPIchael", "author_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-23T09:19:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": 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agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?

\n", "answer_id": 45356, "answer_text": "agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?", "answer_url": "https://scicomp.stackexchange.com/a/45356", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-28T23:38:38+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-28T23:38:38+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4908EA3E-0E5A-46B6-82FF-012ABEE708AC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4908EA3E-0E5A-46B6-82FF-012ABEE708AC/view-source"}], "score": 0, "updated_at": "2026-01-28T23:38:38+00:00"}, {"answer_html": "

@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.

\n

I agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.

\n

Where I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.

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DNA absolutely behaves like an instruction architecture in many ways.

\n

base pairs as symbolic primitives,

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transcription/translation as interpretation layers,

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proteins as functional execution mechanisms,

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evolutionary pressure as recursive optimization.

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But living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.

\n

That is the missing bridge between classical computation and biological emergence.

\n

Traditional computational systems optimize for. Correctness,efficiency,reproducibility.

\n

Living systems additionally optimize for.

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Resilience,continuity of identity,

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adaptive self-preservation under entropy.

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This is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.

\n

Your point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.

\n", "answer_id": 45458, "answer_text": "@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.\n\n\n\n\nI agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.\n\n\n\n\nWhere I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.\n\n\n\n\nDNA absolutely behaves like an instruction architecture in many ways.\n\n\n\n\nbase pairs as symbolic primitives,\n\n\n\n\ntranscription/translation as interpretation layers,\n\n\n\n\nproteins as functional execution mechanisms,\n\n\n\n\nevolutionary pressure as recursive optimization.\n\n\n\n\nBut living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.\n\n\n\n\nThat is the missing bridge between classical computation and biological emergence.\n\n\n\n\nTraditional computational systems optimize for. Correctness,efficiency,reproducibility.\n\n\n\n\nLiving systems additionally optimize for.\n\n\n\n\nResilience,continuity of identity,\n\n\n\n\nadaptive self-preservation under entropy.\n\n\n\n\nThis is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.\n\n\n\n\nYour point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.", "answer_url": "https://scicomp.stackexchange.com/a/45458", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-05-25T18:11:24+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:49.393498+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/bdd73bdc9d483cfaf7d50f2075e853261f39886330cd6d24a17f7b3b2fb731e5_1790825329894890800_0.json", "raw_sha256": "dfbb76df9ebacfee7e902db64890f154a777bd3049356aee472798c591424d79", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=2&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T18:11:24+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "C604D2B7-0178-49D4-A6C8-19D400D58DBA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/C604D2B7-0178-49D4-A6C8-19D400D58DBA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T19:50:36+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "AC307800-ED33-4C65-80F7-C107BC7B020B", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/AC307800-ED33-4C65-80F7-C107BC7B020B/view-source"}], "score": 0, "updated_at": "2026-05-25T19:50:36+00:00"}], "domain": "computational_science", "external_links": ["https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html", "https://en.wikipedia.org/wiki/CRISPR_gene_editing", "https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life", "https://en.wikipedia.org/wiki/Non-cellular_life", "https://en.wikipedia.org/wiki/Obelisk_(biology", "https://en.wikipedia.org/wiki/Quine_(computing", "https://en.wikipedia.org/wiki/Turing_completeness", "https://i.sstatic.net/yiV9XU0w.png", "https://light.bio/", "https://www.nature.com/articles/nature.2015.18448"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:44.584971+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/272744bcc95b58699f7df6e6979b288bb8b00a80ab9c7982dbe170a6d0b63584_1790825325025901700_0.json", "raw_sha256": "27a81850a40920682c29ada76a2b55e80340a5c82764a3e9dde8a9c2ba23db4e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Donte Lightfoot", "question_author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "question_author_user_type": "registered", "question_created_at": "2026-01-22T13:28:11+00:00", "question_html": "

Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.

\n

My current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks

\n

Using a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

*What would a biological ISA even look like?

\n

*How do we define computational depth in continuous, non-Markovian systems?

\n

*Where do current synthetic biology toolchains fundamentally break?

\n

**What would count as a convincing experimental demonstration?

\n", "question_id": 45347, "question_license": "CC BY-SA 4.0", "question_score": 5, "question_text": "Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.\n\n\n\n\nMy current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks\n\n\n\n\nUsing a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\n*What would a biological ISA even look like?\n\n\n\n\n*How do we define computational depth in continuous, non-Markovian systems?\n\n\n\n\n*Where do current synthetic biology toolchains fundamentally break?\n\n\n\n\n**What would count as a convincing experimental demonstration?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-22T13:28:11+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "0E691519-A338-4491-A061-23454917E13E", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/0E691519-A338-4491-A061-23454917E13E/view-source"}, {"content_license": null, "contributor": {"display_name": "Community", "profile_url": "https://scicomp.stackexchange.com/users/-1/community", "user_type": "moderator"}, "created_at": "2026-02-05T01:09:22+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD/view-source"}, {"content_license": null, "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-02-16T22:12:47+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4CA194AA-003B-4D32-97C1-8BAF607E2849", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4CA194AA-003B-4D32-97C1-8BAF607E2849/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45347/can-biological-systems-act-as-executable-computational-hardware", "split": "test", "split_group": "97e14d3d54a21fa41336b1233350eadd23e8fc11ef129f4ee948c64444040981", "tags": ["quantum-mechanics", "computational-biology", "reproducibility"], "thread_id": "scicomp:45347", "title": "Can Biological Systems Act as Executable Computational Hardware?"}} {"citation_context": "here has been recent progress in actually writing code snippets into existing cells DNA via CRISPR (https://en.wikipedia.org/wiki/CRISPR_gene_editing). Since the overall process of how a particular genetic change translates to changes in marcoscopic", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/CRISPR_gene_editing", "kind": "external_url", "post_id": 45349, "post_url": "https://scicomp.stackexchange.com/a/45349", "product": "citations", "record_id": "Scientific-Citation-Graph:d157a8787abc0a68f2be3a81", "split": "test", "thread": {"accepted_answer_id": 45458, "answers": [{"answer_html": "

Great Question!

\n

One thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.

\n

Maybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine.

\n

One thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete: Game of life,card games, Minecraft and you can safely add humans to the list.

\n

If you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)

\n

Coming back to your first question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

I would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.

\n

\"The

\n

Whether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells, and whatever this is). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.

\n

Also, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)

\n

There has been recent progress in actually writing code snippets into existing cells DNA via CRISPR. Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs or glowing petunias.

\n

(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)

\n", "answer_id": 45349, "answer_text": "Great Question!\n\n\n\n\nOne thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.\n\n\n\n\nMaybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine (https://en.wikipedia.org/wiki/Quine_(computing)).\n\n\n\n\nOne thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete (https://en.wikipedia.org/wiki/Turing_completeness): Game of life (https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life),card games, Minecraft (https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html) and you can safely add humans to the list.\n\n\n\n\nIf you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)\n\n\n\n\nComing back to your first question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\nI would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.\n\n\n\n\n[image: The four base pairs forming the 'instruction set' (wiki); source: https://i.sstatic.net/yiV9XU0w.png] (https://i.sstatic.net/yiV9XU0w.png)\n\n\n\n\nWhether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells (https://en.wikipedia.org/wiki/Non-cellular_life), and whatever this is (https://en.wikipedia.org/wiki/Obelisk_(biology))). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.\n\n\n\n\nAlso, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)\n\n\n\n\nThere has been recent progress in actually writing code snippets into existing cells DNA via CRISPR (https://en.wikipedia.org/wiki/CRISPR_gene_editing). Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs (https://www.nature.com/articles/nature.2015.18448) or glowing petunias (https://light.bio/).\n\n\n\n\n(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)", "answer_url": "https://scicomp.stackexchange.com/a/45349", "author": "MPIchael", "author_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-23T09:19:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": 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agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?

\n", "answer_id": 45356, "answer_text": "agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?", "answer_url": "https://scicomp.stackexchange.com/a/45356", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-28T23:38:38+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-28T23:38:38+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4908EA3E-0E5A-46B6-82FF-012ABEE708AC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4908EA3E-0E5A-46B6-82FF-012ABEE708AC/view-source"}], "score": 0, "updated_at": "2026-01-28T23:38:38+00:00"}, {"answer_html": "

@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.

\n

I agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.

\n

Where I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.

\n

DNA absolutely behaves like an instruction architecture in many ways.

\n

base pairs as symbolic primitives,

\n

transcription/translation as interpretation layers,

\n

proteins as functional execution mechanisms,

\n

evolutionary pressure as recursive optimization.

\n

But living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.

\n

That is the missing bridge between classical computation and biological emergence.

\n

Traditional computational systems optimize for. Correctness,efficiency,reproducibility.

\n

Living systems additionally optimize for.

\n

Resilience,continuity of identity,

\n

adaptive self-preservation under entropy.

\n

This is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.

\n

Your point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.

\n", "answer_id": 45458, "answer_text": "@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.\n\n\n\n\nI agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.\n\n\n\n\nWhere I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.\n\n\n\n\nDNA absolutely behaves like an instruction architecture in many ways.\n\n\n\n\nbase pairs as symbolic primitives,\n\n\n\n\ntranscription/translation as interpretation layers,\n\n\n\n\nproteins as functional execution mechanisms,\n\n\n\n\nevolutionary pressure as recursive optimization.\n\n\n\n\nBut living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.\n\n\n\n\nThat is the missing bridge between classical computation and biological emergence.\n\n\n\n\nTraditional computational systems optimize for. Correctness,efficiency,reproducibility.\n\n\n\n\nLiving systems additionally optimize for.\n\n\n\n\nResilience,continuity of identity,\n\n\n\n\nadaptive self-preservation under entropy.\n\n\n\n\nThis is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.\n\n\n\n\nYour point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.", "answer_url": "https://scicomp.stackexchange.com/a/45458", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-05-25T18:11:24+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:49.393498+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/bdd73bdc9d483cfaf7d50f2075e853261f39886330cd6d24a17f7b3b2fb731e5_1790825329894890800_0.json", "raw_sha256": "dfbb76df9ebacfee7e902db64890f154a777bd3049356aee472798c591424d79", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=2&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T18:11:24+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "C604D2B7-0178-49D4-A6C8-19D400D58DBA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/C604D2B7-0178-49D4-A6C8-19D400D58DBA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T19:50:36+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "AC307800-ED33-4C65-80F7-C107BC7B020B", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/AC307800-ED33-4C65-80F7-C107BC7B020B/view-source"}], "score": 0, "updated_at": "2026-05-25T19:50:36+00:00"}], "domain": "computational_science", "external_links": ["https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html", "https://en.wikipedia.org/wiki/CRISPR_gene_editing", "https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life", "https://en.wikipedia.org/wiki/Non-cellular_life", "https://en.wikipedia.org/wiki/Obelisk_(biology", "https://en.wikipedia.org/wiki/Quine_(computing", "https://en.wikipedia.org/wiki/Turing_completeness", "https://i.sstatic.net/yiV9XU0w.png", "https://light.bio/", "https://www.nature.com/articles/nature.2015.18448"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:44.584971+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/272744bcc95b58699f7df6e6979b288bb8b00a80ab9c7982dbe170a6d0b63584_1790825325025901700_0.json", "raw_sha256": "27a81850a40920682c29ada76a2b55e80340a5c82764a3e9dde8a9c2ba23db4e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Donte Lightfoot", "question_author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "question_author_user_type": "registered", "question_created_at": "2026-01-22T13:28:11+00:00", "question_html": "

Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.

\n

My current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks

\n

Using a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

*What would a biological ISA even look like?

\n

*How do we define computational depth in continuous, non-Markovian systems?

\n

*Where do current synthetic biology toolchains fundamentally break?

\n

**What would count as a convincing experimental demonstration?

\n", "question_id": 45347, "question_license": "CC BY-SA 4.0", "question_score": 5, "question_text": "Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.\n\n\n\n\nMy current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks\n\n\n\n\nUsing a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\n*What would a biological ISA even look like?\n\n\n\n\n*How do we define computational depth in continuous, non-Markovian systems?\n\n\n\n\n*Where do current synthetic biology toolchains fundamentally break?\n\n\n\n\n**What would count as a convincing experimental demonstration?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-22T13:28:11+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "0E691519-A338-4491-A061-23454917E13E", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/0E691519-A338-4491-A061-23454917E13E/view-source"}, {"content_license": null, "contributor": {"display_name": "Community", "profile_url": "https://scicomp.stackexchange.com/users/-1/community", "user_type": "moderator"}, "created_at": "2026-02-05T01:09:22+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD/view-source"}, {"content_license": null, "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-02-16T22:12:47+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4CA194AA-003B-4D32-97C1-8BAF607E2849", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4CA194AA-003B-4D32-97C1-8BAF607E2849/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45347/can-biological-systems-act-as-executable-computational-hardware", "split": "test", "split_group": "97e14d3d54a21fa41336b1233350eadd23e8fc11ef129f4ee948c64444040981", "tags": ["quantum-mechanics", "computational-biology", "reproducibility"], "thread_id": "scicomp:45347", "title": "Can Biological Systems Act as Executable Computational Hardware?"}} {"citation_context": "re proven to be touring complete (https://en.wikipedia.org/wiki/Turing_completeness): Game of life (https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life),card games, Minecraft (https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html) and yo", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life", "kind": "external_url", "post_id": 45349, "post_url": "https://scicomp.stackexchange.com/a/45349", "product": "citations", "record_id": "Scientific-Citation-Graph:01a19ecbc49d2550f16d2e12", "split": "test", "thread": {"accepted_answer_id": 45458, "answers": [{"answer_html": "

Great Question!

\n

One thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.

\n

Maybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine.

\n

One thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete: Game of life,card games, Minecraft and you can safely add humans to the list.

\n

If you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)

\n

Coming back to your first question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

I would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.

\n

\"The

\n

Whether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells, and whatever this is). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.

\n

Also, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)

\n

There has been recent progress in actually writing code snippets into existing cells DNA via CRISPR. Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs or glowing petunias.

\n

(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)

\n", "answer_id": 45349, "answer_text": "Great Question!\n\n\n\n\nOne thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.\n\n\n\n\nMaybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine (https://en.wikipedia.org/wiki/Quine_(computing)).\n\n\n\n\nOne thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete (https://en.wikipedia.org/wiki/Turing_completeness): Game of life (https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life),card games, Minecraft (https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html) and you can safely add humans to the list.\n\n\n\n\nIf you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)\n\n\n\n\nComing back to your first question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\nI would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.\n\n\n\n\n[image: The four base pairs forming the 'instruction set' (wiki); source: https://i.sstatic.net/yiV9XU0w.png] (https://i.sstatic.net/yiV9XU0w.png)\n\n\n\n\nWhether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells (https://en.wikipedia.org/wiki/Non-cellular_life), and whatever this is (https://en.wikipedia.org/wiki/Obelisk_(biology))). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.\n\n\n\n\nAlso, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)\n\n\n\n\nThere has been recent progress in actually writing code snippets into existing cells DNA via CRISPR (https://en.wikipedia.org/wiki/CRISPR_gene_editing). Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs (https://www.nature.com/articles/nature.2015.18448) or glowing petunias (https://light.bio/).\n\n\n\n\n(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)", "answer_url": "https://scicomp.stackexchange.com/a/45349", "author": "MPIchael", "author_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-23T09:19:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": 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agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?

\n", "answer_id": 45356, "answer_text": "agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?", "answer_url": "https://scicomp.stackexchange.com/a/45356", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-28T23:38:38+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-28T23:38:38+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4908EA3E-0E5A-46B6-82FF-012ABEE708AC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4908EA3E-0E5A-46B6-82FF-012ABEE708AC/view-source"}], "score": 0, "updated_at": "2026-01-28T23:38:38+00:00"}, {"answer_html": "

@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.

\n

I agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.

\n

Where I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.

\n

DNA absolutely behaves like an instruction architecture in many ways.

\n

base pairs as symbolic primitives,

\n

transcription/translation as interpretation layers,

\n

proteins as functional execution mechanisms,

\n

evolutionary pressure as recursive optimization.

\n

But living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.

\n

That is the missing bridge between classical computation and biological emergence.

\n

Traditional computational systems optimize for. Correctness,efficiency,reproducibility.

\n

Living systems additionally optimize for.

\n

Resilience,continuity of identity,

\n

adaptive self-preservation under entropy.

\n

This is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.

\n

Your point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.

\n", "answer_id": 45458, "answer_text": "@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.\n\n\n\n\nI agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.\n\n\n\n\nWhere I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.\n\n\n\n\nDNA absolutely behaves like an instruction architecture in many ways.\n\n\n\n\nbase pairs as symbolic primitives,\n\n\n\n\ntranscription/translation as interpretation layers,\n\n\n\n\nproteins as functional execution mechanisms,\n\n\n\n\nevolutionary pressure as recursive optimization.\n\n\n\n\nBut living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.\n\n\n\n\nThat is the missing bridge between classical computation and biological emergence.\n\n\n\n\nTraditional computational systems optimize for. Correctness,efficiency,reproducibility.\n\n\n\n\nLiving systems additionally optimize for.\n\n\n\n\nResilience,continuity of identity,\n\n\n\n\nadaptive self-preservation under entropy.\n\n\n\n\nThis is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.\n\n\n\n\nYour point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.", "answer_url": "https://scicomp.stackexchange.com/a/45458", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-05-25T18:11:24+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:49.393498+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/bdd73bdc9d483cfaf7d50f2075e853261f39886330cd6d24a17f7b3b2fb731e5_1790825329894890800_0.json", "raw_sha256": "dfbb76df9ebacfee7e902db64890f154a777bd3049356aee472798c591424d79", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=2&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T18:11:24+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "C604D2B7-0178-49D4-A6C8-19D400D58DBA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/C604D2B7-0178-49D4-A6C8-19D400D58DBA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T19:50:36+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "AC307800-ED33-4C65-80F7-C107BC7B020B", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/AC307800-ED33-4C65-80F7-C107BC7B020B/view-source"}], "score": 0, "updated_at": "2026-05-25T19:50:36+00:00"}], "domain": "computational_science", "external_links": ["https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html", "https://en.wikipedia.org/wiki/CRISPR_gene_editing", "https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life", "https://en.wikipedia.org/wiki/Non-cellular_life", "https://en.wikipedia.org/wiki/Obelisk_(biology", "https://en.wikipedia.org/wiki/Quine_(computing", "https://en.wikipedia.org/wiki/Turing_completeness", "https://i.sstatic.net/yiV9XU0w.png", "https://light.bio/", "https://www.nature.com/articles/nature.2015.18448"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:44.584971+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/272744bcc95b58699f7df6e6979b288bb8b00a80ab9c7982dbe170a6d0b63584_1790825325025901700_0.json", "raw_sha256": "27a81850a40920682c29ada76a2b55e80340a5c82764a3e9dde8a9c2ba23db4e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Donte Lightfoot", "question_author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "question_author_user_type": "registered", "question_created_at": "2026-01-22T13:28:11+00:00", "question_html": "

Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.

\n

My current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks

\n

Using a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

*What would a biological ISA even look like?

\n

*How do we define computational depth in continuous, non-Markovian systems?

\n

*Where do current synthetic biology toolchains fundamentally break?

\n

**What would count as a convincing experimental demonstration?

\n", "question_id": 45347, "question_license": "CC BY-SA 4.0", "question_score": 5, "question_text": "Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.\n\n\n\n\nMy current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks\n\n\n\n\nUsing a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\n*What would a biological ISA even look like?\n\n\n\n\n*How do we define computational depth in continuous, non-Markovian systems?\n\n\n\n\n*Where do current synthetic biology toolchains fundamentally break?\n\n\n\n\n**What would count as a convincing experimental demonstration?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-22T13:28:11+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "0E691519-A338-4491-A061-23454917E13E", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/0E691519-A338-4491-A061-23454917E13E/view-source"}, {"content_license": null, "contributor": {"display_name": "Community", "profile_url": "https://scicomp.stackexchange.com/users/-1/community", "user_type": "moderator"}, "created_at": "2026-02-05T01:09:22+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD/view-source"}, {"content_license": null, "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-02-16T22:12:47+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4CA194AA-003B-4D32-97C1-8BAF607E2849", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4CA194AA-003B-4D32-97C1-8BAF607E2849/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45347/can-biological-systems-act-as-executable-computational-hardware", "split": "test", "split_group": "97e14d3d54a21fa41336b1233350eadd23e8fc11ef129f4ee948c64444040981", "tags": ["quantum-mechanics", "computational-biology", "reproducibility"], "thread_id": "scicomp:45347", "title": "Can Biological Systems Act as Executable Computational Hardware?"}} {"citation_context": "way to do it is a very interesting question in itself (There are living things which are not cells (https://en.wikipedia.org/wiki/Non-cellular_life), and whatever this is (https://en.wikipedia.org/wiki/Obelisk_(biology))). Maybe there are simpler ", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Non-cellular_life", "kind": "external_url", "post_id": 45349, "post_url": "https://scicomp.stackexchange.com/a/45349", "product": "citations", "record_id": "Scientific-Citation-Graph:b46a128ffd5bdd8c1006ede0", "split": "test", "thread": {"accepted_answer_id": 45458, "answers": [{"answer_html": "

Great Question!

\n

One thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.

\n

Maybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine.

\n

One thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete: Game of life,card games, Minecraft and you can safely add humans to the list.

\n

If you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)

\n

Coming back to your first question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

I would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.

\n

\"The

\n

Whether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells, and whatever this is). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.

\n

Also, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)

\n

There has been recent progress in actually writing code snippets into existing cells DNA via CRISPR. Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs or glowing petunias.

\n

(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)

\n", "answer_id": 45349, "answer_text": "Great Question!\n\n\n\n\nOne thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.\n\n\n\n\nMaybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine (https://en.wikipedia.org/wiki/Quine_(computing)).\n\n\n\n\nOne thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete (https://en.wikipedia.org/wiki/Turing_completeness): Game of life (https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life),card games, Minecraft (https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html) and you can safely add humans to the list.\n\n\n\n\nIf you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)\n\n\n\n\nComing back to your first question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\nI would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.\n\n\n\n\n[image: The four base pairs forming the 'instruction set' (wiki); source: https://i.sstatic.net/yiV9XU0w.png] (https://i.sstatic.net/yiV9XU0w.png)\n\n\n\n\nWhether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells (https://en.wikipedia.org/wiki/Non-cellular_life), and whatever this is (https://en.wikipedia.org/wiki/Obelisk_(biology))). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.\n\n\n\n\nAlso, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)\n\n\n\n\nThere has been recent progress in actually writing code snippets into existing cells DNA via CRISPR (https://en.wikipedia.org/wiki/CRISPR_gene_editing). Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs (https://www.nature.com/articles/nature.2015.18448) or glowing petunias (https://light.bio/).\n\n\n\n\n(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)", "answer_url": "https://scicomp.stackexchange.com/a/45349", "author": "MPIchael", "author_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-23T09:19:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": 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agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?

\n", "answer_id": 45356, "answer_text": "agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?", "answer_url": "https://scicomp.stackexchange.com/a/45356", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-28T23:38:38+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-28T23:38:38+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4908EA3E-0E5A-46B6-82FF-012ABEE708AC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4908EA3E-0E5A-46B6-82FF-012ABEE708AC/view-source"}], "score": 0, "updated_at": "2026-01-28T23:38:38+00:00"}, {"answer_html": "

@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.

\n

I agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.

\n

Where I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.

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DNA absolutely behaves like an instruction architecture in many ways.

\n

base pairs as symbolic primitives,

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transcription/translation as interpretation layers,

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proteins as functional execution mechanisms,

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evolutionary pressure as recursive optimization.

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But living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.

\n

That is the missing bridge between classical computation and biological emergence.

\n

Traditional computational systems optimize for. Correctness,efficiency,reproducibility.

\n

Living systems additionally optimize for.

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Resilience,continuity of identity,

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adaptive self-preservation under entropy.

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This is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.

\n

Your point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.

\n", "answer_id": 45458, "answer_text": "@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.\n\n\n\n\nI agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.\n\n\n\n\nWhere I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.\n\n\n\n\nDNA absolutely behaves like an instruction architecture in many ways.\n\n\n\n\nbase pairs as symbolic primitives,\n\n\n\n\ntranscription/translation as interpretation layers,\n\n\n\n\nproteins as functional execution mechanisms,\n\n\n\n\nevolutionary pressure as recursive optimization.\n\n\n\n\nBut living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.\n\n\n\n\nThat is the missing bridge between classical computation and biological emergence.\n\n\n\n\nTraditional computational systems optimize for. Correctness,efficiency,reproducibility.\n\n\n\n\nLiving systems additionally optimize for.\n\n\n\n\nResilience,continuity of identity,\n\n\n\n\nadaptive self-preservation under entropy.\n\n\n\n\nThis is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.\n\n\n\n\nYour point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.", "answer_url": "https://scicomp.stackexchange.com/a/45458", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-05-25T18:11:24+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:49.393498+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/bdd73bdc9d483cfaf7d50f2075e853261f39886330cd6d24a17f7b3b2fb731e5_1790825329894890800_0.json", "raw_sha256": "dfbb76df9ebacfee7e902db64890f154a777bd3049356aee472798c591424d79", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=2&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T18:11:24+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "C604D2B7-0178-49D4-A6C8-19D400D58DBA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/C604D2B7-0178-49D4-A6C8-19D400D58DBA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T19:50:36+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "AC307800-ED33-4C65-80F7-C107BC7B020B", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/AC307800-ED33-4C65-80F7-C107BC7B020B/view-source"}], "score": 0, "updated_at": "2026-05-25T19:50:36+00:00"}], "domain": "computational_science", "external_links": ["https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html", "https://en.wikipedia.org/wiki/CRISPR_gene_editing", "https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life", "https://en.wikipedia.org/wiki/Non-cellular_life", "https://en.wikipedia.org/wiki/Obelisk_(biology", "https://en.wikipedia.org/wiki/Quine_(computing", "https://en.wikipedia.org/wiki/Turing_completeness", "https://i.sstatic.net/yiV9XU0w.png", "https://light.bio/", "https://www.nature.com/articles/nature.2015.18448"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:44.584971+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/272744bcc95b58699f7df6e6979b288bb8b00a80ab9c7982dbe170a6d0b63584_1790825325025901700_0.json", "raw_sha256": "27a81850a40920682c29ada76a2b55e80340a5c82764a3e9dde8a9c2ba23db4e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Donte Lightfoot", "question_author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "question_author_user_type": "registered", "question_created_at": "2026-01-22T13:28:11+00:00", "question_html": "

Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.

\n

My current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks

\n

Using a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

*What would a biological ISA even look like?

\n

*How do we define computational depth in continuous, non-Markovian systems?

\n

*Where do current synthetic biology toolchains fundamentally break?

\n

**What would count as a convincing experimental demonstration?

\n", "question_id": 45347, "question_license": "CC BY-SA 4.0", "question_score": 5, "question_text": "Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.\n\n\n\n\nMy current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks\n\n\n\n\nUsing a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\n*What would a biological ISA even look like?\n\n\n\n\n*How do we define computational depth in continuous, non-Markovian systems?\n\n\n\n\n*Where do current synthetic biology toolchains fundamentally break?\n\n\n\n\n**What would count as a convincing experimental demonstration?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-22T13:28:11+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "0E691519-A338-4491-A061-23454917E13E", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/0E691519-A338-4491-A061-23454917E13E/view-source"}, {"content_license": null, "contributor": {"display_name": "Community", "profile_url": "https://scicomp.stackexchange.com/users/-1/community", "user_type": "moderator"}, "created_at": "2026-02-05T01:09:22+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD/view-source"}, {"content_license": null, "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-02-16T22:12:47+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4CA194AA-003B-4D32-97C1-8BAF607E2849", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4CA194AA-003B-4D32-97C1-8BAF607E2849/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45347/can-biological-systems-act-as-executable-computational-hardware", "split": "test", "split_group": "97e14d3d54a21fa41336b1233350eadd23e8fc11ef129f4ee948c64444040981", "tags": ["quantum-mechanics", "computational-biology", "reproducibility"], "thread_id": "scicomp:45347", "title": "Can Biological Systems Act as Executable Computational Hardware?"}} {"citation_context": "things which are not cells (https://en.wikipedia.org/wiki/Non-cellular_life), and whatever this is (https://en.wikipedia.org/wiki/Obelisk_(biology))). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.\n\n\n\n\nAls", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Obelisk_(biology", "kind": "external_url", "post_id": 45349, "post_url": "https://scicomp.stackexchange.com/a/45349", "product": "citations", "record_id": "Scientific-Citation-Graph:b43a562b346b846203d66ccf", "split": "test", "thread": {"accepted_answer_id": 45458, "answers": [{"answer_html": "

Great Question!

\n

One thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.

\n

Maybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine.

\n

One thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete: Game of life,card games, Minecraft and you can safely add humans to the list.

\n

If you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)

\n

Coming back to your first question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

I would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.

\n

\"The

\n

Whether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells, and whatever this is). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.

\n

Also, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)

\n

There has been recent progress in actually writing code snippets into existing cells DNA via CRISPR. Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs or glowing petunias.

\n

(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)

\n", "answer_id": 45349, "answer_text": "Great Question!\n\n\n\n\nOne thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.\n\n\n\n\nMaybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine (https://en.wikipedia.org/wiki/Quine_(computing)).\n\n\n\n\nOne thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete (https://en.wikipedia.org/wiki/Turing_completeness): Game of life (https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life),card games, Minecraft (https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html) and you can safely add humans to the list.\n\n\n\n\nIf you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)\n\n\n\n\nComing back to your first question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\nI would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.\n\n\n\n\n[image: The four base pairs forming the 'instruction set' (wiki); source: https://i.sstatic.net/yiV9XU0w.png] (https://i.sstatic.net/yiV9XU0w.png)\n\n\n\n\nWhether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells (https://en.wikipedia.org/wiki/Non-cellular_life), and whatever this is (https://en.wikipedia.org/wiki/Obelisk_(biology))). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.\n\n\n\n\nAlso, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)\n\n\n\n\nThere has been recent progress in actually writing code snippets into existing cells DNA via CRISPR (https://en.wikipedia.org/wiki/CRISPR_gene_editing). Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs (https://www.nature.com/articles/nature.2015.18448) or glowing petunias (https://light.bio/).\n\n\n\n\n(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)", "answer_url": "https://scicomp.stackexchange.com/a/45349", "author": "MPIchael", "author_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-23T09:19:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": 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agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?

\n", "answer_id": 45356, "answer_text": "agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?", "answer_url": "https://scicomp.stackexchange.com/a/45356", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-28T23:38:38+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-28T23:38:38+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4908EA3E-0E5A-46B6-82FF-012ABEE708AC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4908EA3E-0E5A-46B6-82FF-012ABEE708AC/view-source"}], "score": 0, "updated_at": "2026-01-28T23:38:38+00:00"}, {"answer_html": "

@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.

\n

I agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.

\n

Where I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.

\n

DNA absolutely behaves like an instruction architecture in many ways.

\n

base pairs as symbolic primitives,

\n

transcription/translation as interpretation layers,

\n

proteins as functional execution mechanisms,

\n

evolutionary pressure as recursive optimization.

\n

But living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.

\n

That is the missing bridge between classical computation and biological emergence.

\n

Traditional computational systems optimize for. Correctness,efficiency,reproducibility.

\n

Living systems additionally optimize for.

\n

Resilience,continuity of identity,

\n

adaptive self-preservation under entropy.

\n

This is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.

\n

Your point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.

\n", "answer_id": 45458, "answer_text": "@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.\n\n\n\n\nI agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.\n\n\n\n\nWhere I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.\n\n\n\n\nDNA absolutely behaves like an instruction architecture in many ways.\n\n\n\n\nbase pairs as symbolic primitives,\n\n\n\n\ntranscription/translation as interpretation layers,\n\n\n\n\nproteins as functional execution mechanisms,\n\n\n\n\nevolutionary pressure as recursive optimization.\n\n\n\n\nBut living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.\n\n\n\n\nThat is the missing bridge between classical computation and biological emergence.\n\n\n\n\nTraditional computational systems optimize for. Correctness,efficiency,reproducibility.\n\n\n\n\nLiving systems additionally optimize for.\n\n\n\n\nResilience,continuity of identity,\n\n\n\n\nadaptive self-preservation under entropy.\n\n\n\n\nThis is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.\n\n\n\n\nYour point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.", "answer_url": "https://scicomp.stackexchange.com/a/45458", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-05-25T18:11:24+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:49.393498+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/bdd73bdc9d483cfaf7d50f2075e853261f39886330cd6d24a17f7b3b2fb731e5_1790825329894890800_0.json", "raw_sha256": "dfbb76df9ebacfee7e902db64890f154a777bd3049356aee472798c591424d79", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=2&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T18:11:24+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "C604D2B7-0178-49D4-A6C8-19D400D58DBA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/C604D2B7-0178-49D4-A6C8-19D400D58DBA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T19:50:36+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "AC307800-ED33-4C65-80F7-C107BC7B020B", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/AC307800-ED33-4C65-80F7-C107BC7B020B/view-source"}], "score": 0, "updated_at": "2026-05-25T19:50:36+00:00"}], "domain": "computational_science", "external_links": ["https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html", "https://en.wikipedia.org/wiki/CRISPR_gene_editing", "https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life", "https://en.wikipedia.org/wiki/Non-cellular_life", "https://en.wikipedia.org/wiki/Obelisk_(biology", "https://en.wikipedia.org/wiki/Quine_(computing", "https://en.wikipedia.org/wiki/Turing_completeness", "https://i.sstatic.net/yiV9XU0w.png", "https://light.bio/", "https://www.nature.com/articles/nature.2015.18448"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:44.584971+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/272744bcc95b58699f7df6e6979b288bb8b00a80ab9c7982dbe170a6d0b63584_1790825325025901700_0.json", "raw_sha256": "27a81850a40920682c29ada76a2b55e80340a5c82764a3e9dde8a9c2ba23db4e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Donte Lightfoot", "question_author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "question_author_user_type": "registered", "question_created_at": "2026-01-22T13:28:11+00:00", "question_html": "

Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.

\n

My current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks

\n

Using a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

*What would a biological ISA even look like?

\n

*How do we define computational depth in continuous, non-Markovian systems?

\n

*Where do current synthetic biology toolchains fundamentally break?

\n

**What would count as a convincing experimental demonstration?

\n", "question_id": 45347, "question_license": "CC BY-SA 4.0", "question_score": 5, "question_text": "Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.\n\n\n\n\nMy current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks\n\n\n\n\nUsing a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\n*What would a biological ISA even look like?\n\n\n\n\n*How do we define computational depth in continuous, non-Markovian systems?\n\n\n\n\n*Where do current synthetic biology toolchains fundamentally break?\n\n\n\n\n**What would count as a convincing experimental demonstration?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-22T13:28:11+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "0E691519-A338-4491-A061-23454917E13E", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/0E691519-A338-4491-A061-23454917E13E/view-source"}, {"content_license": null, "contributor": {"display_name": "Community", "profile_url": "https://scicomp.stackexchange.com/users/-1/community", "user_type": "moderator"}, "created_at": "2026-02-05T01:09:22+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD/view-source"}, {"content_license": null, "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-02-16T22:12:47+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4CA194AA-003B-4D32-97C1-8BAF607E2849", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4CA194AA-003B-4D32-97C1-8BAF607E2849/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45347/can-biological-systems-act-as-executable-computational-hardware", "split": "test", "split_group": "97e14d3d54a21fa41336b1233350eadd23e8fc11ef129f4ee948c64444040981", "tags": ["quantum-mechanics", "computational-biology", "reproducibility"], "thread_id": "scicomp:45347", "title": "Can Biological Systems Act as Executable Computational Hardware?"}} {"citation_context": " then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine (https://en.wikipedia.org/wiki/Quine_(computing)).\n\n\n\n\nOne thing interesting about computation is that it seems to be extremely abundant. It is nea", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Quine_(computing", "kind": "external_url", "post_id": 45349, "post_url": "https://scicomp.stackexchange.com/a/45349", "product": "citations", "record_id": "Scientific-Citation-Graph:ebfded6f65254878d86efff5", "split": "test", "thread": {"accepted_answer_id": 45458, "answers": [{"answer_html": "

Great Question!

\n

One thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.

\n

Maybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine.

\n

One thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete: Game of life,card games, Minecraft and you can safely add humans to the list.

\n

If you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)

\n

Coming back to your first question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

I would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.

\n

\"The

\n

Whether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells, and whatever this is). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.

\n

Also, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)

\n

There has been recent progress in actually writing code snippets into existing cells DNA via CRISPR. Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs or glowing petunias.

\n

(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)

\n", "answer_id": 45349, "answer_text": "Great Question!\n\n\n\n\nOne thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.\n\n\n\n\nMaybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine (https://en.wikipedia.org/wiki/Quine_(computing)).\n\n\n\n\nOne thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete (https://en.wikipedia.org/wiki/Turing_completeness): Game of life (https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life),card games, Minecraft (https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html) and you can safely add humans to the list.\n\n\n\n\nIf you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)\n\n\n\n\nComing back to your first question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\nI would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.\n\n\n\n\n[image: The four base pairs forming the 'instruction set' (wiki); source: https://i.sstatic.net/yiV9XU0w.png] (https://i.sstatic.net/yiV9XU0w.png)\n\n\n\n\nWhether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells (https://en.wikipedia.org/wiki/Non-cellular_life), and whatever this is (https://en.wikipedia.org/wiki/Obelisk_(biology))). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.\n\n\n\n\nAlso, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)\n\n\n\n\nThere has been recent progress in actually writing code snippets into existing cells DNA via CRISPR (https://en.wikipedia.org/wiki/CRISPR_gene_editing). Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs (https://www.nature.com/articles/nature.2015.18448) or glowing petunias (https://light.bio/).\n\n\n\n\n(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)", "answer_url": "https://scicomp.stackexchange.com/a/45349", "author": "MPIchael", "author_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-23T09:19:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": 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agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?

\n", "answer_id": 45356, "answer_text": "agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?", "answer_url": "https://scicomp.stackexchange.com/a/45356", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-28T23:38:38+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-28T23:38:38+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4908EA3E-0E5A-46B6-82FF-012ABEE708AC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4908EA3E-0E5A-46B6-82FF-012ABEE708AC/view-source"}], "score": 0, "updated_at": "2026-01-28T23:38:38+00:00"}, {"answer_html": "

@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.

\n

I agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.

\n

Where I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.

\n

DNA absolutely behaves like an instruction architecture in many ways.

\n

base pairs as symbolic primitives,

\n

transcription/translation as interpretation layers,

\n

proteins as functional execution mechanisms,

\n

evolutionary pressure as recursive optimization.

\n

But living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.

\n

That is the missing bridge between classical computation and biological emergence.

\n

Traditional computational systems optimize for. Correctness,efficiency,reproducibility.

\n

Living systems additionally optimize for.

\n

Resilience,continuity of identity,

\n

adaptive self-preservation under entropy.

\n

This is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.

\n

Your point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.

\n", "answer_id": 45458, "answer_text": "@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.\n\n\n\n\nI agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.\n\n\n\n\nWhere I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.\n\n\n\n\nDNA absolutely behaves like an instruction architecture in many ways.\n\n\n\n\nbase pairs as symbolic primitives,\n\n\n\n\ntranscription/translation as interpretation layers,\n\n\n\n\nproteins as functional execution mechanisms,\n\n\n\n\nevolutionary pressure as recursive optimization.\n\n\n\n\nBut living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.\n\n\n\n\nThat is the missing bridge between classical computation and biological emergence.\n\n\n\n\nTraditional computational systems optimize for. Correctness,efficiency,reproducibility.\n\n\n\n\nLiving systems additionally optimize for.\n\n\n\n\nResilience,continuity of identity,\n\n\n\n\nadaptive self-preservation under entropy.\n\n\n\n\nThis is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.\n\n\n\n\nYour point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.", "answer_url": "https://scicomp.stackexchange.com/a/45458", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-05-25T18:11:24+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:49.393498+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/bdd73bdc9d483cfaf7d50f2075e853261f39886330cd6d24a17f7b3b2fb731e5_1790825329894890800_0.json", "raw_sha256": "dfbb76df9ebacfee7e902db64890f154a777bd3049356aee472798c591424d79", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=2&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T18:11:24+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "C604D2B7-0178-49D4-A6C8-19D400D58DBA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/C604D2B7-0178-49D4-A6C8-19D400D58DBA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T19:50:36+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "AC307800-ED33-4C65-80F7-C107BC7B020B", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/AC307800-ED33-4C65-80F7-C107BC7B020B/view-source"}], "score": 0, "updated_at": "2026-05-25T19:50:36+00:00"}], "domain": "computational_science", "external_links": ["https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html", "https://en.wikipedia.org/wiki/CRISPR_gene_editing", "https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life", "https://en.wikipedia.org/wiki/Non-cellular_life", "https://en.wikipedia.org/wiki/Obelisk_(biology", "https://en.wikipedia.org/wiki/Quine_(computing", "https://en.wikipedia.org/wiki/Turing_completeness", "https://i.sstatic.net/yiV9XU0w.png", "https://light.bio/", "https://www.nature.com/articles/nature.2015.18448"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:44.584971+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/272744bcc95b58699f7df6e6979b288bb8b00a80ab9c7982dbe170a6d0b63584_1790825325025901700_0.json", "raw_sha256": "27a81850a40920682c29ada76a2b55e80340a5c82764a3e9dde8a9c2ba23db4e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Donte Lightfoot", "question_author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "question_author_user_type": "registered", "question_created_at": "2026-01-22T13:28:11+00:00", "question_html": "

Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.

\n

My current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks

\n

Using a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

*What would a biological ISA even look like?

\n

*How do we define computational depth in continuous, non-Markovian systems?

\n

*Where do current synthetic biology toolchains fundamentally break?

\n

**What would count as a convincing experimental demonstration?

\n", "question_id": 45347, "question_license": "CC BY-SA 4.0", "question_score": 5, "question_text": "Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.\n\n\n\n\nMy current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks\n\n\n\n\nUsing a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\n*What would a biological ISA even look like?\n\n\n\n\n*How do we define computational depth in continuous, non-Markovian systems?\n\n\n\n\n*Where do current synthetic biology toolchains fundamentally break?\n\n\n\n\n**What would count as a convincing experimental demonstration?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-22T13:28:11+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "0E691519-A338-4491-A061-23454917E13E", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/0E691519-A338-4491-A061-23454917E13E/view-source"}, {"content_license": null, "contributor": {"display_name": "Community", "profile_url": "https://scicomp.stackexchange.com/users/-1/community", "user_type": "moderator"}, "created_at": "2026-02-05T01:09:22+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD/view-source"}, {"content_license": null, "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-02-16T22:12:47+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4CA194AA-003B-4D32-97C1-8BAF607E2849", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4CA194AA-003B-4D32-97C1-8BAF607E2849/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45347/can-biological-systems-act-as-executable-computational-hardware", "split": "test", "split_group": "97e14d3d54a21fa41336b1233350eadd23e8fc11ef129f4ee948c64444040981", "tags": ["quantum-mechanics", "computational-biology", "reproducibility"], "thread_id": "scicomp:45347", "title": "Can Biological Systems Act as Executable Computational Hardware?"}} {"citation_context": " nearly everywhere!! There is a fun collection of systems which were proven to be touring complete (https://en.wikipedia.org/wiki/Turing_completeness): Game of life (https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life),card games, Minecraft (https", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Turing_completeness", "kind": "external_url", "post_id": 45349, "post_url": "https://scicomp.stackexchange.com/a/45349", "product": "citations", "record_id": "Scientific-Citation-Graph:c07088e951a2c2bb4d4bcd26", "split": "test", "thread": {"accepted_answer_id": 45458, "answers": [{"answer_html": "

Great Question!

\n

One thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.

\n

Maybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine.

\n

One thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete: Game of life,card games, Minecraft and you can safely add humans to the list.

\n

If you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)

\n

Coming back to your first question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

I would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.

\n

\"The

\n

Whether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells, and whatever this is). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.

\n

Also, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)

\n

There has been recent progress in actually writing code snippets into existing cells DNA via CRISPR. Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs or glowing petunias.

\n

(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)

\n", "answer_id": 45349, "answer_text": "Great Question!\n\n\n\n\nOne thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.\n\n\n\n\nMaybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine (https://en.wikipedia.org/wiki/Quine_(computing)).\n\n\n\n\nOne thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete (https://en.wikipedia.org/wiki/Turing_completeness): Game of life (https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life),card games, Minecraft (https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html) and you can safely add humans to the list.\n\n\n\n\nIf you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)\n\n\n\n\nComing back to your first question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\nI would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.\n\n\n\n\n[image: The four base pairs forming the 'instruction set' (wiki); source: https://i.sstatic.net/yiV9XU0w.png] (https://i.sstatic.net/yiV9XU0w.png)\n\n\n\n\nWhether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells (https://en.wikipedia.org/wiki/Non-cellular_life), and whatever this is (https://en.wikipedia.org/wiki/Obelisk_(biology))). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.\n\n\n\n\nAlso, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)\n\n\n\n\nThere has been recent progress in actually writing code snippets into existing cells DNA via CRISPR (https://en.wikipedia.org/wiki/CRISPR_gene_editing). Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs (https://www.nature.com/articles/nature.2015.18448) or glowing petunias (https://light.bio/).\n\n\n\n\n(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)", "answer_url": "https://scicomp.stackexchange.com/a/45349", "author": "MPIchael", "author_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-23T09:19:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": 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agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?

\n", "answer_id": 45356, "answer_text": "agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?", "answer_url": "https://scicomp.stackexchange.com/a/45356", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-28T23:38:38+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-28T23:38:38+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4908EA3E-0E5A-46B6-82FF-012ABEE708AC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4908EA3E-0E5A-46B6-82FF-012ABEE708AC/view-source"}], "score": 0, "updated_at": "2026-01-28T23:38:38+00:00"}, {"answer_html": "

@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.

\n

I agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.

\n

Where I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.

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DNA absolutely behaves like an instruction architecture in many ways.

\n

base pairs as symbolic primitives,

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transcription/translation as interpretation layers,

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proteins as functional execution mechanisms,

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evolutionary pressure as recursive optimization.

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But living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.

\n

That is the missing bridge between classical computation and biological emergence.

\n

Traditional computational systems optimize for. Correctness,efficiency,reproducibility.

\n

Living systems additionally optimize for.

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Resilience,continuity of identity,

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adaptive self-preservation under entropy.

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This is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.

\n

Your point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.

\n", "answer_id": 45458, "answer_text": "@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.\n\n\n\n\nI agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.\n\n\n\n\nWhere I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.\n\n\n\n\nDNA absolutely behaves like an instruction architecture in many ways.\n\n\n\n\nbase pairs as symbolic primitives,\n\n\n\n\ntranscription/translation as interpretation layers,\n\n\n\n\nproteins as functional execution mechanisms,\n\n\n\n\nevolutionary pressure as recursive optimization.\n\n\n\n\nBut living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.\n\n\n\n\nThat is the missing bridge between classical computation and biological emergence.\n\n\n\n\nTraditional computational systems optimize for. Correctness,efficiency,reproducibility.\n\n\n\n\nLiving systems additionally optimize for.\n\n\n\n\nResilience,continuity of identity,\n\n\n\n\nadaptive self-preservation under entropy.\n\n\n\n\nThis is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.\n\n\n\n\nYour point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.", "answer_url": "https://scicomp.stackexchange.com/a/45458", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-05-25T18:11:24+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:49.393498+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/bdd73bdc9d483cfaf7d50f2075e853261f39886330cd6d24a17f7b3b2fb731e5_1790825329894890800_0.json", "raw_sha256": "dfbb76df9ebacfee7e902db64890f154a777bd3049356aee472798c591424d79", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=2&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T18:11:24+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "C604D2B7-0178-49D4-A6C8-19D400D58DBA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/C604D2B7-0178-49D4-A6C8-19D400D58DBA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T19:50:36+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "AC307800-ED33-4C65-80F7-C107BC7B020B", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/AC307800-ED33-4C65-80F7-C107BC7B020B/view-source"}], "score": 0, "updated_at": "2026-05-25T19:50:36+00:00"}], "domain": "computational_science", "external_links": ["https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html", "https://en.wikipedia.org/wiki/CRISPR_gene_editing", "https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life", "https://en.wikipedia.org/wiki/Non-cellular_life", "https://en.wikipedia.org/wiki/Obelisk_(biology", "https://en.wikipedia.org/wiki/Quine_(computing", "https://en.wikipedia.org/wiki/Turing_completeness", "https://i.sstatic.net/yiV9XU0w.png", "https://light.bio/", "https://www.nature.com/articles/nature.2015.18448"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:44.584971+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/272744bcc95b58699f7df6e6979b288bb8b00a80ab9c7982dbe170a6d0b63584_1790825325025901700_0.json", "raw_sha256": "27a81850a40920682c29ada76a2b55e80340a5c82764a3e9dde8a9c2ba23db4e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Donte Lightfoot", "question_author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "question_author_user_type": "registered", "question_created_at": "2026-01-22T13:28:11+00:00", "question_html": "

Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.

\n

My current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks

\n

Using a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

*What would a biological ISA even look like?

\n

*How do we define computational depth in continuous, non-Markovian systems?

\n

*Where do current synthetic biology toolchains fundamentally break?

\n

**What would count as a convincing experimental demonstration?

\n", "question_id": 45347, "question_license": "CC BY-SA 4.0", "question_score": 5, "question_text": "Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.\n\n\n\n\nMy current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks\n\n\n\n\nUsing a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\n*What would a biological ISA even look like?\n\n\n\n\n*How do we define computational depth in continuous, non-Markovian systems?\n\n\n\n\n*Where do current synthetic biology toolchains fundamentally break?\n\n\n\n\n**What would count as a convincing experimental demonstration?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-22T13:28:11+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "0E691519-A338-4491-A061-23454917E13E", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/0E691519-A338-4491-A061-23454917E13E/view-source"}, {"content_license": null, "contributor": {"display_name": "Community", "profile_url": "https://scicomp.stackexchange.com/users/-1/community", "user_type": "moderator"}, "created_at": "2026-02-05T01:09:22+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD/view-source"}, {"content_license": null, "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-02-16T22:12:47+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4CA194AA-003B-4D32-97C1-8BAF607E2849", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4CA194AA-003B-4D32-97C1-8BAF607E2849/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45347/can-biological-systems-act-as-executable-computational-hardware", "split": "test", "split_group": "97e14d3d54a21fa41336b1233350eadd23e8fc11ef129f4ee948c64444040981", "tags": ["quantum-mechanics", "computational-biology", "reproducibility"], "thread_id": "scicomp:45347", "title": "Can Biological Systems Act as Executable Computational Hardware?"}} {"citation_context": " and virus behaviour.\n\n\n\n\n[image: The four base pairs forming the 'instruction set' (wiki); source: https://i.sstatic.net/yiV9XU0w.png] (https://i.sstatic.net/yiV9XU0w.png)\n\n\n\n\nWhether or not this system of coding is the only way to d", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://i.sstatic.net/yiV9XU0w.png", "kind": "external_url", "post_id": 45349, "post_url": "https://scicomp.stackexchange.com/a/45349", "product": "citations", "record_id": "Scientific-Citation-Graph:865fecda42a7cd7e1b45b3f3", "split": "test", "thread": {"accepted_answer_id": 45458, "answers": [{"answer_html": "

Great Question!

\n

One thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.

\n

Maybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine.

\n

One thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete: Game of life,card games, Minecraft and you can safely add humans to the list.

\n

If you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)

\n

Coming back to your first question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

I would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.

\n

\"The

\n

Whether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells, and whatever this is). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.

\n

Also, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)

\n

There has been recent progress in actually writing code snippets into existing cells DNA via CRISPR. Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs or glowing petunias.

\n

(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)

\n", "answer_id": 45349, "answer_text": "Great Question!\n\n\n\n\nOne thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.\n\n\n\n\nMaybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine (https://en.wikipedia.org/wiki/Quine_(computing)).\n\n\n\n\nOne thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete (https://en.wikipedia.org/wiki/Turing_completeness): Game of life (https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life),card games, Minecraft (https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html) and you can safely add humans to the list.\n\n\n\n\nIf you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)\n\n\n\n\nComing back to your first question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\nI would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.\n\n\n\n\n[image: The four base pairs forming the 'instruction set' (wiki); source: https://i.sstatic.net/yiV9XU0w.png] (https://i.sstatic.net/yiV9XU0w.png)\n\n\n\n\nWhether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells (https://en.wikipedia.org/wiki/Non-cellular_life), and whatever this is (https://en.wikipedia.org/wiki/Obelisk_(biology))). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.\n\n\n\n\nAlso, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)\n\n\n\n\nThere has been recent progress in actually writing code snippets into existing cells DNA via CRISPR (https://en.wikipedia.org/wiki/CRISPR_gene_editing). Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs (https://www.nature.com/articles/nature.2015.18448) or glowing petunias (https://light.bio/).\n\n\n\n\n(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)", "answer_url": "https://scicomp.stackexchange.com/a/45349", "author": "MPIchael", "author_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-23T09:19:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": 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agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?

\n", "answer_id": 45356, "answer_text": "agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?", "answer_url": "https://scicomp.stackexchange.com/a/45356", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-28T23:38:38+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-28T23:38:38+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4908EA3E-0E5A-46B6-82FF-012ABEE708AC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4908EA3E-0E5A-46B6-82FF-012ABEE708AC/view-source"}], "score": 0, "updated_at": "2026-01-28T23:38:38+00:00"}, {"answer_html": "

@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.

\n

I agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.

\n

Where I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.

\n

DNA absolutely behaves like an instruction architecture in many ways.

\n

base pairs as symbolic primitives,

\n

transcription/translation as interpretation layers,

\n

proteins as functional execution mechanisms,

\n

evolutionary pressure as recursive optimization.

\n

But living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.

\n

That is the missing bridge between classical computation and biological emergence.

\n

Traditional computational systems optimize for. Correctness,efficiency,reproducibility.

\n

Living systems additionally optimize for.

\n

Resilience,continuity of identity,

\n

adaptive self-preservation under entropy.

\n

This is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.

\n

Your point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.

\n", "answer_id": 45458, "answer_text": "@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.\n\n\n\n\nI agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.\n\n\n\n\nWhere I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.\n\n\n\n\nDNA absolutely behaves like an instruction architecture in many ways.\n\n\n\n\nbase pairs as symbolic primitives,\n\n\n\n\ntranscription/translation as interpretation layers,\n\n\n\n\nproteins as functional execution mechanisms,\n\n\n\n\nevolutionary pressure as recursive optimization.\n\n\n\n\nBut living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.\n\n\n\n\nThat is the missing bridge between classical computation and biological emergence.\n\n\n\n\nTraditional computational systems optimize for. Correctness,efficiency,reproducibility.\n\n\n\n\nLiving systems additionally optimize for.\n\n\n\n\nResilience,continuity of identity,\n\n\n\n\nadaptive self-preservation under entropy.\n\n\n\n\nThis is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.\n\n\n\n\nYour point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.", "answer_url": "https://scicomp.stackexchange.com/a/45458", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-05-25T18:11:24+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:49.393498+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/bdd73bdc9d483cfaf7d50f2075e853261f39886330cd6d24a17f7b3b2fb731e5_1790825329894890800_0.json", "raw_sha256": "dfbb76df9ebacfee7e902db64890f154a777bd3049356aee472798c591424d79", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=2&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T18:11:24+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "C604D2B7-0178-49D4-A6C8-19D400D58DBA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/C604D2B7-0178-49D4-A6C8-19D400D58DBA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T19:50:36+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "AC307800-ED33-4C65-80F7-C107BC7B020B", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/AC307800-ED33-4C65-80F7-C107BC7B020B/view-source"}], "score": 0, "updated_at": "2026-05-25T19:50:36+00:00"}], "domain": "computational_science", "external_links": ["https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html", "https://en.wikipedia.org/wiki/CRISPR_gene_editing", "https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life", "https://en.wikipedia.org/wiki/Non-cellular_life", "https://en.wikipedia.org/wiki/Obelisk_(biology", "https://en.wikipedia.org/wiki/Quine_(computing", "https://en.wikipedia.org/wiki/Turing_completeness", "https://i.sstatic.net/yiV9XU0w.png", "https://light.bio/", "https://www.nature.com/articles/nature.2015.18448"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:44.584971+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/272744bcc95b58699f7df6e6979b288bb8b00a80ab9c7982dbe170a6d0b63584_1790825325025901700_0.json", "raw_sha256": "27a81850a40920682c29ada76a2b55e80340a5c82764a3e9dde8a9c2ba23db4e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Donte Lightfoot", "question_author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "question_author_user_type": "registered", "question_created_at": "2026-01-22T13:28:11+00:00", "question_html": "

Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.

\n

My current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks

\n

Using a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

*What would a biological ISA even look like?

\n

*How do we define computational depth in continuous, non-Markovian systems?

\n

*Where do current synthetic biology toolchains fundamentally break?

\n

**What would count as a convincing experimental demonstration?

\n", "question_id": 45347, "question_license": "CC BY-SA 4.0", "question_score": 5, "question_text": "Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.\n\n\n\n\nMy current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks\n\n\n\n\nUsing a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\n*What would a biological ISA even look like?\n\n\n\n\n*How do we define computational depth in continuous, non-Markovian systems?\n\n\n\n\n*Where do current synthetic biology toolchains fundamentally break?\n\n\n\n\n**What would count as a convincing experimental demonstration?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-22T13:28:11+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "0E691519-A338-4491-A061-23454917E13E", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/0E691519-A338-4491-A061-23454917E13E/view-source"}, {"content_license": null, "contributor": {"display_name": "Community", "profile_url": "https://scicomp.stackexchange.com/users/-1/community", "user_type": "moderator"}, "created_at": "2026-02-05T01:09:22+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD/view-source"}, {"content_license": null, "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-02-16T22:12:47+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4CA194AA-003B-4D32-97C1-8BAF607E2849", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4CA194AA-003B-4D32-97C1-8BAF607E2849/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45347/can-biological-systems-act-as-executable-computational-hardware", "split": "test", "split_group": "97e14d3d54a21fa41336b1233350eadd23e8fc11ef129f4ee948c64444040981", "tags": ["quantum-mechanics", "computational-biology", "reproducibility"], "thread_id": "scicomp:45347", "title": "Can Biological Systems Act as Executable Computational Hardware?"}} {"citation_context": "ed results like micro-pigs (https://www.nature.com/articles/nature.2015.18448) or glowing petunias (https://light.bio/).\n\n\n\n\n(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://light.bio/", "kind": "external_url", "post_id": 45349, "post_url": "https://scicomp.stackexchange.com/a/45349", "product": "citations", "record_id": "Scientific-Citation-Graph:c30aa29ed26f1d0f03932c87", "split": "test", "thread": {"accepted_answer_id": 45458, "answers": [{"answer_html": "

Great Question!

\n

One thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.

\n

Maybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine.

\n

One thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete: Game of life,card games, Minecraft and you can safely add humans to the list.

\n

If you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)

\n

Coming back to your first question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

I would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.

\n

\"The

\n

Whether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells, and whatever this is). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.

\n

Also, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)

\n

There has been recent progress in actually writing code snippets into existing cells DNA via CRISPR. Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs or glowing petunias.

\n

(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)

\n", "answer_id": 45349, "answer_text": "Great Question!\n\n\n\n\nOne thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.\n\n\n\n\nMaybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine (https://en.wikipedia.org/wiki/Quine_(computing)).\n\n\n\n\nOne thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete (https://en.wikipedia.org/wiki/Turing_completeness): Game of life (https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life),card games, Minecraft (https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html) and you can safely add humans to the list.\n\n\n\n\nIf you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)\n\n\n\n\nComing back to your first question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\nI would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.\n\n\n\n\n[image: The four base pairs forming the 'instruction set' (wiki); source: https://i.sstatic.net/yiV9XU0w.png] (https://i.sstatic.net/yiV9XU0w.png)\n\n\n\n\nWhether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells (https://en.wikipedia.org/wiki/Non-cellular_life), and whatever this is (https://en.wikipedia.org/wiki/Obelisk_(biology))). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.\n\n\n\n\nAlso, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)\n\n\n\n\nThere has been recent progress in actually writing code snippets into existing cells DNA via CRISPR (https://en.wikipedia.org/wiki/CRISPR_gene_editing). Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs (https://www.nature.com/articles/nature.2015.18448) or glowing petunias (https://light.bio/).\n\n\n\n\n(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)", "answer_url": "https://scicomp.stackexchange.com/a/45349", "author": "MPIchael", "author_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-23T09:19:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": 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agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?

\n", "answer_id": 45356, "answer_text": "agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?", "answer_url": "https://scicomp.stackexchange.com/a/45356", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-28T23:38:38+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-28T23:38:38+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4908EA3E-0E5A-46B6-82FF-012ABEE708AC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4908EA3E-0E5A-46B6-82FF-012ABEE708AC/view-source"}], "score": 0, "updated_at": "2026-01-28T23:38:38+00:00"}, {"answer_html": "

@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.

\n

I agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.

\n

Where I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.

\n

DNA absolutely behaves like an instruction architecture in many ways.

\n

base pairs as symbolic primitives,

\n

transcription/translation as interpretation layers,

\n

proteins as functional execution mechanisms,

\n

evolutionary pressure as recursive optimization.

\n

But living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.

\n

That is the missing bridge between classical computation and biological emergence.

\n

Traditional computational systems optimize for. Correctness,efficiency,reproducibility.

\n

Living systems additionally optimize for.

\n

Resilience,continuity of identity,

\n

adaptive self-preservation under entropy.

\n

This is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.

\n

Your point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.

\n", "answer_id": 45458, "answer_text": "@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.\n\n\n\n\nI agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.\n\n\n\n\nWhere I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.\n\n\n\n\nDNA absolutely behaves like an instruction architecture in many ways.\n\n\n\n\nbase pairs as symbolic primitives,\n\n\n\n\ntranscription/translation as interpretation layers,\n\n\n\n\nproteins as functional execution mechanisms,\n\n\n\n\nevolutionary pressure as recursive optimization.\n\n\n\n\nBut living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.\n\n\n\n\nThat is the missing bridge between classical computation and biological emergence.\n\n\n\n\nTraditional computational systems optimize for. Correctness,efficiency,reproducibility.\n\n\n\n\nLiving systems additionally optimize for.\n\n\n\n\nResilience,continuity of identity,\n\n\n\n\nadaptive self-preservation under entropy.\n\n\n\n\nThis is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.\n\n\n\n\nYour point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.", "answer_url": "https://scicomp.stackexchange.com/a/45458", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-05-25T18:11:24+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:49.393498+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/bdd73bdc9d483cfaf7d50f2075e853261f39886330cd6d24a17f7b3b2fb731e5_1790825329894890800_0.json", "raw_sha256": "dfbb76df9ebacfee7e902db64890f154a777bd3049356aee472798c591424d79", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=2&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T18:11:24+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "C604D2B7-0178-49D4-A6C8-19D400D58DBA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/C604D2B7-0178-49D4-A6C8-19D400D58DBA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T19:50:36+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "AC307800-ED33-4C65-80F7-C107BC7B020B", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/AC307800-ED33-4C65-80F7-C107BC7B020B/view-source"}], "score": 0, "updated_at": "2026-05-25T19:50:36+00:00"}], "domain": "computational_science", "external_links": ["https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html", "https://en.wikipedia.org/wiki/CRISPR_gene_editing", "https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life", "https://en.wikipedia.org/wiki/Non-cellular_life", "https://en.wikipedia.org/wiki/Obelisk_(biology", "https://en.wikipedia.org/wiki/Quine_(computing", "https://en.wikipedia.org/wiki/Turing_completeness", "https://i.sstatic.net/yiV9XU0w.png", "https://light.bio/", "https://www.nature.com/articles/nature.2015.18448"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:44.584971+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/272744bcc95b58699f7df6e6979b288bb8b00a80ab9c7982dbe170a6d0b63584_1790825325025901700_0.json", "raw_sha256": "27a81850a40920682c29ada76a2b55e80340a5c82764a3e9dde8a9c2ba23db4e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Donte Lightfoot", "question_author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "question_author_user_type": "registered", "question_created_at": "2026-01-22T13:28:11+00:00", "question_html": "

Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.

\n

My current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks

\n

Using a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

*What would a biological ISA even look like?

\n

*How do we define computational depth in continuous, non-Markovian systems?

\n

*Where do current synthetic biology toolchains fundamentally break?

\n

**What would count as a convincing experimental demonstration?

\n", "question_id": 45347, "question_license": "CC BY-SA 4.0", "question_score": 5, "question_text": "Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.\n\n\n\n\nMy current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks\n\n\n\n\nUsing a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\n*What would a biological ISA even look like?\n\n\n\n\n*How do we define computational depth in continuous, non-Markovian systems?\n\n\n\n\n*Where do current synthetic biology toolchains fundamentally break?\n\n\n\n\n**What would count as a convincing experimental demonstration?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-22T13:28:11+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "0E691519-A338-4491-A061-23454917E13E", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/0E691519-A338-4491-A061-23454917E13E/view-source"}, {"content_license": null, "contributor": {"display_name": "Community", "profile_url": "https://scicomp.stackexchange.com/users/-1/community", "user_type": "moderator"}, "created_at": "2026-02-05T01:09:22+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD/view-source"}, {"content_license": null, "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-02-16T22:12:47+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4CA194AA-003B-4D32-97C1-8BAF607E2849", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4CA194AA-003B-4D32-97C1-8BAF607E2849/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45347/can-biological-systems-act-as-executable-computational-hardware", "split": "test", "split_group": "97e14d3d54a21fa41336b1233350eadd23e8fc11ef129f4ee948c64444040981", "tags": ["quantum-mechanics", "computational-biology", "reproducibility"], "thread_id": "scicomp:45347", "title": "Can Biological Systems Act as Executable Computational Hardware?"}} {"citation_context": "into a larger unknown codebase and see what happens, with totally expected results like micro-pigs (https://www.nature.com/articles/nature.2015.18448) or glowing petunias (https://light.bio/).\n\n\n\n\n(I think it is unfortunate that there is so little o", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.nature.com/articles/nature.2015.18448", "kind": "external_url", "post_id": 45349, "post_url": "https://scicomp.stackexchange.com/a/45349", "product": "citations", "record_id": "Scientific-Citation-Graph:542f5ccedc7189b963f43a85", "split": "test", "thread": {"accepted_answer_id": 45458, "answers": [{"answer_html": "

Great Question!

\n

One thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.

\n

Maybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine.

\n

One thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete: Game of life,card games, Minecraft and you can safely add humans to the list.

\n

If you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)

\n

Coming back to your first question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

I would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.

\n

\"The

\n

Whether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells, and whatever this is). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.

\n

Also, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)

\n

There has been recent progress in actually writing code snippets into existing cells DNA via CRISPR. Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs or glowing petunias.

\n

(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)

\n", "answer_id": 45349, "answer_text": "Great Question!\n\n\n\n\nOne thing to keep in mind is, that the distinction between what is 'biological' and what is 'artificial' is essentially pointless. From a physics and chemistry perspective we start out with the periodic table of atoms, work our way up to combinations of them (molecules) and then we have very large structures made out of the same (dead!) stuff (proteins). At some point in this complexity ladder the structures gain some interesting function. They can be switched into altering states by contact with other molecules and can be manipulated by light, heat or radiation.\n\n\n\n\nMaybe the final step in that ladder is complex life, where you have a large quantity of atoms arranged in a certain way, which we call a cell. This cell has a core where its source code is stored (DNA). This DNA is made up of four base pairs (you could call that a ISA) and some proteins which read and then interpret this information. In computer speak, the DNA of a self-replicating cell is a quine (https://en.wikipedia.org/wiki/Quine_(computing)).\n\n\n\n\nOne thing interesting about computation is that it seems to be extremely abundant. It is nearly everywhere!! There is a fun collection of systems which were proven to be touring complete (https://en.wikipedia.org/wiki/Turing_completeness): Game of life (https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life),card games, Minecraft (https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html) and you can safely add humans to the list.\n\n\n\n\nIf you approach it from the perspective of trying to find the 'simplest' most reduced system of biological computation you end up at that very vague barrier of what is 'organic (chemistry)' and 'inorganic (chemistry)'. (The presence of carbon is a very arbitrary distinction imho.)\n\n\n\n\nComing back to your first question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\nI would say the most interesting instruction set for living matter would be the DNA base pairs (AGTC) itself, and how exacly it transfers into cell and virus behaviour.\n\n\n\n\n[image: The four base pairs forming the 'instruction set' (wiki); source: https://i.sstatic.net/yiV9XU0w.png] (https://i.sstatic.net/yiV9XU0w.png)\n\n\n\n\nWhether or not this system of coding is the only way to do it is a very interesting question in itself (There are living things which are not cells (https://en.wikipedia.org/wiki/Non-cellular_life), and whatever this is (https://en.wikipedia.org/wiki/Obelisk_(biology))). Maybe there are simpler ways to do it and evolution has simply not come up with it yet.\n\n\n\n\nAlso, DNA is the ultimate legacy code from hell, as it is extremely old, has never been formally refactured, consists 100% of random trial and errors followed by occasional brutal deletion and has 0% documentation attached. And then these programs combine and mix instructions in naughty ways! (There are also no unit-tests.)\n\n\n\n\nThere has been recent progress in actually writing code snippets into existing cells DNA via CRISPR (https://en.wikipedia.org/wiki/CRISPR_gene_editing). Since the overall process of how a particular genetic change translates to changes in marcoscopic behaviour is poorly understood, we are essentially copy-pasting small code snippets into a larger unknown codebase and see what happens, with totally expected results like micro-pigs (https://www.nature.com/articles/nature.2015.18448) or glowing petunias (https://light.bio/).\n\n\n\n\n(I think it is unfortunate that there is so little overlap of the silicon-computational-crowd and the genomics people. We could learn quite a bit from each other.)", "answer_url": "https://scicomp.stackexchange.com/a/45349", "author": "MPIchael", "author_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-23T09:19:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": 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agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?

\n", "answer_id": 45356, "answer_text": "agree with the reductionist framing: biologically vs artificially implemented computation is mostly a false distinction at the level of physics. Where I disagree is in identifying DNA base pairs as the relevant “instruction set.”\nDNA is primarily a storage and replication medium. Most real-time computation in living systems occurs in continuous biochemical and biophysical dynamics: reaction–diffusion fields, protein conformational landscapes, ion-channel oscillations, mechanical couplings, and intracellular signaling networks. These are memory-rich dynamical systems, not symbolic code execution.\nIf biology is treated as executable hardware, the meaningful ISA is not AGTC, but the minimal set of controllable dynamical primitives: how physical state trajectories can be driven, coupled, composed, and read out under realistic constraints.\nIn that sense, the core question becomes architectural rather than symbolic:\nWhat are the smallest experimentally controllable dynamical operations that enable reproducible computation with bounded resource cost?", "answer_url": "https://scicomp.stackexchange.com/a/45356", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-01-28T23:38:38+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-28T23:38:38+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4908EA3E-0E5A-46B6-82FF-012ABEE708AC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4908EA3E-0E5A-46B6-82FF-012ABEE708AC/view-source"}], "score": 0, "updated_at": "2026-01-28T23:38:38+00:00"}, {"answer_html": "

@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.

\n

I agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.

\n

Where I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.

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DNA absolutely behaves like an instruction architecture in many ways.

\n

base pairs as symbolic primitives,

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transcription/translation as interpretation layers,

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proteins as functional execution mechanisms,

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evolutionary pressure as recursive optimization.

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But living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.

\n

That is the missing bridge between classical computation and biological emergence.

\n

Traditional computational systems optimize for. Correctness,efficiency,reproducibility.

\n

Living systems additionally optimize for.

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Resilience,continuity of identity,

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adaptive self-preservation under entropy.

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This is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.

\n

Your point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.

\n", "answer_id": 45458, "answer_text": "@MPIchael, Your framing is compelling because it recognizes computation as an emergent property of organized matter rather than something exclusive to silicon systems.\n\n\n\n\nI agree with the broader point that biological and artificial systems are not fundamentally separate categories at the physical level — both arise from structured interactions between matter, energy, and information.\n\n\n\n\nWhere I think the discussion becomes even more interesting is in the distinction between mechanistic computation and narrative coherence.\n\n\n\n\nDNA absolutely behaves like an instruction architecture in many ways.\n\n\n\n\nbase pairs as symbolic primitives,\n\n\n\n\ntranscription/translation as interpretation layers,\n\n\n\n\nproteins as functional execution mechanisms,\n\n\n\n\nevolutionary pressure as recursive optimization.\n\n\n\n\nBut living systems appear to possess something beyond deterministic instruction execution. Biological systems are not merely computing output they continuously preserve self consistency across time, environment, and adaptation. In other words, life seems less like static code execution and more like recursive coherence maintenance.\n\n\n\n\nThat is the missing bridge between classical computation and biological emergence.\n\n\n\n\nTraditional computational systems optimize for. Correctness,efficiency,reproducibility.\n\n\n\n\nLiving systems additionally optimize for.\n\n\n\n\nResilience,continuity of identity,\n\n\n\n\nadaptive self-preservation under entropy.\n\n\n\n\nThis is why biological systems tolerate ambiguity, redundancy, mutation, and incomplete information far better than engineered software systems. Evolution did not produce clean architecture; it produced survivable coherence.\n\n\n\n\nYour point about CRISPR is especially important. Right now, much of genetic engineering resembles modifying undocumented legacy infrastructure without fully understanding the higher-order behavioral dependencies. We can alter symbolic primitives (genes), but we still struggle to model the emergent narrative consequences across the entire organism.", "answer_url": "https://scicomp.stackexchange.com/a/45458", "author": "Donte Lightfoot", "author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-05-25T18:11:24+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:49.393498+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/bdd73bdc9d483cfaf7d50f2075e853261f39886330cd6d24a17f7b3b2fb731e5_1790825329894890800_0.json", "raw_sha256": "dfbb76df9ebacfee7e902db64890f154a777bd3049356aee472798c591424d79", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=2&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45347, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T18:11:24+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "C604D2B7-0178-49D4-A6C8-19D400D58DBA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/C604D2B7-0178-49D4-A6C8-19D400D58DBA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-05-25T19:50:36+00:00", "raw_file": "raw/codex_api_v1/09cbe10ae05462240864407122b451f89c4541eb0ee757adda70c0629772d57a_1790825351806992800_0.json", "raw_sha256": "34f3f34325937951c51090d8305fb513e1e88ef2ed40dcec5c0fe96d5710ba75", "revision_guid": "AC307800-ED33-4C65-80F7-C107BC7B020B", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/AC307800-ED33-4C65-80F7-C107BC7B020B/view-source"}], "score": 0, "updated_at": "2026-05-25T19:50:36+00:00"}], "domain": "computational_science", "external_links": ["https://beza1e1.tuxen.de/articles/accidentally_turing_complete.html", "https://en.wikipedia.org/wiki/CRISPR_gene_editing", "https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life", "https://en.wikipedia.org/wiki/Non-cellular_life", "https://en.wikipedia.org/wiki/Obelisk_(biology", "https://en.wikipedia.org/wiki/Quine_(computing", "https://en.wikipedia.org/wiki/Turing_completeness", "https://i.sstatic.net/yiV9XU0w.png", "https://light.bio/", "https://www.nature.com/articles/nature.2015.18448"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:44.584971+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/272744bcc95b58699f7df6e6979b288bb8b00a80ab9c7982dbe170a6d0b63584_1790825325025901700_0.json", "raw_sha256": "27a81850a40920682c29ada76a2b55e80340a5c82764a3e9dde8a9c2ba23db4e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Donte Lightfoot", "question_author_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "question_author_user_type": "registered", "question_created_at": "2026-01-22T13:28:11+00:00", "question_html": "

Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.

\n

My current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks

\n

Using a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:

\n

Can we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?

\n

*What would a biological ISA even look like?

\n

*How do we define computational depth in continuous, non-Markovian systems?

\n

*Where do current synthetic biology toolchains fundamentally break?

\n

**What would count as a convincing experimental demonstration?

\n", "question_id": 45347, "question_license": "CC BY-SA 4.0", "question_score": 5, "question_text": "Most bio-computation treats biology as inspiration for algorithms. I’m approaching it from the opposite direction: treating biological substrates themselves as the computing hardware.\n\n\n\n\nMy current work explores encoding computation directly into:\nProtein folding landscapes\nReaction–diffusion fields\nNon-Markovian intracellular signaling\nOscillatory metabolic and ionic networks\n\n\n\n\nUsing a dynamical systems framework,\nI’m compiling mathematical operators and quantum-inspired circuit topologies into biological processes, where computation emerges from continuous, memory-rich dynamics rather than discrete clocked logic.\nCore question:\n\n\n\n\nCan we define a rigorous computational instruction set for living matter, where biochemical dynamics are the computation?\n\n\n\n\n*What would a biological ISA even look like?\n\n\n\n\n*How do we define computational depth in continuous, non-Markovian systems?\n\n\n\n\n*Where do current synthetic biology toolchains fundamentally break?\n\n\n\n\n**What would count as a convincing experimental demonstration?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-01-22T13:28:11+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "0E691519-A338-4491-A061-23454917E13E", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/0E691519-A338-4491-A061-23454917E13E/view-source"}, {"content_license": null, "contributor": {"display_name": "Community", "profile_url": "https://scicomp.stackexchange.com/users/-1/community", "user_type": "moderator"}, "created_at": "2026-02-05T01:09:22+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/EADA9E8C-CC8B-4BFF-85D2-36B5D470F7DD/view-source"}, {"content_license": null, "contributor": {"display_name": "Donte Lightfoot", "profile_url": "https://scicomp.stackexchange.com/users/56387/donte-lightfoot", "user_type": "registered"}, "created_at": "2026-02-16T22:12:47+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "4CA194AA-003B-4D32-97C1-8BAF607E2849", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/4CA194AA-003B-4D32-97C1-8BAF607E2849/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45347/can-biological-systems-act-as-executable-computational-hardware", "split": "test", "split_group": "97e14d3d54a21fa41336b1233350eadd23e8fc11ef129f4ee948c64444040981", "tags": ["quantum-mechanics", "computational-biology", "reproducibility"], "thread_id": "scicomp:45347", "title": "Can Biological Systems Act as Executable Computational Hardware?"}} {"citation_context": "have to be calculated sequentially!\n\n\n\n\nThere is a prominent list of problems wich are \"P-complete (https://en.wikipedia.org/wiki/P-complete)\" and can never be parallized. I would have assumed that if any learning is done where information ", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/P-complete", "kind": "external_url", "post_id": 45366, "post_url": "https://scicomp.stackexchange.com/questions/45366/is-federated-learning-a-computationaly-sound-idea", "product": "citations", "record_id": "Scientific-Citation-Graph:eee95fe576321a6b62414245", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

Disclaimer, I'm not an expert in this, I'm just repeating things I've heard from CS colleagues.\nThere are two parts to your question.\nFirst, is it feasible to distribute ML model training among many distant compute nodes that might have high communication latency?\nI don't know enough to answer this.

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Second, if you want to train a model on private data, can you do that in a way that does not leak private data?\nThere is a field of research that aims to answer this question called differential privacy.\nThe nightmare scenario is that a group of large hospital systems train a ML model on patient data but some bad actor is able to execute a reconstruction attack that reveals that you, MPIchael, are not a human but rather a large bird.\nDifferential privacy aims to prevent such attacks through intentionally injecting noise into the data such that information about any individual is untrustworthy despite the fact that global aggregate results still have the same statistical average as what is desired.\nThis section on the differential privacy wiki is a succinct example.

\n

So it would appear that information in the training data can in fact remain confidential; the mechanism is the intentional injection of noise; and there is a rigorous mathematical theory describing how much noise you need to inject given the number of samples.

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Now, the counter-argument.\nThe field of ML has a lot of hype.\nA lot of people have a financial interest in maintaining this hype.\nPart of that hype is that it will revolutionize healthcare.\nA reasonable person could ask how we can train ML models to solve problems in healthcare when all that data falls under HIPAA.\nIt suits the interests of people with lots of money to be able to say that differential privacy is a theoretically sound answer to this objection.\nIt's possible that (1) there are exploitable flaws in the theory of differential privacy itself, or (2) there are flaws in the practical application of this theory, such that it doesn't provide the privacy protection that the theory claims.\nThe first feels far-fetched to me and I don't know enough to have a hunch about the second.\nBut it's also important to acknowledge where there are vested interests.\nTo make an analogy, there is a mathematical theory of public-key cryptography.\nThis theory is a necessary component of practical cybersecurity, but it is far from sufficient: I can transmit password hashes using a cryptographically-secure hash function, but if a user chooses "password" as his password, then a malicious actor can guess that.

\n", "answer_id": 45367, "answer_text": "Disclaimer, I'm not an expert in this, I'm just repeating things I've heard from CS colleagues.\nThere are two parts to your question.\nFirst, is it feasible to distribute ML model training among many distant compute nodes that might have high communication latency?\nI don't know enough to answer this.\n\n\n\n\nSecond, if you want to train a model on private data, can you do that in a way that does not leak private data?\nThere is a field of research that aims to answer this question called differential privacy (https://en.wikipedia.org/wiki/Differential_privacy).\nThe nightmare scenario is that a group of large hospital systems train a ML model on patient data but some bad actor is able to execute a reconstruction attack (https://en.wikipedia.org/wiki/Reconstruction_attack) that reveals that you, MPIchael, are not a human but rather a large bird.\nDifferential privacy aims to prevent such attacks through intentionally injecting noise into the data such that information about any individual is untrustworthy despite the fact that global aggregate results still have the same statistical average as what is desired.\nThis section (https://en.wikipedia.org/wiki/Differential_privacy#Randomized_response) on the differential privacy wiki is a succinct example.\n\n\n\n\nSo it would appear that information in the training data can in fact remain confidential; the mechanism is the intentional injection of noise; and there is a rigorous mathematical theory describing how much noise you need to inject given the number of samples.\n\n\n\n\nNow, the counter-argument.\nThe field of ML has a lot of hype.\nA lot of people have a financial interest in maintaining this hype.\nPart of that hype is that it will revolutionize healthcare.\nA reasonable person could ask how we can train ML models to solve problems in healthcare when all that data falls under HIPAA.\nIt suits the interests of people with lots of money to be able to say that differential privacy is a theoretically sound answer to this objection.\nIt's possible that (1) there are exploitable flaws in the theory of differential privacy itself, or (2) there are flaws in the practical application of this theory, such that it doesn't provide the privacy protection that the theory claims.\nThe first feels far-fetched to me and I don't know enough to have a hunch about the second.\nBut it's also important to acknowledge where there are vested interests.\nTo make an analogy, there is a mathematical theory of public-key cryptography.\nThis theory is a necessary component of practical cybersecurity, but it is far from sufficient: I can transmit password hashes using a cryptographically-secure hash function, but if a user chooses \"password\" as his password, then a malicious actor can guess that.", "answer_url": "https://scicomp.stackexchange.com/a/45367", "author": "Daniel Shapero", "author_url": "https://scicomp.stackexchange.com/users/3481/daniel-shapero", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-02-12T18:36:02+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45366, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Daniel Shapero", "profile_url": "https://scicomp.stackexchange.com/users/3481/daniel-shapero", "user_type": "registered"}, "created_at": "2026-02-12T18:36:02+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "E77DB701-1B32-4706-A801-DAF6D024D5E4", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/E77DB701-1B32-4706-A801-DAF6D024D5E4/view-source"}], "score": 4, "updated_at": "2026-02-12T18:36:02+00:00"}, {"answer_html": "

Many machine learning algorithms, under the hood, try to determine some internal parameters of a class of functions (say, the weights and biases of a neural network) by minimizing an objective function that is a sum over the training set. Let's say that the neural network or whatever other approach you want to use corresponds to an operator $F(x; \\cdot)$ that maps an input $a$ to an output $b=F(x;a)$ where the vector $x$ corresponds to the internal parameters. The machine learning part is to determine the best internal parameters $x$ for given input/output data sets.

\n

If you have training inputs $a_i$ and corresponding correct answers $b_i$, then a typical approach is to minimize the objective function\n$$\n f(x) = \\frac 12 \\sum_i \\left( b_i - F(x;a_i) \\right)^2.\n$$\nIf you use the usual steepest descent algorithm, you will need to compute\n$$\n \\nabla_x f(x) = -\\sum_i \\left( b_i - F(x;a_i) \\right) \\nabla_x F(x;a_i).\n$$\nThis is computable in a perfectly distributed manner if a central processor sends the current $x$ to other machines who, given their own knowledge of $a_i,b_i$ can compute the gradient contribution for data point $i$ without ever sending $a_i$ or $b_i$ to another process -- preserving the privacy of the data from the rest of the world, including the process that then updates the current parameters $x$ through the gradient $\\nabla f$.

\n", "answer_id": 45374, "answer_text": "Many machine learning algorithms, under the hood, try to determine some internal parameters of a class of functions (say, the weights and biases of a neural network) by minimizing an objective function that is a sum over the training set. Let's say that the neural network or whatever other approach you want to use corresponds to an operator $F(x; \\cdot)$ that maps an input $a$ to an output $b=F(x;a)$ where the vector $x$ corresponds to the internal parameters. The machine learning part is to determine the best internal parameters $x$ for given input/output data sets.\n\n\n\n\nIf you have training inputs $a_i$ and corresponding correct answers $b_i$, then a typical approach is to minimize the objective function\n$$\n f(x) = \\frac 12 \\sum_i \\left( b_i - F(x;a_i) \\right)^2.\n$$\nIf you use the usual steepest descent algorithm, you will need to compute\n$$\n \\nabla_x f(x) = -\\sum_i \\left( b_i - F(x;a_i) \\right) \\nabla_x F(x;a_i).\n$$\nThis is computable in a perfectly distributed manner if a central processor sends the current $x$ to other machines who, given their own knowledge of $a_i,b_i$ can compute the gradient contribution for data point $i$ without ever sending $a_i$ or $b_i$ to another process -- preserving the privacy of the data from the rest of the world, including the process that then updates the current parameters $x$ through the gradient $\\nabla f$.", "answer_url": "https://scicomp.stackexchange.com/a/45374", "author": "Wolfgang Bangerth", "author_url": "https://scicomp.stackexchange.com/users/393/wolfgang-bangerth", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-02-14T05:37:48+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45366, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Wolfgang Bangerth", "profile_url": "https://scicomp.stackexchange.com/users/393/wolfgang-bangerth", "user_type": "registered"}, "created_at": "2026-02-14T05:37:48+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "0D5DD87B-5B83-423D-9881-0AA2556859E2", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/0D5DD87B-5B83-423D-9881-0AA2556859E2/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Wolfgang Bangerth", "profile_url": "https://scicomp.stackexchange.com/users/393/wolfgang-bangerth", "user_type": "registered"}, "created_at": "2026-02-19T23:03:54+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "384FD55C-E139-4B7B-BDD7-ED16AA122B8B", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/384FD55C-E139-4B7B-BDD7-ED16AA122B8B/view-source"}], "score": 4, "updated_at": "2026-02-19T23:03:54+00:00"}], "domain": "computational_science", "external_links": ["https://en.wikipedia.org/wiki/Differential_privacy", "https://en.wikipedia.org/wiki/Differential_privacy#Randomized_response", "https://en.wikipedia.org/wiki/P-complete", "https://en.wikipedia.org/wiki/Reconstruction_attack"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:44.584971+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/272744bcc95b58699f7df6e6979b288bb8b00a80ab9c7982dbe170a6d0b63584_1790825325025901700_0.json", "raw_sha256": "27a81850a40920682c29ada76a2b55e80340a5c82764a3e9dde8a9c2ba23db4e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "MPIchael", "question_author_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "question_author_user_type": "registered", "question_created_at": "2026-02-12T11:38:00+00:00", "question_html": "

I came into contact with projects pushing some "federated learning" approaches for training AI models. The idea behind federated learning is that machine learning algorithms can be trained decentrally on a set of data chunks, so that sensitive data does not leave data providers, and the computing power can be separated into nodes.

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I have done some distributed HPC before and the idea struck me as very odd since not all computations can be neatly paralellized. Any computation where there are reasonable intermediate results, that can be put together at a later stage, can be done in parallel like calculating a mean value or combining stochastic distributions. Explicit timestepping methods have to be calculated sequentially!

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There is a prominent list of problems wich are "P-complete" and can never be parallized. I would have assumed that if any learning is done where information from more than on chunk is needed in combination, then that would also fall into the category of algorithms which can not be reasonably parallelized.

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One explanation I could see is that information from the chunks is not actually left in place, but that the decentralized algorithms merely compress the info and then the actual learning is done at the recombination stage. That would completely defy the selling point of privacy of training data!

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The other explanation I can come up with is that these ML methods are essentially limited to calculating high level statistics about their training data. These could be collected separately and then recombined. This would make sense to me, but then we should call it high dimensional linear regression and not artificial intelligence.

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Any 'learning' that would require information from multiple chunks which are distributed seems impossible to me.

\n

How does "Federated Learning" actually work? How can information of the training data be left confidential?

\n", "question_id": 45366, "question_license": "CC BY-SA 4.0", "question_score": 3, "question_text": "I came into contact with projects pushing some \"federated learning\" approaches for training AI models. The idea behind federated learning is that machine learning algorithms can be trained decentrally on a set of data chunks, so that sensitive data does not leave data providers, and the computing power can be separated into nodes.\n\n\n\n\nI have done some distributed HPC before and the idea struck me as very odd since not all computations can be neatly paralellized. Any computation where there are reasonable intermediate results, that can be put together at a later stage, can be done in parallel like calculating a mean value or combining stochastic distributions. Explicit timestepping methods have to be calculated sequentially!\n\n\n\n\nThere is a prominent list of problems wich are \"P-complete (https://en.wikipedia.org/wiki/P-complete)\" and can never be parallized. I would have assumed that if any learning is done where information from more than on chunk is needed in combination, then that would also fall into the category of algorithms which can not be reasonably parallelized.\n\n\n\n\nOne explanation I could see is that information from the chunks is not actually left in place, but that the decentralized algorithms merely compress the info and then the actual learning is done at the recombination stage. That would completely defy the selling point of privacy of training data!\n\n\n\n\nThe other explanation I can come up with is that these ML methods are essentially limited to calculating high level statistics about their training data. These could be collected separately and then recombined. This would make sense to me, but then we should call it high dimensional linear regression and not artificial intelligence.\n\n\n\n\nAny 'learning' that would require information from multiple chunks which are distributed seems impossible to me.\n\n\n\n\nHow does \"Federated Learning\" actually work? How can information of the training data be left confidential?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MPIchael", "profile_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "user_type": "registered"}, "created_at": "2026-02-12T11:38:00+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "F4054CE7-4D32-4BF3-9451-F79096A1E0EF", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/F4054CE7-4D32-4BF3-9451-F79096A1E0EF/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-02-13T00:47:30+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "1EC62651-6157-48CF-9911-09F9F1340AB1", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://scicomp.stackexchange.com/revisions/1EC62651-6157-48CF-9911-09F9F1340AB1/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45366/is-federated-learning-a-computationaly-sound-idea", "split": "test", "split_group": "1c83d94409976ab407c4c0691435e4f90d777304123956cbb24b2cf869fae846", "tags": ["machine-learning"], "thread_id": "scicomp:45366", "title": "Is \"Federated Learning\" a computationaly sound idea?"}} {"citation_context": "e data?\nThere is a field of research that aims to answer this question called differential privacy (https://en.wikipedia.org/wiki/Differential_privacy).\nThe nightmare scenario is that a group of large hospital systems train a ML model on patient data", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Differential_privacy", "kind": "external_url", "post_id": 45367, "post_url": "https://scicomp.stackexchange.com/a/45367", "product": "citations", "record_id": "Scientific-Citation-Graph:951acf3d8188cdc5d5edc3d1", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

Disclaimer, I'm not an expert in this, I'm just repeating things I've heard from CS colleagues.\nThere are two parts to your question.\nFirst, is it feasible to distribute ML model training among many distant compute nodes that might have high communication latency?\nI don't know enough to answer this.

\n

Second, if you want to train a model on private data, can you do that in a way that does not leak private data?\nThere is a field of research that aims to answer this question called differential privacy.\nThe nightmare scenario is that a group of large hospital systems train a ML model on patient data but some bad actor is able to execute a reconstruction attack that reveals that you, MPIchael, are not a human but rather a large bird.\nDifferential privacy aims to prevent such attacks through intentionally injecting noise into the data such that information about any individual is untrustworthy despite the fact that global aggregate results still have the same statistical average as what is desired.\nThis section on the differential privacy wiki is a succinct example.

\n

So it would appear that information in the training data can in fact remain confidential; the mechanism is the intentional injection of noise; and there is a rigorous mathematical theory describing how much noise you need to inject given the number of samples.

\n

Now, the counter-argument.\nThe field of ML has a lot of hype.\nA lot of people have a financial interest in maintaining this hype.\nPart of that hype is that it will revolutionize healthcare.\nA reasonable person could ask how we can train ML models to solve problems in healthcare when all that data falls under HIPAA.\nIt suits the interests of people with lots of money to be able to say that differential privacy is a theoretically sound answer to this objection.\nIt's possible that (1) there are exploitable flaws in the theory of differential privacy itself, or (2) there are flaws in the practical application of this theory, such that it doesn't provide the privacy protection that the theory claims.\nThe first feels far-fetched to me and I don't know enough to have a hunch about the second.\nBut it's also important to acknowledge where there are vested interests.\nTo make an analogy, there is a mathematical theory of public-key cryptography.\nThis theory is a necessary component of practical cybersecurity, but it is far from sufficient: I can transmit password hashes using a cryptographically-secure hash function, but if a user chooses "password" as his password, then a malicious actor can guess that.

\n", "answer_id": 45367, "answer_text": "Disclaimer, I'm not an expert in this, I'm just repeating things I've heard from CS colleagues.\nThere are two parts to your question.\nFirst, is it feasible to distribute ML model training among many distant compute nodes that might have high communication latency?\nI don't know enough to answer this.\n\n\n\n\nSecond, if you want to train a model on private data, can you do that in a way that does not leak private data?\nThere is a field of research that aims to answer this question called differential privacy (https://en.wikipedia.org/wiki/Differential_privacy).\nThe nightmare scenario is that a group of large hospital systems train a ML model on patient data but some bad actor is able to execute a reconstruction attack (https://en.wikipedia.org/wiki/Reconstruction_attack) that reveals that you, MPIchael, are not a human but rather a large bird.\nDifferential privacy aims to prevent such attacks through intentionally injecting noise into the data such that information about any individual is untrustworthy despite the fact that global aggregate results still have the same statistical average as what is desired.\nThis section (https://en.wikipedia.org/wiki/Differential_privacy#Randomized_response) on the differential privacy wiki is a succinct example.\n\n\n\n\nSo it would appear that information in the training data can in fact remain confidential; the mechanism is the intentional injection of noise; and there is a rigorous mathematical theory describing how much noise you need to inject given the number of samples.\n\n\n\n\nNow, the counter-argument.\nThe field of ML has a lot of hype.\nA lot of people have a financial interest in maintaining this hype.\nPart of that hype is that it will revolutionize healthcare.\nA reasonable person could ask how we can train ML models to solve problems in healthcare when all that data falls under HIPAA.\nIt suits the interests of people with lots of money to be able to say that differential privacy is a theoretically sound answer to this objection.\nIt's possible that (1) there are exploitable flaws in the theory of differential privacy itself, or (2) there are flaws in the practical application of this theory, such that it doesn't provide the privacy protection that the theory claims.\nThe first feels far-fetched to me and I don't know enough to have a hunch about the second.\nBut it's also important to acknowledge where there are vested interests.\nTo make an analogy, there is a mathematical theory of public-key cryptography.\nThis theory is a necessary component of practical cybersecurity, but it is far from sufficient: I can transmit password hashes using a cryptographically-secure hash function, but if a user chooses \"password\" as his password, then a malicious actor can guess that.", "answer_url": "https://scicomp.stackexchange.com/a/45367", "author": "Daniel Shapero", "author_url": "https://scicomp.stackexchange.com/users/3481/daniel-shapero", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-02-12T18:36:02+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45366, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Daniel Shapero", "profile_url": "https://scicomp.stackexchange.com/users/3481/daniel-shapero", "user_type": "registered"}, "created_at": "2026-02-12T18:36:02+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "E77DB701-1B32-4706-A801-DAF6D024D5E4", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/E77DB701-1B32-4706-A801-DAF6D024D5E4/view-source"}], "score": 4, "updated_at": "2026-02-12T18:36:02+00:00"}, {"answer_html": "

Many machine learning algorithms, under the hood, try to determine some internal parameters of a class of functions (say, the weights and biases of a neural network) by minimizing an objective function that is a sum over the training set. Let's say that the neural network or whatever other approach you want to use corresponds to an operator $F(x; \\cdot)$ that maps an input $a$ to an output $b=F(x;a)$ where the vector $x$ corresponds to the internal parameters. The machine learning part is to determine the best internal parameters $x$ for given input/output data sets.

\n

If you have training inputs $a_i$ and corresponding correct answers $b_i$, then a typical approach is to minimize the objective function\n$$\n f(x) = \\frac 12 \\sum_i \\left( b_i - F(x;a_i) \\right)^2.\n$$\nIf you use the usual steepest descent algorithm, you will need to compute\n$$\n \\nabla_x f(x) = -\\sum_i \\left( b_i - F(x;a_i) \\right) \\nabla_x F(x;a_i).\n$$\nThis is computable in a perfectly distributed manner if a central processor sends the current $x$ to other machines who, given their own knowledge of $a_i,b_i$ can compute the gradient contribution for data point $i$ without ever sending $a_i$ or $b_i$ to another process -- preserving the privacy of the data from the rest of the world, including the process that then updates the current parameters $x$ through the gradient $\\nabla f$.

\n", "answer_id": 45374, "answer_text": "Many machine learning algorithms, under the hood, try to determine some internal parameters of a class of functions (say, the weights and biases of a neural network) by minimizing an objective function that is a sum over the training set. Let's say that the neural network or whatever other approach you want to use corresponds to an operator $F(x; \\cdot)$ that maps an input $a$ to an output $b=F(x;a)$ where the vector $x$ corresponds to the internal parameters. The machine learning part is to determine the best internal parameters $x$ for given input/output data sets.\n\n\n\n\nIf you have training inputs $a_i$ and corresponding correct answers $b_i$, then a typical approach is to minimize the objective function\n$$\n f(x) = \\frac 12 \\sum_i \\left( b_i - F(x;a_i) \\right)^2.\n$$\nIf you use the usual steepest descent algorithm, you will need to compute\n$$\n \\nabla_x f(x) = -\\sum_i \\left( b_i - F(x;a_i) \\right) \\nabla_x F(x;a_i).\n$$\nThis is computable in a perfectly distributed manner if a central processor sends the current $x$ to other machines who, given their own knowledge of $a_i,b_i$ can compute the gradient contribution for data point $i$ without ever sending $a_i$ or $b_i$ to another process -- preserving the privacy of the data from the rest of the world, including the process that then updates the current parameters $x$ through the gradient $\\nabla f$.", "answer_url": "https://scicomp.stackexchange.com/a/45374", "author": "Wolfgang Bangerth", "author_url": "https://scicomp.stackexchange.com/users/393/wolfgang-bangerth", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-02-14T05:37:48+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; 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mechanical HTML-to-text; no LLM rewriting"}, "question_author": "MPIchael", "question_author_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "question_author_user_type": "registered", "question_created_at": "2026-02-12T11:38:00+00:00", "question_html": "

I came into contact with projects pushing some "federated learning" approaches for training AI models. The idea behind federated learning is that machine learning algorithms can be trained decentrally on a set of data chunks, so that sensitive data does not leave data providers, and the computing power can be separated into nodes.

\n

I have done some distributed HPC before and the idea struck me as very odd since not all computations can be neatly paralellized. Any computation where there are reasonable intermediate results, that can be put together at a later stage, can be done in parallel like calculating a mean value or combining stochastic distributions. Explicit timestepping methods have to be calculated sequentially!

\n

There is a prominent list of problems wich are "P-complete" and can never be parallized. I would have assumed that if any learning is done where information from more than on chunk is needed in combination, then that would also fall into the category of algorithms which can not be reasonably parallelized.

\n

One explanation I could see is that information from the chunks is not actually left in place, but that the decentralized algorithms merely compress the info and then the actual learning is done at the recombination stage. That would completely defy the selling point of privacy of training data!

\n

The other explanation I can come up with is that these ML methods are essentially limited to calculating high level statistics about their training data. These could be collected separately and then recombined. This would make sense to me, but then we should call it high dimensional linear regression and not artificial intelligence.

\n

Any 'learning' that would require information from multiple chunks which are distributed seems impossible to me.

\n

How does "Federated Learning" actually work? How can information of the training data be left confidential?

\n", "question_id": 45366, "question_license": "CC BY-SA 4.0", "question_score": 3, "question_text": "I came into contact with projects pushing some \"federated learning\" approaches for training AI models. The idea behind federated learning is that machine learning algorithms can be trained decentrally on a set of data chunks, so that sensitive data does not leave data providers, and the computing power can be separated into nodes.\n\n\n\n\nI have done some distributed HPC before and the idea struck me as very odd since not all computations can be neatly paralellized. Any computation where there are reasonable intermediate results, that can be put together at a later stage, can be done in parallel like calculating a mean value or combining stochastic distributions. Explicit timestepping methods have to be calculated sequentially!\n\n\n\n\nThere is a prominent list of problems wich are \"P-complete (https://en.wikipedia.org/wiki/P-complete)\" and can never be parallized. I would have assumed that if any learning is done where information from more than on chunk is needed in combination, then that would also fall into the category of algorithms which can not be reasonably parallelized.\n\n\n\n\nOne explanation I could see is that information from the chunks is not actually left in place, but that the decentralized algorithms merely compress the info and then the actual learning is done at the recombination stage. That would completely defy the selling point of privacy of training data!\n\n\n\n\nThe other explanation I can come up with is that these ML methods are essentially limited to calculating high level statistics about their training data. These could be collected separately and then recombined. This would make sense to me, but then we should call it high dimensional linear regression and not artificial intelligence.\n\n\n\n\nAny 'learning' that would require information from multiple chunks which are distributed seems impossible to me.\n\n\n\n\nHow does \"Federated Learning\" actually work? How can information of the training data be left confidential?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MPIchael", "profile_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "user_type": "registered"}, "created_at": "2026-02-12T11:38:00+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "F4054CE7-4D32-4BF3-9451-F79096A1E0EF", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/F4054CE7-4D32-4BF3-9451-F79096A1E0EF/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-02-13T00:47:30+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "1EC62651-6157-48CF-9911-09F9F1340AB1", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://scicomp.stackexchange.com/revisions/1EC62651-6157-48CF-9911-09F9F1340AB1/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45366/is-federated-learning-a-computationaly-sound-idea", "split": "test", "split_group": "1c83d94409976ab407c4c0691435e4f90d777304123956cbb24b2cf869fae846", "tags": ["machine-learning"], "thread_id": "scicomp:45366", "title": "Is \"Federated Learning\" a computationaly sound idea?"}} {"citation_context": " global aggregate results still have the same statistical average as what is desired.\nThis section (https://en.wikipedia.org/wiki/Differential_privacy#Randomized_response) on the differential privacy wiki is a succinct example.\n\n\n\n\nSo it would appear that information in", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Differential_privacy#Randomized_response", "kind": "external_url", "post_id": 45367, "post_url": "https://scicomp.stackexchange.com/a/45367", "product": "citations", "record_id": "Scientific-Citation-Graph:385437068487215a00ab69ab", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

Disclaimer, I'm not an expert in this, I'm just repeating things I've heard from CS colleagues.\nThere are two parts to your question.\nFirst, is it feasible to distribute ML model training among many distant compute nodes that might have high communication latency?\nI don't know enough to answer this.

\n

Second, if you want to train a model on private data, can you do that in a way that does not leak private data?\nThere is a field of research that aims to answer this question called differential privacy.\nThe nightmare scenario is that a group of large hospital systems train a ML model on patient data but some bad actor is able to execute a reconstruction attack that reveals that you, MPIchael, are not a human but rather a large bird.\nDifferential privacy aims to prevent such attacks through intentionally injecting noise into the data such that information about any individual is untrustworthy despite the fact that global aggregate results still have the same statistical average as what is desired.\nThis section on the differential privacy wiki is a succinct example.

\n

So it would appear that information in the training data can in fact remain confidential; the mechanism is the intentional injection of noise; and there is a rigorous mathematical theory describing how much noise you need to inject given the number of samples.

\n

Now, the counter-argument.\nThe field of ML has a lot of hype.\nA lot of people have a financial interest in maintaining this hype.\nPart of that hype is that it will revolutionize healthcare.\nA reasonable person could ask how we can train ML models to solve problems in healthcare when all that data falls under HIPAA.\nIt suits the interests of people with lots of money to be able to say that differential privacy is a theoretically sound answer to this objection.\nIt's possible that (1) there are exploitable flaws in the theory of differential privacy itself, or (2) there are flaws in the practical application of this theory, such that it doesn't provide the privacy protection that the theory claims.\nThe first feels far-fetched to me and I don't know enough to have a hunch about the second.\nBut it's also important to acknowledge where there are vested interests.\nTo make an analogy, there is a mathematical theory of public-key cryptography.\nThis theory is a necessary component of practical cybersecurity, but it is far from sufficient: I can transmit password hashes using a cryptographically-secure hash function, but if a user chooses "password" as his password, then a malicious actor can guess that.

\n", "answer_id": 45367, "answer_text": "Disclaimer, I'm not an expert in this, I'm just repeating things I've heard from CS colleagues.\nThere are two parts to your question.\nFirst, is it feasible to distribute ML model training among many distant compute nodes that might have high communication latency?\nI don't know enough to answer this.\n\n\n\n\nSecond, if you want to train a model on private data, can you do that in a way that does not leak private data?\nThere is a field of research that aims to answer this question called differential privacy (https://en.wikipedia.org/wiki/Differential_privacy).\nThe nightmare scenario is that a group of large hospital systems train a ML model on patient data but some bad actor is able to execute a reconstruction attack (https://en.wikipedia.org/wiki/Reconstruction_attack) that reveals that you, MPIchael, are not a human but rather a large bird.\nDifferential privacy aims to prevent such attacks through intentionally injecting noise into the data such that information about any individual is untrustworthy despite the fact that global aggregate results still have the same statistical average as what is desired.\nThis section (https://en.wikipedia.org/wiki/Differential_privacy#Randomized_response) on the differential privacy wiki is a succinct example.\n\n\n\n\nSo it would appear that information in the training data can in fact remain confidential; the mechanism is the intentional injection of noise; and there is a rigorous mathematical theory describing how much noise you need to inject given the number of samples.\n\n\n\n\nNow, the counter-argument.\nThe field of ML has a lot of hype.\nA lot of people have a financial interest in maintaining this hype.\nPart of that hype is that it will revolutionize healthcare.\nA reasonable person could ask how we can train ML models to solve problems in healthcare when all that data falls under HIPAA.\nIt suits the interests of people with lots of money to be able to say that differential privacy is a theoretically sound answer to this objection.\nIt's possible that (1) there are exploitable flaws in the theory of differential privacy itself, or (2) there are flaws in the practical application of this theory, such that it doesn't provide the privacy protection that the theory claims.\nThe first feels far-fetched to me and I don't know enough to have a hunch about the second.\nBut it's also important to acknowledge where there are vested interests.\nTo make an analogy, there is a mathematical theory of public-key cryptography.\nThis theory is a necessary component of practical cybersecurity, but it is far from sufficient: I can transmit password hashes using a cryptographically-secure hash function, but if a user chooses \"password\" as his password, then a malicious actor can guess that.", "answer_url": "https://scicomp.stackexchange.com/a/45367", "author": "Daniel Shapero", "author_url": "https://scicomp.stackexchange.com/users/3481/daniel-shapero", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-02-12T18:36:02+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45366, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Daniel Shapero", "profile_url": "https://scicomp.stackexchange.com/users/3481/daniel-shapero", "user_type": "registered"}, "created_at": "2026-02-12T18:36:02+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "E77DB701-1B32-4706-A801-DAF6D024D5E4", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/E77DB701-1B32-4706-A801-DAF6D024D5E4/view-source"}], "score": 4, "updated_at": "2026-02-12T18:36:02+00:00"}, {"answer_html": "

Many machine learning algorithms, under the hood, try to determine some internal parameters of a class of functions (say, the weights and biases of a neural network) by minimizing an objective function that is a sum over the training set. Let's say that the neural network or whatever other approach you want to use corresponds to an operator $F(x; \\cdot)$ that maps an input $a$ to an output $b=F(x;a)$ where the vector $x$ corresponds to the internal parameters. The machine learning part is to determine the best internal parameters $x$ for given input/output data sets.

\n

If you have training inputs $a_i$ and corresponding correct answers $b_i$, then a typical approach is to minimize the objective function\n$$\n f(x) = \\frac 12 \\sum_i \\left( b_i - F(x;a_i) \\right)^2.\n$$\nIf you use the usual steepest descent algorithm, you will need to compute\n$$\n \\nabla_x f(x) = -\\sum_i \\left( b_i - F(x;a_i) \\right) \\nabla_x F(x;a_i).\n$$\nThis is computable in a perfectly distributed manner if a central processor sends the current $x$ to other machines who, given their own knowledge of $a_i,b_i$ can compute the gradient contribution for data point $i$ without ever sending $a_i$ or $b_i$ to another process -- preserving the privacy of the data from the rest of the world, including the process that then updates the current parameters $x$ through the gradient $\\nabla f$.

\n", "answer_id": 45374, "answer_text": "Many machine learning algorithms, under the hood, try to determine some internal parameters of a class of functions (say, the weights and biases of a neural network) by minimizing an objective function that is a sum over the training set. Let's say that the neural network or whatever other approach you want to use corresponds to an operator $F(x; \\cdot)$ that maps an input $a$ to an output $b=F(x;a)$ where the vector $x$ corresponds to the internal parameters. The machine learning part is to determine the best internal parameters $x$ for given input/output data sets.\n\n\n\n\nIf you have training inputs $a_i$ and corresponding correct answers $b_i$, then a typical approach is to minimize the objective function\n$$\n f(x) = \\frac 12 \\sum_i \\left( b_i - F(x;a_i) \\right)^2.\n$$\nIf you use the usual steepest descent algorithm, you will need to compute\n$$\n \\nabla_x f(x) = -\\sum_i \\left( b_i - F(x;a_i) \\right) \\nabla_x F(x;a_i).\n$$\nThis is computable in a perfectly distributed manner if a central processor sends the current $x$ to other machines who, given their own knowledge of $a_i,b_i$ can compute the gradient contribution for data point $i$ without ever sending $a_i$ or $b_i$ to another process -- preserving the privacy of the data from the rest of the world, including the process that then updates the current parameters $x$ through the gradient $\\nabla f$.", "answer_url": "https://scicomp.stackexchange.com/a/45374", "author": "Wolfgang Bangerth", "author_url": "https://scicomp.stackexchange.com/users/393/wolfgang-bangerth", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-02-14T05:37:48+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; 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mechanical HTML-to-text; no LLM rewriting"}, "question_author": "MPIchael", "question_author_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "question_author_user_type": "registered", "question_created_at": "2026-02-12T11:38:00+00:00", "question_html": "

I came into contact with projects pushing some "federated learning" approaches for training AI models. The idea behind federated learning is that machine learning algorithms can be trained decentrally on a set of data chunks, so that sensitive data does not leave data providers, and the computing power can be separated into nodes.

\n

I have done some distributed HPC before and the idea struck me as very odd since not all computations can be neatly paralellized. Any computation where there are reasonable intermediate results, that can be put together at a later stage, can be done in parallel like calculating a mean value or combining stochastic distributions. Explicit timestepping methods have to be calculated sequentially!

\n

There is a prominent list of problems wich are "P-complete" and can never be parallized. I would have assumed that if any learning is done where information from more than on chunk is needed in combination, then that would also fall into the category of algorithms which can not be reasonably parallelized.

\n

One explanation I could see is that information from the chunks is not actually left in place, but that the decentralized algorithms merely compress the info and then the actual learning is done at the recombination stage. That would completely defy the selling point of privacy of training data!

\n

The other explanation I can come up with is that these ML methods are essentially limited to calculating high level statistics about their training data. These could be collected separately and then recombined. This would make sense to me, but then we should call it high dimensional linear regression and not artificial intelligence.

\n

Any 'learning' that would require information from multiple chunks which are distributed seems impossible to me.

\n

How does "Federated Learning" actually work? How can information of the training data be left confidential?

\n", "question_id": 45366, "question_license": "CC BY-SA 4.0", "question_score": 3, "question_text": "I came into contact with projects pushing some \"federated learning\" approaches for training AI models. The idea behind federated learning is that machine learning algorithms can be trained decentrally on a set of data chunks, so that sensitive data does not leave data providers, and the computing power can be separated into nodes.\n\n\n\n\nI have done some distributed HPC before and the idea struck me as very odd since not all computations can be neatly paralellized. Any computation where there are reasonable intermediate results, that can be put together at a later stage, can be done in parallel like calculating a mean value or combining stochastic distributions. Explicit timestepping methods have to be calculated sequentially!\n\n\n\n\nThere is a prominent list of problems wich are \"P-complete (https://en.wikipedia.org/wiki/P-complete)\" and can never be parallized. I would have assumed that if any learning is done where information from more than on chunk is needed in combination, then that would also fall into the category of algorithms which can not be reasonably parallelized.\n\n\n\n\nOne explanation I could see is that information from the chunks is not actually left in place, but that the decentralized algorithms merely compress the info and then the actual learning is done at the recombination stage. That would completely defy the selling point of privacy of training data!\n\n\n\n\nThe other explanation I can come up with is that these ML methods are essentially limited to calculating high level statistics about their training data. These could be collected separately and then recombined. This would make sense to me, but then we should call it high dimensional linear regression and not artificial intelligence.\n\n\n\n\nAny 'learning' that would require information from multiple chunks which are distributed seems impossible to me.\n\n\n\n\nHow does \"Federated Learning\" actually work? How can information of the training data be left confidential?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MPIchael", "profile_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "user_type": "registered"}, "created_at": "2026-02-12T11:38:00+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "F4054CE7-4D32-4BF3-9451-F79096A1E0EF", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/F4054CE7-4D32-4BF3-9451-F79096A1E0EF/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-02-13T00:47:30+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "1EC62651-6157-48CF-9911-09F9F1340AB1", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://scicomp.stackexchange.com/revisions/1EC62651-6157-48CF-9911-09F9F1340AB1/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45366/is-federated-learning-a-computationaly-sound-idea", "split": "test", "split_group": "1c83d94409976ab407c4c0691435e4f90d777304123956cbb24b2cf869fae846", "tags": ["machine-learning"], "thread_id": "scicomp:45366", "title": "Is \"Federated Learning\" a computationaly sound idea?"}} {"citation_context": "ems train a ML model on patient data but some bad actor is able to execute a reconstruction attack (https://en.wikipedia.org/wiki/Reconstruction_attack) that reveals that you, MPIchael, are not a human but rather a large bird.\nDifferential privacy aim", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Reconstruction_attack", "kind": "external_url", "post_id": 45367, "post_url": "https://scicomp.stackexchange.com/a/45367", "product": "citations", "record_id": "Scientific-Citation-Graph:87afa405ac40961bba41acc3", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

Disclaimer, I'm not an expert in this, I'm just repeating things I've heard from CS colleagues.\nThere are two parts to your question.\nFirst, is it feasible to distribute ML model training among many distant compute nodes that might have high communication latency?\nI don't know enough to answer this.

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Second, if you want to train a model on private data, can you do that in a way that does not leak private data?\nThere is a field of research that aims to answer this question called differential privacy.\nThe nightmare scenario is that a group of large hospital systems train a ML model on patient data but some bad actor is able to execute a reconstruction attack that reveals that you, MPIchael, are not a human but rather a large bird.\nDifferential privacy aims to prevent such attacks through intentionally injecting noise into the data such that information about any individual is untrustworthy despite the fact that global aggregate results still have the same statistical average as what is desired.\nThis section on the differential privacy wiki is a succinct example.

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So it would appear that information in the training data can in fact remain confidential; the mechanism is the intentional injection of noise; and there is a rigorous mathematical theory describing how much noise you need to inject given the number of samples.

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Now, the counter-argument.\nThe field of ML has a lot of hype.\nA lot of people have a financial interest in maintaining this hype.\nPart of that hype is that it will revolutionize healthcare.\nA reasonable person could ask how we can train ML models to solve problems in healthcare when all that data falls under HIPAA.\nIt suits the interests of people with lots of money to be able to say that differential privacy is a theoretically sound answer to this objection.\nIt's possible that (1) there are exploitable flaws in the theory of differential privacy itself, or (2) there are flaws in the practical application of this theory, such that it doesn't provide the privacy protection that the theory claims.\nThe first feels far-fetched to me and I don't know enough to have a hunch about the second.\nBut it's also important to acknowledge where there are vested interests.\nTo make an analogy, there is a mathematical theory of public-key cryptography.\nThis theory is a necessary component of practical cybersecurity, but it is far from sufficient: I can transmit password hashes using a cryptographically-secure hash function, but if a user chooses "password" as his password, then a malicious actor can guess that.

\n", "answer_id": 45367, "answer_text": "Disclaimer, I'm not an expert in this, I'm just repeating things I've heard from CS colleagues.\nThere are two parts to your question.\nFirst, is it feasible to distribute ML model training among many distant compute nodes that might have high communication latency?\nI don't know enough to answer this.\n\n\n\n\nSecond, if you want to train a model on private data, can you do that in a way that does not leak private data?\nThere is a field of research that aims to answer this question called differential privacy (https://en.wikipedia.org/wiki/Differential_privacy).\nThe nightmare scenario is that a group of large hospital systems train a ML model on patient data but some bad actor is able to execute a reconstruction attack (https://en.wikipedia.org/wiki/Reconstruction_attack) that reveals that you, MPIchael, are not a human but rather a large bird.\nDifferential privacy aims to prevent such attacks through intentionally injecting noise into the data such that information about any individual is untrustworthy despite the fact that global aggregate results still have the same statistical average as what is desired.\nThis section (https://en.wikipedia.org/wiki/Differential_privacy#Randomized_response) on the differential privacy wiki is a succinct example.\n\n\n\n\nSo it would appear that information in the training data can in fact remain confidential; the mechanism is the intentional injection of noise; and there is a rigorous mathematical theory describing how much noise you need to inject given the number of samples.\n\n\n\n\nNow, the counter-argument.\nThe field of ML has a lot of hype.\nA lot of people have a financial interest in maintaining this hype.\nPart of that hype is that it will revolutionize healthcare.\nA reasonable person could ask how we can train ML models to solve problems in healthcare when all that data falls under HIPAA.\nIt suits the interests of people with lots of money to be able to say that differential privacy is a theoretically sound answer to this objection.\nIt's possible that (1) there are exploitable flaws in the theory of differential privacy itself, or (2) there are flaws in the practical application of this theory, such that it doesn't provide the privacy protection that the theory claims.\nThe first feels far-fetched to me and I don't know enough to have a hunch about the second.\nBut it's also important to acknowledge where there are vested interests.\nTo make an analogy, there is a mathematical theory of public-key cryptography.\nThis theory is a necessary component of practical cybersecurity, but it is far from sufficient: I can transmit password hashes using a cryptographically-secure hash function, but if a user chooses \"password\" as his password, then a malicious actor can guess that.", "answer_url": "https://scicomp.stackexchange.com/a/45367", "author": "Daniel Shapero", "author_url": "https://scicomp.stackexchange.com/users/3481/daniel-shapero", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-02-12T18:36:02+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45366, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Daniel Shapero", "profile_url": "https://scicomp.stackexchange.com/users/3481/daniel-shapero", "user_type": "registered"}, "created_at": "2026-02-12T18:36:02+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "E77DB701-1B32-4706-A801-DAF6D024D5E4", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/E77DB701-1B32-4706-A801-DAF6D024D5E4/view-source"}], "score": 4, "updated_at": "2026-02-12T18:36:02+00:00"}, {"answer_html": "

Many machine learning algorithms, under the hood, try to determine some internal parameters of a class of functions (say, the weights and biases of a neural network) by minimizing an objective function that is a sum over the training set. Let's say that the neural network or whatever other approach you want to use corresponds to an operator $F(x; \\cdot)$ that maps an input $a$ to an output $b=F(x;a)$ where the vector $x$ corresponds to the internal parameters. The machine learning part is to determine the best internal parameters $x$ for given input/output data sets.

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If you have training inputs $a_i$ and corresponding correct answers $b_i$, then a typical approach is to minimize the objective function\n$$\n f(x) = \\frac 12 \\sum_i \\left( b_i - F(x;a_i) \\right)^2.\n$$\nIf you use the usual steepest descent algorithm, you will need to compute\n$$\n \\nabla_x f(x) = -\\sum_i \\left( b_i - F(x;a_i) \\right) \\nabla_x F(x;a_i).\n$$\nThis is computable in a perfectly distributed manner if a central processor sends the current $x$ to other machines who, given their own knowledge of $a_i,b_i$ can compute the gradient contribution for data point $i$ without ever sending $a_i$ or $b_i$ to another process -- preserving the privacy of the data from the rest of the world, including the process that then updates the current parameters $x$ through the gradient $\\nabla f$.

\n", "answer_id": 45374, "answer_text": "Many machine learning algorithms, under the hood, try to determine some internal parameters of a class of functions (say, the weights and biases of a neural network) by minimizing an objective function that is a sum over the training set. Let's say that the neural network or whatever other approach you want to use corresponds to an operator $F(x; \\cdot)$ that maps an input $a$ to an output $b=F(x;a)$ where the vector $x$ corresponds to the internal parameters. The machine learning part is to determine the best internal parameters $x$ for given input/output data sets.\n\n\n\n\nIf you have training inputs $a_i$ and corresponding correct answers $b_i$, then a typical approach is to minimize the objective function\n$$\n f(x) = \\frac 12 \\sum_i \\left( b_i - F(x;a_i) \\right)^2.\n$$\nIf you use the usual steepest descent algorithm, you will need to compute\n$$\n \\nabla_x f(x) = -\\sum_i \\left( b_i - F(x;a_i) \\right) \\nabla_x F(x;a_i).\n$$\nThis is computable in a perfectly distributed manner if a central processor sends the current $x$ to other machines who, given their own knowledge of $a_i,b_i$ can compute the gradient contribution for data point $i$ without ever sending $a_i$ or $b_i$ to another process -- preserving the privacy of the data from the rest of the world, including the process that then updates the current parameters $x$ through the gradient $\\nabla f$.", "answer_url": "https://scicomp.stackexchange.com/a/45374", "author": "Wolfgang Bangerth", "author_url": "https://scicomp.stackexchange.com/users/393/wolfgang-bangerth", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-02-14T05:37:48+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:47.033952+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/cb6e5f564c84a92c4e121c0637c99292018f8935652e423630f2001099a2410f_1790825327386675300_0.json", "raw_sha256": "1a957289f56621bebd21cb45dd99baaedb2c3bc11cb28d700558e4bbcaa19695", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; 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mechanical HTML-to-text; no LLM rewriting"}, "question_author": "MPIchael", "question_author_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "question_author_user_type": "registered", "question_created_at": "2026-02-12T11:38:00+00:00", "question_html": "

I came into contact with projects pushing some "federated learning" approaches for training AI models. The idea behind federated learning is that machine learning algorithms can be trained decentrally on a set of data chunks, so that sensitive data does not leave data providers, and the computing power can be separated into nodes.

\n

I have done some distributed HPC before and the idea struck me as very odd since not all computations can be neatly paralellized. Any computation where there are reasonable intermediate results, that can be put together at a later stage, can be done in parallel like calculating a mean value or combining stochastic distributions. Explicit timestepping methods have to be calculated sequentially!

\n

There is a prominent list of problems wich are "P-complete" and can never be parallized. I would have assumed that if any learning is done where information from more than on chunk is needed in combination, then that would also fall into the category of algorithms which can not be reasonably parallelized.

\n

One explanation I could see is that information from the chunks is not actually left in place, but that the decentralized algorithms merely compress the info and then the actual learning is done at the recombination stage. That would completely defy the selling point of privacy of training data!

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The other explanation I can come up with is that these ML methods are essentially limited to calculating high level statistics about their training data. These could be collected separately and then recombined. This would make sense to me, but then we should call it high dimensional linear regression and not artificial intelligence.

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Any 'learning' that would require information from multiple chunks which are distributed seems impossible to me.

\n

How does "Federated Learning" actually work? How can information of the training data be left confidential?

\n", "question_id": 45366, "question_license": "CC BY-SA 4.0", "question_score": 3, "question_text": "I came into contact with projects pushing some \"federated learning\" approaches for training AI models. The idea behind federated learning is that machine learning algorithms can be trained decentrally on a set of data chunks, so that sensitive data does not leave data providers, and the computing power can be separated into nodes.\n\n\n\n\nI have done some distributed HPC before and the idea struck me as very odd since not all computations can be neatly paralellized. Any computation where there are reasonable intermediate results, that can be put together at a later stage, can be done in parallel like calculating a mean value or combining stochastic distributions. Explicit timestepping methods have to be calculated sequentially!\n\n\n\n\nThere is a prominent list of problems wich are \"P-complete (https://en.wikipedia.org/wiki/P-complete)\" and can never be parallized. I would have assumed that if any learning is done where information from more than on chunk is needed in combination, then that would also fall into the category of algorithms which can not be reasonably parallelized.\n\n\n\n\nOne explanation I could see is that information from the chunks is not actually left in place, but that the decentralized algorithms merely compress the info and then the actual learning is done at the recombination stage. That would completely defy the selling point of privacy of training data!\n\n\n\n\nThe other explanation I can come up with is that these ML methods are essentially limited to calculating high level statistics about their training data. These could be collected separately and then recombined. This would make sense to me, but then we should call it high dimensional linear regression and not artificial intelligence.\n\n\n\n\nAny 'learning' that would require information from multiple chunks which are distributed seems impossible to me.\n\n\n\n\nHow does \"Federated Learning\" actually work? How can information of the training data be left confidential?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MPIchael", "profile_url": "https://scicomp.stackexchange.com/users/28636/mpichael", "user_type": "registered"}, "created_at": "2026-02-12T11:38:00+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "F4054CE7-4D32-4BF3-9451-F79096A1E0EF", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/F4054CE7-4D32-4BF3-9451-F79096A1E0EF/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-02-13T00:47:30+00:00", "raw_file": "raw/codex_api_v1/d49b4ef7856602e9d6b1a79d56b143976504b0637af4b266f03f2b60112c6c15_1790825353984908500_0.json", "raw_sha256": "4ebc32b188652be208cbfb32007d2c8fcbe5419e5ab336ca46a3e9eb5ef04d0e", "revision_guid": "1EC62651-6157-48CF-9911-09F9F1340AB1", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://scicomp.stackexchange.com/revisions/1EC62651-6157-48CF-9911-09F9F1340AB1/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45366/is-federated-learning-a-computationaly-sound-idea", "split": "test", "split_group": "1c83d94409976ab407c4c0691435e4f90d777304123956cbb24b2cf869fae846", "tags": ["machine-learning"], "thread_id": "scicomp:45366", "title": "Is \"Federated Learning\" a computationaly sound idea?"}} {"citation_context": "way to apply such a boundary condition to my domain?\n\n\n\n\n[image: distribution of strain yy; source: https://i.sstatic.net/IYN9P6iW.png] (https://i.sstatic.net/IYN9P6iW.png)\n\n\n\n\nIn the uploaded figure, the plot has to be completely lig", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://i.sstatic.net/IYN9P6iW.png", "kind": "external_url", "post_id": 45507, "post_url": "https://scicomp.stackexchange.com/questions/45507/prescribed-displacement-in-fem-extension-in-2d-square", "product": "citations", "record_id": "Scientific-Citation-Graph:f07b37e6dadefb23dd436e87", "split": "test", "thread": {"accepted_answer_id": 45509, "answers": [{"answer_html": "

Remove the $u_y=0$ BC from the left and right edges. Then apply a\n$u_y=0$ BC only to a single FEM node in the model-- say at the lower left corner.\nApplying the $u_y=0$ BC at a single node insures that you do not over-constrain the\nmodel in an undesirable way.

\n", "answer_id": 45509, "answer_text": "Remove the $u_y=0$ BC from the left and right edges. Then apply a\n$u_y=0$ BC only to a single FEM node in the model-- say at the lower left corner.\nApplying the $u_y=0$ BC at a single node insures that you do not over-constrain the\nmodel in an undesirable way.", "answer_url": "https://scicomp.stackexchange.com/a/45509", "author": "Bill Greene", "author_url": "https://scicomp.stackexchange.com/users/3441/bill-greene", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-08-03T09:42:06+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:49.393498+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/bdd73bdc9d483cfaf7d50f2075e853261f39886330cd6d24a17f7b3b2fb731e5_1790825329894890800_0.json", "raw_sha256": "dfbb76df9ebacfee7e902db64890f154a777bd3049356aee472798c591424d79", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/45545;45541;45538;45533;45532;45530;45523;45513;45510;45507;45499;45493;45488;45487;45479;45474;45472;45463;45461;45447;45444;45436;45428;45425;45424;45423;45422;45416;45414;45410;45404;45401;45396;45391;45389;45387;45380;45377;45376;45375;45369;45366;45365;45363;45362;45359;45350;45347;45344;45336;45334;45331;45326;45322;45316;45313;45311;45309;45305;45302;45300;45291;45289;45285;45276;45269;45263;45262;45261;45253;45247;45246;45238;45236;45230;45229;45208;45201;45200;45185;45183;45171;45167;45165;45158;45154;45146;45141;45139;45134;45129;45127;45122;45114;45112;45108;45105;45100;45098;45096/answers?filter=withbody&order=asc&page=2&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 45507, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Bill Greene", "profile_url": "https://scicomp.stackexchange.com/users/3441/bill-greene", "user_type": "registered"}, "created_at": "2026-08-03T09:42:06+00:00", "raw_file": "raw/codex_api_v1/388d30597d4ce2c68c96b784f7bf92098fad8c44850c54687d3a3028cce83504_1790825358707940600_0.json", "raw_sha256": "798328140b22ca830f996dc29957e2ed66bad007670d3eb6cfce6a5d1c2b82b7", "revision_guid": "E0463B5C-BB55-419B-8C02-79D20AD61D61", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/E0463B5C-BB55-419B-8C02-79D20AD61D61/view-source"}], "score": 4, "updated_at": "2026-08-03T09:42:06+00:00"}], "domain": "computational_science", "external_links": ["https://i.sstatic.net/IYN9P6iW.png"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:28:44.584971+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/272744bcc95b58699f7df6e6979b288bb8b00a80ab9c7982dbe170a6d0b63584_1790825325025901700_0.json", "raw_sha256": "27a81850a40920682c29ada76a2b55e80340a5c82764a3e9dde8a9c2ba23db4e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=scicomp&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Rasa R. Behboud", "question_author_url": "https://scicomp.stackexchange.com/users/57047/rasa-r-behboud", "question_author_user_type": "registered", "question_created_at": "2026-08-02T12:20:11+00:00", "question_html": "

Consider a solid 2D square that is under extension by prescribed displacement from the left and right edges, and the other edges are traction-free. How can we assign the boundary condition in this case?

\n

If we fix the nodes of the left and right edges in the $y$ direction and apply the prescribed displacement in $+x$ and $-x$ directions, we would see the extension throughout the domain. Although we see that with the constraint we chose (fix the y direction of the left and right edges' nodes), we have 0 u_y displacements in the left and right edges in FEM, when we solve this problem analytically, we see that the y displacement of those nodes should be nonzero. In other words, near the edges we have a noticeable difference between the analytical solution and FEM solution. Hence, I want to know what is the best way to apply such a boundary condition to my domain?

\n

\"distribution

\n

In the uploaded figure, the plot has to be completely light blue ($-0.06$), which is a constant amount ($-0.2 \\nu$), but it is not. There are red, yellow, and even dark blue regions, and it does not seem quite correct.

\n", "question_id": 45507, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "Consider a solid 2D square that is under extension by prescribed displacement from the left and right edges, and the other edges are traction-free. How can we assign the boundary condition in this case?\n\n\n\n\nIf we fix the nodes of the left and right edges in the $y$ direction and apply the prescribed displacement in $+x$ and $-x$ directions, we would see the extension throughout the domain. Although we see that with the constraint we chose (fix the y direction of the left and right edges' nodes), we have 0 u_y displacements in the left and right edges in FEM, when we solve this problem analytically, we see that the y displacement of those nodes should be nonzero. In other words, near the edges we have a noticeable difference between the analytical solution and FEM solution. Hence, I want to know what is the best way to apply such a boundary condition to my domain?\n\n\n\n\n[image: distribution of strain yy; source: https://i.sstatic.net/IYN9P6iW.png] (https://i.sstatic.net/IYN9P6iW.png)\n\n\n\n\nIn the uploaded figure, the plot has to be completely light blue ($-0.06$), which is a constant amount ($-0.2 \\nu$), but it is not. There are red, yellow, and even dark blue regions, and it does not seem quite correct.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Rasa R. Behboud", "profile_url": "https://scicomp.stackexchange.com/users/57047/rasa-r-behboud", "user_type": "registered"}, "created_at": "2026-08-02T12:20:11+00:00", "raw_file": "raw/codex_api_v1/388d30597d4ce2c68c96b784f7bf92098fad8c44850c54687d3a3028cce83504_1790825358707940600_0.json", "raw_sha256": "798328140b22ca830f996dc29957e2ed66bad007670d3eb6cfce6a5d1c2b82b7", "revision_guid": "3EAF4106-58C0-418C-BDE3-63E226B2373A", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/3EAF4106-58C0-418C-BDE3-63E226B2373A/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Rasa R. Behboud", "profile_url": "https://scicomp.stackexchange.com/users/57047/rasa-r-behboud", "user_type": "registered"}, "created_at": "2026-08-02T12:40:21+00:00", "raw_file": "raw/codex_api_v1/388d30597d4ce2c68c96b784f7bf92098fad8c44850c54687d3a3028cce83504_1790825358707940600_0.json", "raw_sha256": "798328140b22ca830f996dc29957e2ed66bad007670d3eb6cfce6a5d1c2b82b7", "revision_guid": "8CFA8354-0537-473E-8573-F2CDF94AF84C", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/8CFA8354-0537-473E-8573-F2CDF94AF84C/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "nicoguaro", "profile_url": "https://scicomp.stackexchange.com/users/9667/nicoguaro", "user_type": "moderator"}, "created_at": "2026-08-03T12:55:52+00:00", "raw_file": "raw/codex_api_v1/388d30597d4ce2c68c96b784f7bf92098fad8c44850c54687d3a3028cce83504_1790825358707940600_0.json", "raw_sha256": "798328140b22ca830f996dc29957e2ed66bad007670d3eb6cfce6a5d1c2b82b7", "revision_guid": "5B4C03B7-BF21-4BF2-91F8-D0737769344E", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://scicomp.stackexchange.com/revisions/5B4C03B7-BF21-4BF2-91F8-D0737769344E/view-source"}], "source_site": "scicomp", "source_url": "https://scicomp.stackexchange.com/questions/45507/prescribed-displacement-in-fem-extension-in-2d-square", "split": "test", "split_group": "0579c63f296f6a62a9b87cfffc528ab5333116e8ad3fd9212f5c71c4161953f3", "tags": ["finite-element", "matlab", "boundary-conditions", "elasticity"], "thread_id": "scicomp:45507", "title": "Prescribed Displacement in FEM - Extension in 2D square"}} {"citation_context": " 50. This, at least, is what European health agencies tell us.\n\n\n\n\nNative to Europe are phototypes (https://en.wikipedia.org/wiki/Fitzpatrick_scale) I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution sup", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Fitzpatrick_scale", "kind": "external_url", "post_id": 115170, "post_url": "https://biology.stackexchange.com/questions/115170/why-did-evolution-fail-to-protect-humans-against-sun", "product": "citations", "record_id": "Scientific-Citation-Graph:213fdc39d3451e56c2e60da3", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.

\n
\n

Where is the error in my thinking?

\n
\n

The error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.

\n

Evolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable "deficiencies" in humans that make us "imperfectly evolved".

\n

That we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any "reason" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable. If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)

\n

If we're "good enough" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.

\n

Also, somewhat aside to your question are the benefits of UV light to humans. We know that UVB allows us to synthesize Vitamin D, which is critical for survival. There are other possible benefits to UV light as well. It might well happen that we'll discover more concrete benefits.

\n

The question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.

\n", "answer_id": 115175, "answer_text": "I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.\n\n\n\n\n\n\n\nWhere is the error in my thinking?\n\n\n\n\n\n\n\nThe error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.\n\n\n\n\nEvolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable \"deficiencies\" in humans that make us \"imperfectly evolved\".\n\n\n\n\nThat we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any \"reason\" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable (https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/). If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)\n\n\n\n\nIf we're \"good enough\" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.\n\n\n\n\nAlso, somewhat aside to your question are the benefits of UV light to humans (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). We know that UVB allows us to synthesize Vitamin D, which is critical for survival. (https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d) There are other possible benefits to UV light as well (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). It might well happen that we'll discover more concrete benefits.\n\n\n\n\nThe question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.", "answer_url": "https://biology.stackexchange.com/a/115175", "author": "anongoodnurse", "author_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:19:48+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:19:48+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B27F09D5-F235-448E-AFF2-AD09B10346FA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B27F09D5-F235-448E-AFF2-AD09B10346FA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:27:18+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "D6BC325F-2058-42EC-A622-79DDDBAE9D28", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D6BC325F-2058-42EC-A622-79DDDBAE9D28/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:11:51+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "70F33937-681F-4BBB-90ED-DB3715ED6BF6", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/70F33937-681F-4BBB-90ED-DB3715ED6BF6/view-source"}], "score": 25, "updated_at": "2024-08-13T19:27:18+00:00"}, {"answer_html": "

Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is "good enough" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as "selective pressure" refers to selection for reproduction specifically.

\n

https://seer.cancer.gov/statfacts/html/melan.html

\n", "answer_id": 115176, "answer_text": "Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is \"good enough\" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as \"selective pressure\" refers to selection for reproduction specifically.\n\n\n\n\nhttps://seer.cancer.gov/statfacts/html/melan.html (https://seer.cancer.gov/statfacts/html/melan.html)", "answer_url": "https://biology.stackexchange.com/a/115176", "author": "Nuclear Hoagie", "author_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:41:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Nuclear Hoagie", "profile_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "user_type": "registered"}, "created_at": "2024-08-13T19:41:14+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E020D650-7DF7-42B4-A813-C07287A63A06", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E020D650-7DF7-42B4-A813-C07287A63A06/view-source"}], "score": 53, "updated_at": "2024-08-13T19:41:14+00:00"}, {"answer_html": "

Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.

\n
    \n

  • Melanin Production:

    \n

    Melanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.

    \n
    • \n

  • Epidermal Thickening:

    \n

    Another defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.

    \n
    • \n

  • DNA Repair Mechanisms:

    \n

    The human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.

    \n
    • \n

  • Inflammatory Response:

    \n

    The acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.

    \n
    • \n
\n", "answer_id": 115181, "answer_text": "Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.\n\n\n\n\n\n\n\nMelanin Production:\n\n\n\n\nMelanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.\n\n\n\n\n\n\n\n\n\nEpidermal Thickening:\n\n\n\n\nAnother defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.\n\n\n\n\n\n\n\n\n\nDNA Repair Mechanisms:\n\n\n\n\nThe human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase (https://en.wikipedia.org/wiki/Photolyase) repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.\n\n\n\n\n\n\n\n\n\nInflammatory Response:\n\n\n\n\nThe acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.", "answer_url": "https://biology.stackexchange.com/a/115181", "author": "Chris", "author_url": "https://biology.stackexchange.com/users/5144/chris", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T08:30:31+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-14T08:30:31+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "203DF798-60CE-4A5B-942C-F9066DA8BFEC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/203DF798-60CE-4A5B-942C-F9066DA8BFEC/view-source"}], "score": 12, "updated_at": "2024-08-14T08:30:31+00:00"}, {"answer_html": "

To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.

\n", "answer_id": 115184, "answer_text": "To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.", "answer_url": "https://biology.stackexchange.com/a/115184", "author": "Crazymoomin", "author_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T14:44:29+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:44:29+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "34124B84-4C54-404B-BD68-361FC0160072", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/34124B84-4C54-404B-BD68-361FC0160072/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:50:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "90C8EF4F-C093-46C8-845F-34F1CDBE3D76", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/90C8EF4F-C093-46C8-845F-34F1CDBE3D76/view-source"}], "score": 4, "updated_at": "2024-08-14T14:50:43+00:00"}, {"answer_html": "

There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia. It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.

\n

I recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...

\n", "answer_id": 115189, "answer_text": "There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia (https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/). It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.\n\n\n\n\nI recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...", "answer_url": "https://biology.stackexchange.com/a/115189", "author": "Simon Crase", "author_url": "https://biology.stackexchange.com/users/60999/simon-crase", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T06:47:00+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-15T06:47:00+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "06C3F178-4AC5-4566-87E9-1B7866F7776D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/06C3F178-4AC5-4566-87E9-1B7866F7776D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-16T00:56:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E63DE613-A666-4300-87F8-B4DFC7B8CA59", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E63DE613-A666-4300-87F8-B4DFC7B8CA59/view-source"}], "score": 5, "updated_at": "2024-08-16T00:56:43+00:00"}, {"answer_html": "

The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.

\n

Now if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.

\n

Also careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.

\n", "answer_id": 115195, "answer_text": "The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.\n\n\n\n\nNow if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.\n\n\n\n\nAlso careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.", "answer_url": "https://biology.stackexchange.com/a/115195", "author": "gnasher729", "author_url": "https://biology.stackexchange.com/users/10077/gnasher729", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T20:13:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gnasher729", "profile_url": "https://biology.stackexchange.com/users/10077/gnasher729", "user_type": "registered"}, "created_at": "2024-08-15T20:13:04+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B98FEE88-41D0-4F31-8B9A-0D171031B546", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B98FEE88-41D0-4F31-8B9A-0D171031B546/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:10:35+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "261F1C4D-1ECD-48FA-8442-CED29305E440", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/261F1C4D-1ECD-48FA-8442-CED29305E440/view-source"}], "score": 8, "updated_at": "2024-08-15T20:13:04+00:00"}, {"answer_html": "

Because cancer wasn't likely to be one's cause of death. Look at this comparison between 1900 and 2022:

\n

\"enter

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Cancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s:

\n
\n

Cancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’

\n
\n

Evolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:

\n
\n

Devil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.

\n

...

\n

In 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.

\n
\n", "answer_id": 115199, "answer_text": "Because cancer wasn't likely to be one's cause of death. Look at this comparison (https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/) between 1900 and 2022:\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/pzQsLWkf.png] (https://i.sstatic.net/pzQsLWkf.png)\n\n\n\n\nCancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/):\n\n\n\n\n\n\n\nCancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’\n\n\n\n\n\n\n\nEvolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence (https://en.wikipedia.org/wiki/Devil_facial_tumour_disease) from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:\n\n\n\n\n\n\n\nDevil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.\n\n\n\n\n...\n\n\n\n\nIn 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.", "answer_url": "https://biology.stackexchange.com/a/115199", "author": "MilkLife", "author_url": "https://biology.stackexchange.com/users/5492/milklife", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-16T23:47:16+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MilkLife", "profile_url": "https://biology.stackexchange.com/users/5492/milklife", "user_type": "registered"}, "created_at": "2024-08-16T23:47:16+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "FA30453C-1E93-40D2-9D07-DDC697CEF2EA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/FA30453C-1E93-40D2-9D07-DDC697CEF2EA/view-source"}], "score": 0, "updated_at": "2024-08-16T23:47:16+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/Devil_facial_tumour_disease", "https://en.wikipedia.org/wiki/Fitzpatrick_scale", "https://en.wikipedia.org/wiki/Photolyase", "https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/", "https://i.sstatic.net/pzQsLWkf.png", "https://seer.cancer.gov/statfacts/html/melan.html", "https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d", "https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/", "https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:05.762873+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/04ed2aa314c5d877c5d79e42620d1f80988a21de8d429a22d8c6af5280cfd6e8_0.json", "raw_sha256": "6dd355b99094bb9ba2c965ee7dd7b0e95f92a8078d3b2b85b64196fcb6cf717c", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=5&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "gaazkam", "question_author_url": "https://biology.stackexchange.com/users/15177/gaazkam", "question_author_user_type": "registered", "question_created_at": "2024-08-13T05:20:41+00:00", "question_html": "

Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.

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Especially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.

\n

Native to Europe are phototypes I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?

\n

So, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.

\n

Yet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.

\n

Where is the error in my thinking?

\n", "question_id": 115170, "question_license": "CC BY-SA 4.0", "question_score": 17, "question_text": "Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.\n\n\n\n\nEspecially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.\n\n\n\n\nNative to Europe are phototypes (https://en.wikipedia.org/wiki/Fitzpatrick_scale) I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?\n\n\n\n\nSo, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.\n\n\n\n\nYet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.\n\n\n\n\nWhere is the error in my thinking?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:20:41+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "828DB692-880A-4BBF-AD67-13CF3E06456A", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/828DB692-880A-4BBF-AD67-13CF3E06456A/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:26:09+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2024-08-14T08:31:47+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D/view-source"}, {"content_license": null, "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-15T13:36:46+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:12:55+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E7A91925-4841-42A6-89A7-24963075C01F", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/E7A91925-4841-42A6-89A7-24963075C01F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Basil Bourque", "profile_url": "https://biology.stackexchange.com/users/32521/basil-bourque", "user_type": "registered"}, "created_at": "2024-09-02T17:31:11+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "C86E2648-B494-446F-A6EC-EE52D185A1B7", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/C86E2648-B494-446F-A6EC-EE52D185A1B7/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/115170/why-did-evolution-fail-to-protect-humans-against-sun", "split": "test", "split_group": "503625bcfe466937a26431096aee38aeab3e6012cf849f4c5706c832b5d6195c", "tags": ["human-evolution", "skin", "melanin"], "thread_id": "biology:115170", "title": "Why did evolution fail to protect humans against sun?"}} {"citation_context": "/PMC3427189/). We know that UVB allows us to synthesize Vitamin D, which is critical for survival. (https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d) There are other possible benefits to UV light as well (https://www.ncbi.nlm.nih.gov/pmc/articles/P", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d", "kind": "external_url", "post_id": 115175, "post_url": "https://biology.stackexchange.com/a/115175", "product": "citations", "record_id": "Scientific-Citation-Graph:c057de1f529188b0408f1ac2", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.

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\n

Where is the error in my thinking?

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\n

The error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.

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Evolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable "deficiencies" in humans that make us "imperfectly evolved".

\n

That we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any "reason" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable. If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)

\n

If we're "good enough" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.

\n

Also, somewhat aside to your question are the benefits of UV light to humans. We know that UVB allows us to synthesize Vitamin D, which is critical for survival. There are other possible benefits to UV light as well. It might well happen that we'll discover more concrete benefits.

\n

The question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.

\n", "answer_id": 115175, "answer_text": "I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.\n\n\n\n\n\n\n\nWhere is the error in my thinking?\n\n\n\n\n\n\n\nThe error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.\n\n\n\n\nEvolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable \"deficiencies\" in humans that make us \"imperfectly evolved\".\n\n\n\n\nThat we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any \"reason\" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable (https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/). If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)\n\n\n\n\nIf we're \"good enough\" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.\n\n\n\n\nAlso, somewhat aside to your question are the benefits of UV light to humans (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). We know that UVB allows us to synthesize Vitamin D, which is critical for survival. (https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d) There are other possible benefits to UV light as well (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). It might well happen that we'll discover more concrete benefits.\n\n\n\n\nThe question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.", "answer_url": "https://biology.stackexchange.com/a/115175", "author": "anongoodnurse", "author_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:19:48+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:19:48+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B27F09D5-F235-448E-AFF2-AD09B10346FA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B27F09D5-F235-448E-AFF2-AD09B10346FA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:27:18+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "D6BC325F-2058-42EC-A622-79DDDBAE9D28", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D6BC325F-2058-42EC-A622-79DDDBAE9D28/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:11:51+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "70F33937-681F-4BBB-90ED-DB3715ED6BF6", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/70F33937-681F-4BBB-90ED-DB3715ED6BF6/view-source"}], "score": 25, "updated_at": "2024-08-13T19:27:18+00:00"}, {"answer_html": "

Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is "good enough" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as "selective pressure" refers to selection for reproduction specifically.

\n

https://seer.cancer.gov/statfacts/html/melan.html

\n", "answer_id": 115176, "answer_text": "Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is \"good enough\" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as \"selective pressure\" refers to selection for reproduction specifically.\n\n\n\n\nhttps://seer.cancer.gov/statfacts/html/melan.html (https://seer.cancer.gov/statfacts/html/melan.html)", "answer_url": "https://biology.stackexchange.com/a/115176", "author": "Nuclear Hoagie", "author_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:41:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Nuclear Hoagie", "profile_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "user_type": "registered"}, "created_at": "2024-08-13T19:41:14+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E020D650-7DF7-42B4-A813-C07287A63A06", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E020D650-7DF7-42B4-A813-C07287A63A06/view-source"}], "score": 53, "updated_at": "2024-08-13T19:41:14+00:00"}, {"answer_html": "

Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.

\n
    \n

  • Melanin Production:

    \n

    Melanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.

    \n
    • \n

  • Epidermal Thickening:

    \n

    Another defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.

    \n
    • \n

  • DNA Repair Mechanisms:

    \n

    The human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.

    \n
    • \n

  • Inflammatory Response:

    \n

    The acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.

    \n
    • \n
\n", "answer_id": 115181, "answer_text": "Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.\n\n\n\n\n\n\n\nMelanin Production:\n\n\n\n\nMelanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.\n\n\n\n\n\n\n\n\n\nEpidermal Thickening:\n\n\n\n\nAnother defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.\n\n\n\n\n\n\n\n\n\nDNA Repair Mechanisms:\n\n\n\n\nThe human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase (https://en.wikipedia.org/wiki/Photolyase) repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.\n\n\n\n\n\n\n\n\n\nInflammatory Response:\n\n\n\n\nThe acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.", "answer_url": "https://biology.stackexchange.com/a/115181", "author": "Chris", "author_url": "https://biology.stackexchange.com/users/5144/chris", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T08:30:31+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-14T08:30:31+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "203DF798-60CE-4A5B-942C-F9066DA8BFEC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/203DF798-60CE-4A5B-942C-F9066DA8BFEC/view-source"}], "score": 12, "updated_at": "2024-08-14T08:30:31+00:00"}, {"answer_html": "

To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.

\n", "answer_id": 115184, "answer_text": "To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.", "answer_url": "https://biology.stackexchange.com/a/115184", "author": "Crazymoomin", "author_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T14:44:29+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:44:29+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "34124B84-4C54-404B-BD68-361FC0160072", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/34124B84-4C54-404B-BD68-361FC0160072/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:50:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "90C8EF4F-C093-46C8-845F-34F1CDBE3D76", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/90C8EF4F-C093-46C8-845F-34F1CDBE3D76/view-source"}], "score": 4, "updated_at": "2024-08-14T14:50:43+00:00"}, {"answer_html": "

There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia. It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.

\n

I recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...

\n", "answer_id": 115189, "answer_text": "There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia (https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/). It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.\n\n\n\n\nI recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...", "answer_url": "https://biology.stackexchange.com/a/115189", "author": "Simon Crase", "author_url": "https://biology.stackexchange.com/users/60999/simon-crase", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T06:47:00+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-15T06:47:00+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "06C3F178-4AC5-4566-87E9-1B7866F7776D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/06C3F178-4AC5-4566-87E9-1B7866F7776D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-16T00:56:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E63DE613-A666-4300-87F8-B4DFC7B8CA59", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E63DE613-A666-4300-87F8-B4DFC7B8CA59/view-source"}], "score": 5, "updated_at": "2024-08-16T00:56:43+00:00"}, {"answer_html": "

The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.

\n

Now if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.

\n

Also careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.

\n", "answer_id": 115195, "answer_text": "The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.\n\n\n\n\nNow if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.\n\n\n\n\nAlso careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.", "answer_url": "https://biology.stackexchange.com/a/115195", "author": "gnasher729", "author_url": "https://biology.stackexchange.com/users/10077/gnasher729", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T20:13:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gnasher729", "profile_url": "https://biology.stackexchange.com/users/10077/gnasher729", "user_type": "registered"}, "created_at": "2024-08-15T20:13:04+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B98FEE88-41D0-4F31-8B9A-0D171031B546", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B98FEE88-41D0-4F31-8B9A-0D171031B546/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:10:35+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "261F1C4D-1ECD-48FA-8442-CED29305E440", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/261F1C4D-1ECD-48FA-8442-CED29305E440/view-source"}], "score": 8, "updated_at": "2024-08-15T20:13:04+00:00"}, {"answer_html": "

Because cancer wasn't likely to be one's cause of death. Look at this comparison between 1900 and 2022:

\n

\"enter

\n

Cancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s:

\n
\n

Cancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’

\n
\n

Evolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:

\n
\n

Devil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.

\n

...

\n

In 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.

\n
\n", "answer_id": 115199, "answer_text": "Because cancer wasn't likely to be one's cause of death. Look at this comparison (https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/) between 1900 and 2022:\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/pzQsLWkf.png] (https://i.sstatic.net/pzQsLWkf.png)\n\n\n\n\nCancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/):\n\n\n\n\n\n\n\nCancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’\n\n\n\n\n\n\n\nEvolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence (https://en.wikipedia.org/wiki/Devil_facial_tumour_disease) from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:\n\n\n\n\n\n\n\nDevil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.\n\n\n\n\n...\n\n\n\n\nIn 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.", "answer_url": "https://biology.stackexchange.com/a/115199", "author": "MilkLife", "author_url": "https://biology.stackexchange.com/users/5492/milklife", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-16T23:47:16+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MilkLife", "profile_url": "https://biology.stackexchange.com/users/5492/milklife", "user_type": "registered"}, "created_at": "2024-08-16T23:47:16+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "FA30453C-1E93-40D2-9D07-DDC697CEF2EA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/FA30453C-1E93-40D2-9D07-DDC697CEF2EA/view-source"}], "score": 0, "updated_at": "2024-08-16T23:47:16+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/Devil_facial_tumour_disease", "https://en.wikipedia.org/wiki/Fitzpatrick_scale", "https://en.wikipedia.org/wiki/Photolyase", "https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/", "https://i.sstatic.net/pzQsLWkf.png", "https://seer.cancer.gov/statfacts/html/melan.html", "https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d", "https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/", "https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:05.762873+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/04ed2aa314c5d877c5d79e42620d1f80988a21de8d429a22d8c6af5280cfd6e8_0.json", "raw_sha256": "6dd355b99094bb9ba2c965ee7dd7b0e95f92a8078d3b2b85b64196fcb6cf717c", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=5&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "gaazkam", "question_author_url": "https://biology.stackexchange.com/users/15177/gaazkam", "question_author_user_type": "registered", "question_created_at": "2024-08-13T05:20:41+00:00", "question_html": "

Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.

\n

Especially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.

\n

Native to Europe are phototypes I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?

\n

So, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.

\n

Yet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.

\n

Where is the error in my thinking?

\n", "question_id": 115170, "question_license": "CC BY-SA 4.0", "question_score": 17, "question_text": "Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.\n\n\n\n\nEspecially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.\n\n\n\n\nNative to Europe are phototypes (https://en.wikipedia.org/wiki/Fitzpatrick_scale) I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?\n\n\n\n\nSo, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.\n\n\n\n\nYet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.\n\n\n\n\nWhere is the error in my thinking?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:20:41+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "828DB692-880A-4BBF-AD67-13CF3E06456A", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/828DB692-880A-4BBF-AD67-13CF3E06456A/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:26:09+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2024-08-14T08:31:47+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D/view-source"}, {"content_license": null, "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-15T13:36:46+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:12:55+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E7A91925-4841-42A6-89A7-24963075C01F", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/E7A91925-4841-42A6-89A7-24963075C01F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Basil Bourque", "profile_url": "https://biology.stackexchange.com/users/32521/basil-bourque", "user_type": "registered"}, "created_at": "2024-09-02T17:31:11+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "C86E2648-B494-446F-A6EC-EE52D185A1B7", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/C86E2648-B494-446F-A6EC-EE52D185A1B7/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/115170/why-did-evolution-fail-to-protect-humans-against-sun", "split": "test", "split_group": "503625bcfe466937a26431096aee38aeab3e6012cf849f4c5706c832b5d6195c", "tags": ["human-evolution", "skin", "melanin"], "thread_id": "biology:115170", "title": "Why did evolution fail to protect humans against sun?"}} {"citation_context": "ason\" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable (https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/). If a mutation is harmless or beneficial in an environment, it will be passed on and likely persi", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/", "kind": "external_url", "post_id": 115175, "post_url": "https://biology.stackexchange.com/a/115175", "product": "citations", "record_id": "Scientific-Citation-Graph:be60cc7f420ce0f2f14bf52b", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.

\n
\n

Where is the error in my thinking?

\n
\n

The error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.

\n

Evolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable "deficiencies" in humans that make us "imperfectly evolved".

\n

That we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any "reason" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable. If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)

\n

If we're "good enough" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.

\n

Also, somewhat aside to your question are the benefits of UV light to humans. We know that UVB allows us to synthesize Vitamin D, which is critical for survival. There are other possible benefits to UV light as well. It might well happen that we'll discover more concrete benefits.

\n

The question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.

\n", "answer_id": 115175, "answer_text": "I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.\n\n\n\n\n\n\n\nWhere is the error in my thinking?\n\n\n\n\n\n\n\nThe error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.\n\n\n\n\nEvolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable \"deficiencies\" in humans that make us \"imperfectly evolved\".\n\n\n\n\nThat we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any \"reason\" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable (https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/). If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)\n\n\n\n\nIf we're \"good enough\" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.\n\n\n\n\nAlso, somewhat aside to your question are the benefits of UV light to humans (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). We know that UVB allows us to synthesize Vitamin D, which is critical for survival. (https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d) There are other possible benefits to UV light as well (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). It might well happen that we'll discover more concrete benefits.\n\n\n\n\nThe question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.", "answer_url": "https://biology.stackexchange.com/a/115175", "author": "anongoodnurse", "author_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:19:48+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:19:48+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B27F09D5-F235-448E-AFF2-AD09B10346FA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B27F09D5-F235-448E-AFF2-AD09B10346FA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:27:18+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "D6BC325F-2058-42EC-A622-79DDDBAE9D28", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D6BC325F-2058-42EC-A622-79DDDBAE9D28/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:11:51+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "70F33937-681F-4BBB-90ED-DB3715ED6BF6", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/70F33937-681F-4BBB-90ED-DB3715ED6BF6/view-source"}], "score": 25, "updated_at": "2024-08-13T19:27:18+00:00"}, {"answer_html": "

Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is "good enough" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as "selective pressure" refers to selection for reproduction specifically.

\n

https://seer.cancer.gov/statfacts/html/melan.html

\n", "answer_id": 115176, "answer_text": "Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is \"good enough\" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as \"selective pressure\" refers to selection for reproduction specifically.\n\n\n\n\nhttps://seer.cancer.gov/statfacts/html/melan.html (https://seer.cancer.gov/statfacts/html/melan.html)", "answer_url": "https://biology.stackexchange.com/a/115176", "author": "Nuclear Hoagie", "author_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:41:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Nuclear Hoagie", "profile_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "user_type": "registered"}, "created_at": "2024-08-13T19:41:14+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E020D650-7DF7-42B4-A813-C07287A63A06", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E020D650-7DF7-42B4-A813-C07287A63A06/view-source"}], "score": 53, "updated_at": "2024-08-13T19:41:14+00:00"}, {"answer_html": "

Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.

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    \n

  • Melanin Production:

    \n

    Melanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.

    \n
    • \n

  • Epidermal Thickening:

    \n

    Another defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.

    \n
    • \n

  • DNA Repair Mechanisms:

    \n

    The human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.

    \n
    • \n

  • Inflammatory Response:

    \n

    The acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.

    \n
    • \n
\n", "answer_id": 115181, "answer_text": "Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.\n\n\n\n\n\n\n\nMelanin Production:\n\n\n\n\nMelanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.\n\n\n\n\n\n\n\n\n\nEpidermal Thickening:\n\n\n\n\nAnother defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.\n\n\n\n\n\n\n\n\n\nDNA Repair Mechanisms:\n\n\n\n\nThe human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase (https://en.wikipedia.org/wiki/Photolyase) repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.\n\n\n\n\n\n\n\n\n\nInflammatory Response:\n\n\n\n\nThe acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.", "answer_url": "https://biology.stackexchange.com/a/115181", "author": "Chris", "author_url": "https://biology.stackexchange.com/users/5144/chris", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T08:30:31+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-14T08:30:31+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "203DF798-60CE-4A5B-942C-F9066DA8BFEC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/203DF798-60CE-4A5B-942C-F9066DA8BFEC/view-source"}], "score": 12, "updated_at": "2024-08-14T08:30:31+00:00"}, {"answer_html": "

To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.

\n", "answer_id": 115184, "answer_text": "To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.", "answer_url": "https://biology.stackexchange.com/a/115184", "author": "Crazymoomin", "author_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T14:44:29+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:44:29+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "34124B84-4C54-404B-BD68-361FC0160072", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/34124B84-4C54-404B-BD68-361FC0160072/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:50:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "90C8EF4F-C093-46C8-845F-34F1CDBE3D76", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/90C8EF4F-C093-46C8-845F-34F1CDBE3D76/view-source"}], "score": 4, "updated_at": "2024-08-14T14:50:43+00:00"}, {"answer_html": "

There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia. It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.

\n

I recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...

\n", "answer_id": 115189, "answer_text": "There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia (https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/). It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.\n\n\n\n\nI recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...", "answer_url": "https://biology.stackexchange.com/a/115189", "author": "Simon Crase", "author_url": "https://biology.stackexchange.com/users/60999/simon-crase", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T06:47:00+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-15T06:47:00+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "06C3F178-4AC5-4566-87E9-1B7866F7776D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/06C3F178-4AC5-4566-87E9-1B7866F7776D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-16T00:56:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E63DE613-A666-4300-87F8-B4DFC7B8CA59", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E63DE613-A666-4300-87F8-B4DFC7B8CA59/view-source"}], "score": 5, "updated_at": "2024-08-16T00:56:43+00:00"}, {"answer_html": "

The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.

\n

Now if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.

\n

Also careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.

\n", "answer_id": 115195, "answer_text": "The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.\n\n\n\n\nNow if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.\n\n\n\n\nAlso careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.", "answer_url": "https://biology.stackexchange.com/a/115195", "author": "gnasher729", "author_url": "https://biology.stackexchange.com/users/10077/gnasher729", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T20:13:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gnasher729", "profile_url": "https://biology.stackexchange.com/users/10077/gnasher729", "user_type": "registered"}, "created_at": "2024-08-15T20:13:04+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B98FEE88-41D0-4F31-8B9A-0D171031B546", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B98FEE88-41D0-4F31-8B9A-0D171031B546/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:10:35+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "261F1C4D-1ECD-48FA-8442-CED29305E440", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/261F1C4D-1ECD-48FA-8442-CED29305E440/view-source"}], "score": 8, "updated_at": "2024-08-15T20:13:04+00:00"}, {"answer_html": "

Because cancer wasn't likely to be one's cause of death. Look at this comparison between 1900 and 2022:

\n

\"enter

\n

Cancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s:

\n
\n

Cancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’

\n
\n

Evolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:

\n
\n

Devil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.

\n

...

\n

In 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.

\n
\n", "answer_id": 115199, "answer_text": "Because cancer wasn't likely to be one's cause of death. Look at this comparison (https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/) between 1900 and 2022:\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/pzQsLWkf.png] (https://i.sstatic.net/pzQsLWkf.png)\n\n\n\n\nCancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/):\n\n\n\n\n\n\n\nCancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’\n\n\n\n\n\n\n\nEvolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence (https://en.wikipedia.org/wiki/Devil_facial_tumour_disease) from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:\n\n\n\n\n\n\n\nDevil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.\n\n\n\n\n...\n\n\n\n\nIn 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.", "answer_url": "https://biology.stackexchange.com/a/115199", "author": "MilkLife", "author_url": "https://biology.stackexchange.com/users/5492/milklife", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-16T23:47:16+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MilkLife", "profile_url": "https://biology.stackexchange.com/users/5492/milklife", "user_type": "registered"}, "created_at": "2024-08-16T23:47:16+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "FA30453C-1E93-40D2-9D07-DDC697CEF2EA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/FA30453C-1E93-40D2-9D07-DDC697CEF2EA/view-source"}], "score": 0, "updated_at": "2024-08-16T23:47:16+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/Devil_facial_tumour_disease", "https://en.wikipedia.org/wiki/Fitzpatrick_scale", "https://en.wikipedia.org/wiki/Photolyase", "https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/", "https://i.sstatic.net/pzQsLWkf.png", "https://seer.cancer.gov/statfacts/html/melan.html", "https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d", "https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/", "https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:05.762873+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/04ed2aa314c5d877c5d79e42620d1f80988a21de8d429a22d8c6af5280cfd6e8_0.json", "raw_sha256": "6dd355b99094bb9ba2c965ee7dd7b0e95f92a8078d3b2b85b64196fcb6cf717c", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=5&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "gaazkam", "question_author_url": "https://biology.stackexchange.com/users/15177/gaazkam", "question_author_user_type": "registered", "question_created_at": "2024-08-13T05:20:41+00:00", "question_html": "

Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.

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Especially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.

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Native to Europe are phototypes I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?

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So, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.

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Yet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.

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Where is the error in my thinking?

\n", "question_id": 115170, "question_license": "CC BY-SA 4.0", "question_score": 17, "question_text": "Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.\n\n\n\n\nEspecially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.\n\n\n\n\nNative to Europe are phototypes (https://en.wikipedia.org/wiki/Fitzpatrick_scale) I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?\n\n\n\n\nSo, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.\n\n\n\n\nYet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.\n\n\n\n\nWhere is the error in my thinking?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:20:41+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "828DB692-880A-4BBF-AD67-13CF3E06456A", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/828DB692-880A-4BBF-AD67-13CF3E06456A/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:26:09+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2024-08-14T08:31:47+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D/view-source"}, {"content_license": null, "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-15T13:36:46+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:12:55+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E7A91925-4841-42A6-89A7-24963075C01F", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/E7A91925-4841-42A6-89A7-24963075C01F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Basil Bourque", "profile_url": "https://biology.stackexchange.com/users/32521/basil-bourque", "user_type": "registered"}, "created_at": "2024-09-02T17:31:11+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "C86E2648-B494-446F-A6EC-EE52D185A1B7", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/C86E2648-B494-446F-A6EC-EE52D185A1B7/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/115170/why-did-evolution-fail-to-protect-humans-against-sun", "split": "test", "split_group": "503625bcfe466937a26431096aee38aeab3e6012cf849f4c5706c832b5d6195c", "tags": ["human-evolution", "skin", "melanin"], "thread_id": "biology:115170", "title": "Why did evolution fail to protect humans against sun?"}} {"citation_context": "ed imperfections.\n\n\n\n\nAlso, somewhat aside to your question are the benefits of UV light to humans (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). We know that UVB allows us to synthesize Vitamin D, which is critical for survival. (https://www.", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/", "kind": "external_url", "post_id": 115175, "post_url": "https://biology.stackexchange.com/a/115175", "product": "citations", "record_id": "Scientific-Citation-Graph:eeb41514ecb4e5425807dc1b", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.

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Where is the error in my thinking?

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The error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.

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Evolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable "deficiencies" in humans that make us "imperfectly evolved".

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That we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any "reason" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable. If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)

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If we're "good enough" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.

\n

Also, somewhat aside to your question are the benefits of UV light to humans. We know that UVB allows us to synthesize Vitamin D, which is critical for survival. There are other possible benefits to UV light as well. It might well happen that we'll discover more concrete benefits.

\n

The question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.

\n", "answer_id": 115175, "answer_text": "I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.\n\n\n\n\n\n\n\nWhere is the error in my thinking?\n\n\n\n\n\n\n\nThe error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.\n\n\n\n\nEvolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable \"deficiencies\" in humans that make us \"imperfectly evolved\".\n\n\n\n\nThat we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any \"reason\" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable (https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/). If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)\n\n\n\n\nIf we're \"good enough\" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.\n\n\n\n\nAlso, somewhat aside to your question are the benefits of UV light to humans (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). We know that UVB allows us to synthesize Vitamin D, which is critical for survival. (https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d) There are other possible benefits to UV light as well (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). It might well happen that we'll discover more concrete benefits.\n\n\n\n\nThe question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.", "answer_url": "https://biology.stackexchange.com/a/115175", "author": "anongoodnurse", "author_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:19:48+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:19:48+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B27F09D5-F235-448E-AFF2-AD09B10346FA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B27F09D5-F235-448E-AFF2-AD09B10346FA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:27:18+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "D6BC325F-2058-42EC-A622-79DDDBAE9D28", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D6BC325F-2058-42EC-A622-79DDDBAE9D28/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:11:51+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "70F33937-681F-4BBB-90ED-DB3715ED6BF6", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/70F33937-681F-4BBB-90ED-DB3715ED6BF6/view-source"}], "score": 25, "updated_at": "2024-08-13T19:27:18+00:00"}, {"answer_html": "

Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is "good enough" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as "selective pressure" refers to selection for reproduction specifically.

\n

https://seer.cancer.gov/statfacts/html/melan.html

\n", "answer_id": 115176, "answer_text": "Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is \"good enough\" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as \"selective pressure\" refers to selection for reproduction specifically.\n\n\n\n\nhttps://seer.cancer.gov/statfacts/html/melan.html (https://seer.cancer.gov/statfacts/html/melan.html)", "answer_url": "https://biology.stackexchange.com/a/115176", "author": "Nuclear Hoagie", "author_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:41:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Nuclear Hoagie", "profile_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "user_type": "registered"}, "created_at": "2024-08-13T19:41:14+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E020D650-7DF7-42B4-A813-C07287A63A06", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E020D650-7DF7-42B4-A813-C07287A63A06/view-source"}], "score": 53, "updated_at": "2024-08-13T19:41:14+00:00"}, {"answer_html": "

Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.

\n
    \n

  • Melanin Production:

    \n

    Melanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.

    \n
    • \n

  • Epidermal Thickening:

    \n

    Another defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.

    \n
    • \n

  • DNA Repair Mechanisms:

    \n

    The human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.

    \n
    • \n

  • Inflammatory Response:

    \n

    The acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.

    \n
    • \n
\n", "answer_id": 115181, "answer_text": "Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.\n\n\n\n\n\n\n\nMelanin Production:\n\n\n\n\nMelanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.\n\n\n\n\n\n\n\n\n\nEpidermal Thickening:\n\n\n\n\nAnother defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.\n\n\n\n\n\n\n\n\n\nDNA Repair Mechanisms:\n\n\n\n\nThe human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase (https://en.wikipedia.org/wiki/Photolyase) repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.\n\n\n\n\n\n\n\n\n\nInflammatory Response:\n\n\n\n\nThe acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.", "answer_url": "https://biology.stackexchange.com/a/115181", "author": "Chris", "author_url": "https://biology.stackexchange.com/users/5144/chris", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T08:30:31+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-14T08:30:31+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "203DF798-60CE-4A5B-942C-F9066DA8BFEC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/203DF798-60CE-4A5B-942C-F9066DA8BFEC/view-source"}], "score": 12, "updated_at": "2024-08-14T08:30:31+00:00"}, {"answer_html": "

To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.

\n", "answer_id": 115184, "answer_text": "To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.", "answer_url": "https://biology.stackexchange.com/a/115184", "author": "Crazymoomin", "author_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T14:44:29+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:44:29+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "34124B84-4C54-404B-BD68-361FC0160072", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/34124B84-4C54-404B-BD68-361FC0160072/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:50:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "90C8EF4F-C093-46C8-845F-34F1CDBE3D76", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/90C8EF4F-C093-46C8-845F-34F1CDBE3D76/view-source"}], "score": 4, "updated_at": "2024-08-14T14:50:43+00:00"}, {"answer_html": "

There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia. It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.

\n

I recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...

\n", "answer_id": 115189, "answer_text": "There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia (https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/). It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.\n\n\n\n\nI recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...", "answer_url": "https://biology.stackexchange.com/a/115189", "author": "Simon Crase", "author_url": "https://biology.stackexchange.com/users/60999/simon-crase", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T06:47:00+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-15T06:47:00+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "06C3F178-4AC5-4566-87E9-1B7866F7776D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/06C3F178-4AC5-4566-87E9-1B7866F7776D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-16T00:56:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E63DE613-A666-4300-87F8-B4DFC7B8CA59", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E63DE613-A666-4300-87F8-B4DFC7B8CA59/view-source"}], "score": 5, "updated_at": "2024-08-16T00:56:43+00:00"}, {"answer_html": "

The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.

\n

Now if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.

\n

Also careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.

\n", "answer_id": 115195, "answer_text": "The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.\n\n\n\n\nNow if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.\n\n\n\n\nAlso careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.", "answer_url": "https://biology.stackexchange.com/a/115195", "author": "gnasher729", "author_url": "https://biology.stackexchange.com/users/10077/gnasher729", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T20:13:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gnasher729", "profile_url": "https://biology.stackexchange.com/users/10077/gnasher729", "user_type": "registered"}, "created_at": "2024-08-15T20:13:04+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B98FEE88-41D0-4F31-8B9A-0D171031B546", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B98FEE88-41D0-4F31-8B9A-0D171031B546/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:10:35+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "261F1C4D-1ECD-48FA-8442-CED29305E440", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/261F1C4D-1ECD-48FA-8442-CED29305E440/view-source"}], "score": 8, "updated_at": "2024-08-15T20:13:04+00:00"}, {"answer_html": "

Because cancer wasn't likely to be one's cause of death. Look at this comparison between 1900 and 2022:

\n

\"enter

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Cancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s:

\n
\n

Cancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’

\n
\n

Evolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:

\n
\n

Devil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.

\n

...

\n

In 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.

\n
\n", "answer_id": 115199, "answer_text": "Because cancer wasn't likely to be one's cause of death. Look at this comparison (https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/) between 1900 and 2022:\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/pzQsLWkf.png] (https://i.sstatic.net/pzQsLWkf.png)\n\n\n\n\nCancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/):\n\n\n\n\n\n\n\nCancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’\n\n\n\n\n\n\n\nEvolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence (https://en.wikipedia.org/wiki/Devil_facial_tumour_disease) from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:\n\n\n\n\n\n\n\nDevil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.\n\n\n\n\n...\n\n\n\n\nIn 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.", "answer_url": "https://biology.stackexchange.com/a/115199", "author": "MilkLife", "author_url": "https://biology.stackexchange.com/users/5492/milklife", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-16T23:47:16+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MilkLife", "profile_url": "https://biology.stackexchange.com/users/5492/milklife", "user_type": "registered"}, "created_at": "2024-08-16T23:47:16+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "FA30453C-1E93-40D2-9D07-DDC697CEF2EA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/FA30453C-1E93-40D2-9D07-DDC697CEF2EA/view-source"}], "score": 0, "updated_at": "2024-08-16T23:47:16+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/Devil_facial_tumour_disease", "https://en.wikipedia.org/wiki/Fitzpatrick_scale", "https://en.wikipedia.org/wiki/Photolyase", "https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/", "https://i.sstatic.net/pzQsLWkf.png", "https://seer.cancer.gov/statfacts/html/melan.html", "https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d", "https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/", "https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:05.762873+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/04ed2aa314c5d877c5d79e42620d1f80988a21de8d429a22d8c6af5280cfd6e8_0.json", "raw_sha256": "6dd355b99094bb9ba2c965ee7dd7b0e95f92a8078d3b2b85b64196fcb6cf717c", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=5&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "gaazkam", "question_author_url": "https://biology.stackexchange.com/users/15177/gaazkam", "question_author_user_type": "registered", "question_created_at": "2024-08-13T05:20:41+00:00", "question_html": "

Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.

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Especially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.

\n

Native to Europe are phototypes I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?

\n

So, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.

\n

Yet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.

\n

Where is the error in my thinking?

\n", "question_id": 115170, "question_license": "CC BY-SA 4.0", "question_score": 17, "question_text": "Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.\n\n\n\n\nEspecially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.\n\n\n\n\nNative to Europe are phototypes (https://en.wikipedia.org/wiki/Fitzpatrick_scale) I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?\n\n\n\n\nSo, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.\n\n\n\n\nYet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.\n\n\n\n\nWhere is the error in my thinking?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:20:41+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "828DB692-880A-4BBF-AD67-13CF3E06456A", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/828DB692-880A-4BBF-AD67-13CF3E06456A/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:26:09+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2024-08-14T08:31:47+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D/view-source"}, {"content_license": null, "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-15T13:36:46+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:12:55+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E7A91925-4841-42A6-89A7-24963075C01F", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/E7A91925-4841-42A6-89A7-24963075C01F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Basil Bourque", "profile_url": "https://biology.stackexchange.com/users/32521/basil-bourque", "user_type": "registered"}, "created_at": "2024-09-02T17:31:11+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "C86E2648-B494-446F-A6EC-EE52D185A1B7", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/C86E2648-B494-446F-A6EC-EE52D185A1B7/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/115170/why-did-evolution-fail-to-protect-humans-against-sun", "split": "test", "split_group": "503625bcfe466937a26431096aee38aeab3e6012cf849f4c5706c832b5d6195c", "tags": ["human-evolution", "skin", "melanin"], "thread_id": "biology:115170", "title": "Why did evolution fail to protect humans against sun?"}} {"citation_context": "er reproductive age, as \"selective pressure\" refers to selection for reproduction specifically.\n\n\n\n\nhttps://seer.cancer.gov/statfacts/html/melan.html (https://seer.cancer.gov/statfacts/html/melan.html)", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://seer.cancer.gov/statfacts/html/melan.html", "kind": "external_url", "post_id": 115176, "post_url": "https://biology.stackexchange.com/a/115176", "product": "citations", "record_id": "Scientific-Citation-Graph:defec32c82b91f17264f91bb", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.

\n
\n

Where is the error in my thinking?

\n
\n

The error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.

\n

Evolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable "deficiencies" in humans that make us "imperfectly evolved".

\n

That we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any "reason" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable. If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)

\n

If we're "good enough" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.

\n

Also, somewhat aside to your question are the benefits of UV light to humans. We know that UVB allows us to synthesize Vitamin D, which is critical for survival. There are other possible benefits to UV light as well. It might well happen that we'll discover more concrete benefits.

\n

The question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.

\n", "answer_id": 115175, "answer_text": "I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.\n\n\n\n\n\n\n\nWhere is the error in my thinking?\n\n\n\n\n\n\n\nThe error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.\n\n\n\n\nEvolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable \"deficiencies\" in humans that make us \"imperfectly evolved\".\n\n\n\n\nThat we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any \"reason\" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable (https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/). If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)\n\n\n\n\nIf we're \"good enough\" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.\n\n\n\n\nAlso, somewhat aside to your question are the benefits of UV light to humans (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). We know that UVB allows us to synthesize Vitamin D, which is critical for survival. (https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d) There are other possible benefits to UV light as well (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). It might well happen that we'll discover more concrete benefits.\n\n\n\n\nThe question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.", "answer_url": "https://biology.stackexchange.com/a/115175", "author": "anongoodnurse", "author_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:19:48+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:19:48+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B27F09D5-F235-448E-AFF2-AD09B10346FA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B27F09D5-F235-448E-AFF2-AD09B10346FA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:27:18+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "D6BC325F-2058-42EC-A622-79DDDBAE9D28", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D6BC325F-2058-42EC-A622-79DDDBAE9D28/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:11:51+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "70F33937-681F-4BBB-90ED-DB3715ED6BF6", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/70F33937-681F-4BBB-90ED-DB3715ED6BF6/view-source"}], "score": 25, "updated_at": "2024-08-13T19:27:18+00:00"}, {"answer_html": "

Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is "good enough" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as "selective pressure" refers to selection for reproduction specifically.

\n

https://seer.cancer.gov/statfacts/html/melan.html

\n", "answer_id": 115176, "answer_text": "Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is \"good enough\" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as \"selective pressure\" refers to selection for reproduction specifically.\n\n\n\n\nhttps://seer.cancer.gov/statfacts/html/melan.html (https://seer.cancer.gov/statfacts/html/melan.html)", "answer_url": "https://biology.stackexchange.com/a/115176", "author": "Nuclear Hoagie", "author_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:41:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Nuclear Hoagie", "profile_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "user_type": "registered"}, "created_at": "2024-08-13T19:41:14+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E020D650-7DF7-42B4-A813-C07287A63A06", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E020D650-7DF7-42B4-A813-C07287A63A06/view-source"}], "score": 53, "updated_at": "2024-08-13T19:41:14+00:00"}, {"answer_html": "

Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.

\n
    \n

  • Melanin Production:

    \n

    Melanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.

    \n
    • \n

  • Epidermal Thickening:

    \n

    Another defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.

    \n
    • \n

  • DNA Repair Mechanisms:

    \n

    The human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.

    \n
    • \n

  • Inflammatory Response:

    \n

    The acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.

    \n
    • \n
\n", "answer_id": 115181, "answer_text": "Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.\n\n\n\n\n\n\n\nMelanin Production:\n\n\n\n\nMelanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.\n\n\n\n\n\n\n\n\n\nEpidermal Thickening:\n\n\n\n\nAnother defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.\n\n\n\n\n\n\n\n\n\nDNA Repair Mechanisms:\n\n\n\n\nThe human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase (https://en.wikipedia.org/wiki/Photolyase) repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.\n\n\n\n\n\n\n\n\n\nInflammatory Response:\n\n\n\n\nThe acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.", "answer_url": "https://biology.stackexchange.com/a/115181", "author": "Chris", "author_url": "https://biology.stackexchange.com/users/5144/chris", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T08:30:31+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-14T08:30:31+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "203DF798-60CE-4A5B-942C-F9066DA8BFEC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/203DF798-60CE-4A5B-942C-F9066DA8BFEC/view-source"}], "score": 12, "updated_at": "2024-08-14T08:30:31+00:00"}, {"answer_html": "

To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.

\n", "answer_id": 115184, "answer_text": "To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.", "answer_url": "https://biology.stackexchange.com/a/115184", "author": "Crazymoomin", "author_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T14:44:29+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:44:29+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "34124B84-4C54-404B-BD68-361FC0160072", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/34124B84-4C54-404B-BD68-361FC0160072/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:50:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "90C8EF4F-C093-46C8-845F-34F1CDBE3D76", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/90C8EF4F-C093-46C8-845F-34F1CDBE3D76/view-source"}], "score": 4, "updated_at": "2024-08-14T14:50:43+00:00"}, {"answer_html": "

There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia. It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.

\n

I recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...

\n", "answer_id": 115189, "answer_text": "There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia (https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/). It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.\n\n\n\n\nI recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...", "answer_url": "https://biology.stackexchange.com/a/115189", "author": "Simon Crase", "author_url": "https://biology.stackexchange.com/users/60999/simon-crase", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T06:47:00+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-15T06:47:00+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "06C3F178-4AC5-4566-87E9-1B7866F7776D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/06C3F178-4AC5-4566-87E9-1B7866F7776D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-16T00:56:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E63DE613-A666-4300-87F8-B4DFC7B8CA59", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E63DE613-A666-4300-87F8-B4DFC7B8CA59/view-source"}], "score": 5, "updated_at": "2024-08-16T00:56:43+00:00"}, {"answer_html": "

The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.

\n

Now if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.

\n

Also careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.

\n", "answer_id": 115195, "answer_text": "The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.\n\n\n\n\nNow if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.\n\n\n\n\nAlso careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.", "answer_url": "https://biology.stackexchange.com/a/115195", "author": "gnasher729", "author_url": "https://biology.stackexchange.com/users/10077/gnasher729", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T20:13:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gnasher729", "profile_url": "https://biology.stackexchange.com/users/10077/gnasher729", "user_type": "registered"}, "created_at": "2024-08-15T20:13:04+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B98FEE88-41D0-4F31-8B9A-0D171031B546", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B98FEE88-41D0-4F31-8B9A-0D171031B546/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:10:35+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "261F1C4D-1ECD-48FA-8442-CED29305E440", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/261F1C4D-1ECD-48FA-8442-CED29305E440/view-source"}], "score": 8, "updated_at": "2024-08-15T20:13:04+00:00"}, {"answer_html": "

Because cancer wasn't likely to be one's cause of death. Look at this comparison between 1900 and 2022:

\n

\"enter

\n

Cancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s:

\n
\n

Cancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’

\n
\n

Evolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:

\n
\n

Devil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.

\n

...

\n

In 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.

\n
\n", "answer_id": 115199, "answer_text": "Because cancer wasn't likely to be one's cause of death. Look at this comparison (https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/) between 1900 and 2022:\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/pzQsLWkf.png] (https://i.sstatic.net/pzQsLWkf.png)\n\n\n\n\nCancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/):\n\n\n\n\n\n\n\nCancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’\n\n\n\n\n\n\n\nEvolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence (https://en.wikipedia.org/wiki/Devil_facial_tumour_disease) from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:\n\n\n\n\n\n\n\nDevil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.\n\n\n\n\n...\n\n\n\n\nIn 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.", "answer_url": "https://biology.stackexchange.com/a/115199", "author": "MilkLife", "author_url": "https://biology.stackexchange.com/users/5492/milklife", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-16T23:47:16+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MilkLife", "profile_url": "https://biology.stackexchange.com/users/5492/milklife", "user_type": "registered"}, "created_at": "2024-08-16T23:47:16+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "FA30453C-1E93-40D2-9D07-DDC697CEF2EA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/FA30453C-1E93-40D2-9D07-DDC697CEF2EA/view-source"}], "score": 0, "updated_at": "2024-08-16T23:47:16+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/Devil_facial_tumour_disease", "https://en.wikipedia.org/wiki/Fitzpatrick_scale", "https://en.wikipedia.org/wiki/Photolyase", "https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/", "https://i.sstatic.net/pzQsLWkf.png", "https://seer.cancer.gov/statfacts/html/melan.html", "https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d", "https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/", "https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:05.762873+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/04ed2aa314c5d877c5d79e42620d1f80988a21de8d429a22d8c6af5280cfd6e8_0.json", "raw_sha256": "6dd355b99094bb9ba2c965ee7dd7b0e95f92a8078d3b2b85b64196fcb6cf717c", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=5&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "gaazkam", "question_author_url": "https://biology.stackexchange.com/users/15177/gaazkam", "question_author_user_type": "registered", "question_created_at": "2024-08-13T05:20:41+00:00", "question_html": "

Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.

\n

Especially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.

\n

Native to Europe are phototypes I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?

\n

So, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.

\n

Yet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.

\n

Where is the error in my thinking?

\n", "question_id": 115170, "question_license": "CC BY-SA 4.0", "question_score": 17, "question_text": "Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.\n\n\n\n\nEspecially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.\n\n\n\n\nNative to Europe are phototypes (https://en.wikipedia.org/wiki/Fitzpatrick_scale) I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?\n\n\n\n\nSo, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.\n\n\n\n\nYet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.\n\n\n\n\nWhere is the error in my thinking?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:20:41+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "828DB692-880A-4BBF-AD67-13CF3E06456A", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/828DB692-880A-4BBF-AD67-13CF3E06456A/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:26:09+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2024-08-14T08:31:47+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D/view-source"}, {"content_license": null, "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-15T13:36:46+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:12:55+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E7A91925-4841-42A6-89A7-24963075C01F", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/E7A91925-4841-42A6-89A7-24963075C01F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Basil Bourque", "profile_url": "https://biology.stackexchange.com/users/32521/basil-bourque", "user_type": "registered"}, "created_at": "2024-09-02T17:31:11+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "C86E2648-B494-446F-A6EC-EE52D185A1B7", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/C86E2648-B494-446F-A6EC-EE52D185A1B7/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/115170/why-did-evolution-fail-to-protect-humans-against-sun", "split": "test", "split_group": "503625bcfe466937a26431096aee38aeab3e6012cf849f4c5706c832b5d6195c", "tags": ["human-evolution", "skin", "melanin"], "thread_id": "biology:115170", "title": "Why did evolution fail to protect humans against sun?"}} {"citation_context": "th and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase (https://en.wikipedia.org/wiki/Photolyase) repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by U", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Photolyase", "kind": "external_url", "post_id": 115181, "post_url": "https://biology.stackexchange.com/a/115181", "product": "citations", "record_id": "Scientific-Citation-Graph:e925843548bf85c1682caee2", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.

\n
\n

Where is the error in my thinking?

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\n

The error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.

\n

Evolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable "deficiencies" in humans that make us "imperfectly evolved".

\n

That we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any "reason" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable. If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)

\n

If we're "good enough" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.

\n

Also, somewhat aside to your question are the benefits of UV light to humans. We know that UVB allows us to synthesize Vitamin D, which is critical for survival. There are other possible benefits to UV light as well. It might well happen that we'll discover more concrete benefits.

\n

The question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.

\n", "answer_id": 115175, "answer_text": "I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.\n\n\n\n\n\n\n\nWhere is the error in my thinking?\n\n\n\n\n\n\n\nThe error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.\n\n\n\n\nEvolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable \"deficiencies\" in humans that make us \"imperfectly evolved\".\n\n\n\n\nThat we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any \"reason\" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable (https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/). If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)\n\n\n\n\nIf we're \"good enough\" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.\n\n\n\n\nAlso, somewhat aside to your question are the benefits of UV light to humans (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). We know that UVB allows us to synthesize Vitamin D, which is critical for survival. (https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d) There are other possible benefits to UV light as well (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). It might well happen that we'll discover more concrete benefits.\n\n\n\n\nThe question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.", "answer_url": "https://biology.stackexchange.com/a/115175", "author": "anongoodnurse", "author_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:19:48+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:19:48+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B27F09D5-F235-448E-AFF2-AD09B10346FA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B27F09D5-F235-448E-AFF2-AD09B10346FA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:27:18+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "D6BC325F-2058-42EC-A622-79DDDBAE9D28", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D6BC325F-2058-42EC-A622-79DDDBAE9D28/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:11:51+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "70F33937-681F-4BBB-90ED-DB3715ED6BF6", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/70F33937-681F-4BBB-90ED-DB3715ED6BF6/view-source"}], "score": 25, "updated_at": "2024-08-13T19:27:18+00:00"}, {"answer_html": "

Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is "good enough" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as "selective pressure" refers to selection for reproduction specifically.

\n

https://seer.cancer.gov/statfacts/html/melan.html

\n", "answer_id": 115176, "answer_text": "Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is \"good enough\" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as \"selective pressure\" refers to selection for reproduction specifically.\n\n\n\n\nhttps://seer.cancer.gov/statfacts/html/melan.html (https://seer.cancer.gov/statfacts/html/melan.html)", "answer_url": "https://biology.stackexchange.com/a/115176", "author": "Nuclear Hoagie", "author_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:41:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Nuclear Hoagie", "profile_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "user_type": "registered"}, "created_at": "2024-08-13T19:41:14+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E020D650-7DF7-42B4-A813-C07287A63A06", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E020D650-7DF7-42B4-A813-C07287A63A06/view-source"}], "score": 53, "updated_at": "2024-08-13T19:41:14+00:00"}, {"answer_html": "

Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.

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    \n

  • Melanin Production:

    \n

    Melanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.

    \n
    • \n

  • Epidermal Thickening:

    \n

    Another defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.

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    • \n

  • DNA Repair Mechanisms:

    \n

    The human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.

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    • \n

  • Inflammatory Response:

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    The acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.

    \n
    • \n
\n", "answer_id": 115181, "answer_text": "Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.\n\n\n\n\n\n\n\nMelanin Production:\n\n\n\n\nMelanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.\n\n\n\n\n\n\n\n\n\nEpidermal Thickening:\n\n\n\n\nAnother defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.\n\n\n\n\n\n\n\n\n\nDNA Repair Mechanisms:\n\n\n\n\nThe human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase (https://en.wikipedia.org/wiki/Photolyase) repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.\n\n\n\n\n\n\n\n\n\nInflammatory Response:\n\n\n\n\nThe acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.", "answer_url": "https://biology.stackexchange.com/a/115181", "author": "Chris", "author_url": "https://biology.stackexchange.com/users/5144/chris", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T08:30:31+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-14T08:30:31+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "203DF798-60CE-4A5B-942C-F9066DA8BFEC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/203DF798-60CE-4A5B-942C-F9066DA8BFEC/view-source"}], "score": 12, "updated_at": "2024-08-14T08:30:31+00:00"}, {"answer_html": "

To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.

\n", "answer_id": 115184, "answer_text": "To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.", "answer_url": "https://biology.stackexchange.com/a/115184", "author": "Crazymoomin", "author_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T14:44:29+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:44:29+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "34124B84-4C54-404B-BD68-361FC0160072", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/34124B84-4C54-404B-BD68-361FC0160072/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:50:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "90C8EF4F-C093-46C8-845F-34F1CDBE3D76", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/90C8EF4F-C093-46C8-845F-34F1CDBE3D76/view-source"}], "score": 4, "updated_at": "2024-08-14T14:50:43+00:00"}, {"answer_html": "

There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia. It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.

\n

I recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...

\n", "answer_id": 115189, "answer_text": "There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia (https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/). It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.\n\n\n\n\nI recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...", "answer_url": "https://biology.stackexchange.com/a/115189", "author": "Simon Crase", "author_url": "https://biology.stackexchange.com/users/60999/simon-crase", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T06:47:00+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-15T06:47:00+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "06C3F178-4AC5-4566-87E9-1B7866F7776D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/06C3F178-4AC5-4566-87E9-1B7866F7776D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-16T00:56:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E63DE613-A666-4300-87F8-B4DFC7B8CA59", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E63DE613-A666-4300-87F8-B4DFC7B8CA59/view-source"}], "score": 5, "updated_at": "2024-08-16T00:56:43+00:00"}, {"answer_html": "

The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.

\n

Now if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.

\n

Also careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.

\n", "answer_id": 115195, "answer_text": "The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.\n\n\n\n\nNow if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.\n\n\n\n\nAlso careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.", "answer_url": "https://biology.stackexchange.com/a/115195", "author": "gnasher729", "author_url": "https://biology.stackexchange.com/users/10077/gnasher729", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T20:13:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gnasher729", "profile_url": "https://biology.stackexchange.com/users/10077/gnasher729", "user_type": "registered"}, "created_at": "2024-08-15T20:13:04+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B98FEE88-41D0-4F31-8B9A-0D171031B546", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B98FEE88-41D0-4F31-8B9A-0D171031B546/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:10:35+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "261F1C4D-1ECD-48FA-8442-CED29305E440", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/261F1C4D-1ECD-48FA-8442-CED29305E440/view-source"}], "score": 8, "updated_at": "2024-08-15T20:13:04+00:00"}, {"answer_html": "

Because cancer wasn't likely to be one's cause of death. Look at this comparison between 1900 and 2022:

\n

\"enter

\n

Cancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s:

\n
\n

Cancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’

\n
\n

Evolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:

\n
\n

Devil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.

\n

...

\n

In 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.

\n
\n", "answer_id": 115199, "answer_text": "Because cancer wasn't likely to be one's cause of death. Look at this comparison (https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/) between 1900 and 2022:\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/pzQsLWkf.png] (https://i.sstatic.net/pzQsLWkf.png)\n\n\n\n\nCancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/):\n\n\n\n\n\n\n\nCancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’\n\n\n\n\n\n\n\nEvolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence (https://en.wikipedia.org/wiki/Devil_facial_tumour_disease) from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:\n\n\n\n\n\n\n\nDevil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.\n\n\n\n\n...\n\n\n\n\nIn 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.", "answer_url": "https://biology.stackexchange.com/a/115199", "author": "MilkLife", "author_url": "https://biology.stackexchange.com/users/5492/milklife", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-16T23:47:16+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MilkLife", "profile_url": "https://biology.stackexchange.com/users/5492/milklife", "user_type": "registered"}, "created_at": "2024-08-16T23:47:16+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "FA30453C-1E93-40D2-9D07-DDC697CEF2EA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/FA30453C-1E93-40D2-9D07-DDC697CEF2EA/view-source"}], "score": 0, "updated_at": "2024-08-16T23:47:16+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/Devil_facial_tumour_disease", "https://en.wikipedia.org/wiki/Fitzpatrick_scale", "https://en.wikipedia.org/wiki/Photolyase", "https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/", "https://i.sstatic.net/pzQsLWkf.png", "https://seer.cancer.gov/statfacts/html/melan.html", "https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d", "https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/", "https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:05.762873+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/04ed2aa314c5d877c5d79e42620d1f80988a21de8d429a22d8c6af5280cfd6e8_0.json", "raw_sha256": "6dd355b99094bb9ba2c965ee7dd7b0e95f92a8078d3b2b85b64196fcb6cf717c", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=5&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "gaazkam", "question_author_url": "https://biology.stackexchange.com/users/15177/gaazkam", "question_author_user_type": "registered", "question_created_at": "2024-08-13T05:20:41+00:00", "question_html": "

Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.

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Especially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.

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Native to Europe are phototypes I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?

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So, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.

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Yet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.

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Where is the error in my thinking?

\n", "question_id": 115170, "question_license": "CC BY-SA 4.0", "question_score": 17, "question_text": "Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.\n\n\n\n\nEspecially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.\n\n\n\n\nNative to Europe are phototypes (https://en.wikipedia.org/wiki/Fitzpatrick_scale) I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?\n\n\n\n\nSo, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.\n\n\n\n\nYet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.\n\n\n\n\nWhere is the error in my thinking?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:20:41+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "828DB692-880A-4BBF-AD67-13CF3E06456A", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/828DB692-880A-4BBF-AD67-13CF3E06456A/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:26:09+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2024-08-14T08:31:47+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D/view-source"}, {"content_license": null, "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-15T13:36:46+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:12:55+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E7A91925-4841-42A6-89A7-24963075C01F", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/E7A91925-4841-42A6-89A7-24963075C01F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Basil Bourque", "profile_url": "https://biology.stackexchange.com/users/32521/basil-bourque", "user_type": "registered"}, "created_at": "2024-09-02T17:31:11+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "C86E2648-B494-446F-A6EC-EE52D185A1B7", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/C86E2648-B494-446F-A6EC-EE52D185A1B7/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/115170/why-did-evolution-fail-to-protect-humans-against-sun", "split": "test", "split_group": "503625bcfe466937a26431096aee38aeab3e6012cf849f4c5706c832b5d6195c", "tags": ["human-evolution", "skin", "melanin"], "thread_id": "biology:115170", "title": "Why did evolution fail to protect humans against sun?"}} {"citation_context": "r encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia (https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/). It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are ", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/", "kind": "external_url", "post_id": 115189, "post_url": "https://biology.stackexchange.com/a/115189", "product": "citations", "record_id": "Scientific-Citation-Graph:d8433e271cd9c0fd7e64e447", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.

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Where is the error in my thinking?

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The error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.

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Evolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable "deficiencies" in humans that make us "imperfectly evolved".

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That we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any "reason" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable. If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)

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If we're "good enough" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.

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Also, somewhat aside to your question are the benefits of UV light to humans. We know that UVB allows us to synthesize Vitamin D, which is critical for survival. There are other possible benefits to UV light as well. It might well happen that we'll discover more concrete benefits.

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The question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.

\n", "answer_id": 115175, "answer_text": "I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.\n\n\n\n\n\n\n\nWhere is the error in my thinking?\n\n\n\n\n\n\n\nThe error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.\n\n\n\n\nEvolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable \"deficiencies\" in humans that make us \"imperfectly evolved\".\n\n\n\n\nThat we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any \"reason\" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable (https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/). If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)\n\n\n\n\nIf we're \"good enough\" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.\n\n\n\n\nAlso, somewhat aside to your question are the benefits of UV light to humans (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). We know that UVB allows us to synthesize Vitamin D, which is critical for survival. (https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d) There are other possible benefits to UV light as well (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). It might well happen that we'll discover more concrete benefits.\n\n\n\n\nThe question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.", "answer_url": "https://biology.stackexchange.com/a/115175", "author": "anongoodnurse", "author_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:19:48+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:19:48+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B27F09D5-F235-448E-AFF2-AD09B10346FA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B27F09D5-F235-448E-AFF2-AD09B10346FA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:27:18+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "D6BC325F-2058-42EC-A622-79DDDBAE9D28", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D6BC325F-2058-42EC-A622-79DDDBAE9D28/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:11:51+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "70F33937-681F-4BBB-90ED-DB3715ED6BF6", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/70F33937-681F-4BBB-90ED-DB3715ED6BF6/view-source"}], "score": 25, "updated_at": "2024-08-13T19:27:18+00:00"}, {"answer_html": "

Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is "good enough" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as "selective pressure" refers to selection for reproduction specifically.

\n

https://seer.cancer.gov/statfacts/html/melan.html

\n", "answer_id": 115176, "answer_text": "Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is \"good enough\" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as \"selective pressure\" refers to selection for reproduction specifically.\n\n\n\n\nhttps://seer.cancer.gov/statfacts/html/melan.html (https://seer.cancer.gov/statfacts/html/melan.html)", "answer_url": "https://biology.stackexchange.com/a/115176", "author": "Nuclear Hoagie", "author_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:41:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Nuclear Hoagie", "profile_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "user_type": "registered"}, "created_at": "2024-08-13T19:41:14+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E020D650-7DF7-42B4-A813-C07287A63A06", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E020D650-7DF7-42B4-A813-C07287A63A06/view-source"}], "score": 53, "updated_at": "2024-08-13T19:41:14+00:00"}, {"answer_html": "

Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.

\n
    \n

  • Melanin Production:

    \n

    Melanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.

    \n
    • \n

  • Epidermal Thickening:

    \n

    Another defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.

    \n
    • \n

  • DNA Repair Mechanisms:

    \n

    The human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.

    \n
    • \n

  • Inflammatory Response:

    \n

    The acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.

    \n
    • \n
\n", "answer_id": 115181, "answer_text": "Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.\n\n\n\n\n\n\n\nMelanin Production:\n\n\n\n\nMelanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.\n\n\n\n\n\n\n\n\n\nEpidermal Thickening:\n\n\n\n\nAnother defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.\n\n\n\n\n\n\n\n\n\nDNA Repair Mechanisms:\n\n\n\n\nThe human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase (https://en.wikipedia.org/wiki/Photolyase) repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.\n\n\n\n\n\n\n\n\n\nInflammatory Response:\n\n\n\n\nThe acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.", "answer_url": "https://biology.stackexchange.com/a/115181", "author": "Chris", "author_url": "https://biology.stackexchange.com/users/5144/chris", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T08:30:31+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-14T08:30:31+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "203DF798-60CE-4A5B-942C-F9066DA8BFEC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/203DF798-60CE-4A5B-942C-F9066DA8BFEC/view-source"}], "score": 12, "updated_at": "2024-08-14T08:30:31+00:00"}, {"answer_html": "

To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.

\n", "answer_id": 115184, "answer_text": "To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.", "answer_url": "https://biology.stackexchange.com/a/115184", "author": "Crazymoomin", "author_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T14:44:29+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:44:29+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "34124B84-4C54-404B-BD68-361FC0160072", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/34124B84-4C54-404B-BD68-361FC0160072/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:50:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "90C8EF4F-C093-46C8-845F-34F1CDBE3D76", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/90C8EF4F-C093-46C8-845F-34F1CDBE3D76/view-source"}], "score": 4, "updated_at": "2024-08-14T14:50:43+00:00"}, {"answer_html": "

There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia. It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.

\n

I recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...

\n", "answer_id": 115189, "answer_text": "There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia (https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/). It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.\n\n\n\n\nI recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...", "answer_url": "https://biology.stackexchange.com/a/115189", "author": "Simon Crase", "author_url": "https://biology.stackexchange.com/users/60999/simon-crase", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T06:47:00+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-15T06:47:00+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "06C3F178-4AC5-4566-87E9-1B7866F7776D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/06C3F178-4AC5-4566-87E9-1B7866F7776D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-16T00:56:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E63DE613-A666-4300-87F8-B4DFC7B8CA59", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E63DE613-A666-4300-87F8-B4DFC7B8CA59/view-source"}], "score": 5, "updated_at": "2024-08-16T00:56:43+00:00"}, {"answer_html": "

The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.

\n

Now if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.

\n

Also careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.

\n", "answer_id": 115195, "answer_text": "The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.\n\n\n\n\nNow if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.\n\n\n\n\nAlso careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.", "answer_url": "https://biology.stackexchange.com/a/115195", "author": "gnasher729", "author_url": "https://biology.stackexchange.com/users/10077/gnasher729", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T20:13:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gnasher729", "profile_url": "https://biology.stackexchange.com/users/10077/gnasher729", "user_type": "registered"}, "created_at": "2024-08-15T20:13:04+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B98FEE88-41D0-4F31-8B9A-0D171031B546", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B98FEE88-41D0-4F31-8B9A-0D171031B546/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:10:35+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "261F1C4D-1ECD-48FA-8442-CED29305E440", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/261F1C4D-1ECD-48FA-8442-CED29305E440/view-source"}], "score": 8, "updated_at": "2024-08-15T20:13:04+00:00"}, {"answer_html": "

Because cancer wasn't likely to be one's cause of death. Look at this comparison between 1900 and 2022:

\n

\"enter

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Cancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s:

\n
\n

Cancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’

\n
\n

Evolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:

\n
\n

Devil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.

\n

...

\n

In 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.

\n
\n", "answer_id": 115199, "answer_text": "Because cancer wasn't likely to be one's cause of death. Look at this comparison (https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/) between 1900 and 2022:\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/pzQsLWkf.png] (https://i.sstatic.net/pzQsLWkf.png)\n\n\n\n\nCancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/):\n\n\n\n\n\n\n\nCancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’\n\n\n\n\n\n\n\nEvolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence (https://en.wikipedia.org/wiki/Devil_facial_tumour_disease) from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:\n\n\n\n\n\n\n\nDevil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.\n\n\n\n\n...\n\n\n\n\nIn 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.", "answer_url": "https://biology.stackexchange.com/a/115199", "author": "MilkLife", "author_url": "https://biology.stackexchange.com/users/5492/milklife", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-16T23:47:16+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MilkLife", "profile_url": "https://biology.stackexchange.com/users/5492/milklife", "user_type": "registered"}, "created_at": "2024-08-16T23:47:16+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "FA30453C-1E93-40D2-9D07-DDC697CEF2EA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/FA30453C-1E93-40D2-9D07-DDC697CEF2EA/view-source"}], "score": 0, "updated_at": "2024-08-16T23:47:16+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/Devil_facial_tumour_disease", "https://en.wikipedia.org/wiki/Fitzpatrick_scale", "https://en.wikipedia.org/wiki/Photolyase", "https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/", "https://i.sstatic.net/pzQsLWkf.png", "https://seer.cancer.gov/statfacts/html/melan.html", "https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d", "https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/", "https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:05.762873+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/04ed2aa314c5d877c5d79e42620d1f80988a21de8d429a22d8c6af5280cfd6e8_0.json", "raw_sha256": "6dd355b99094bb9ba2c965ee7dd7b0e95f92a8078d3b2b85b64196fcb6cf717c", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=5&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "gaazkam", "question_author_url": "https://biology.stackexchange.com/users/15177/gaazkam", "question_author_user_type": "registered", "question_created_at": "2024-08-13T05:20:41+00:00", "question_html": "

Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.

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Especially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.

\n

Native to Europe are phototypes I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?

\n

So, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.

\n

Yet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.

\n

Where is the error in my thinking?

\n", "question_id": 115170, "question_license": "CC BY-SA 4.0", "question_score": 17, "question_text": "Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.\n\n\n\n\nEspecially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.\n\n\n\n\nNative to Europe are phototypes (https://en.wikipedia.org/wiki/Fitzpatrick_scale) I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?\n\n\n\n\nSo, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.\n\n\n\n\nYet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.\n\n\n\n\nWhere is the error in my thinking?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:20:41+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "828DB692-880A-4BBF-AD67-13CF3E06456A", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/828DB692-880A-4BBF-AD67-13CF3E06456A/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:26:09+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2024-08-14T08:31:47+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D/view-source"}, {"content_license": null, "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-15T13:36:46+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:12:55+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E7A91925-4841-42A6-89A7-24963075C01F", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/E7A91925-4841-42A6-89A7-24963075C01F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Basil Bourque", "profile_url": "https://biology.stackexchange.com/users/32521/basil-bourque", "user_type": "registered"}, "created_at": "2024-09-02T17:31:11+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "C86E2648-B494-446F-A6EC-EE52D185A1B7", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/C86E2648-B494-446F-A6EC-EE52D185A1B7/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/115170/why-did-evolution-fail-to-protect-humans-against-sun", "split": "test", "split_group": "503625bcfe466937a26431096aee38aeab3e6012cf849f4c5706c832b5d6195c", "tags": ["human-evolution", "skin", "melanin"], "thread_id": "biology:115170", "title": "Why did evolution fail to protect humans against sun?"}} {"citation_context": "ist of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence (https://en.wikipedia.org/wiki/Devil_facial_tumour_disease) from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve v", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Devil_facial_tumour_disease", "kind": "external_url", "post_id": 115199, "post_url": "https://biology.stackexchange.com/a/115199", "product": "citations", "record_id": "Scientific-Citation-Graph:094c2f71a76f6aaccf0bfcfc", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.

\n
\n

Where is the error in my thinking?

\n
\n

The error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.

\n

Evolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable "deficiencies" in humans that make us "imperfectly evolved".

\n

That we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any "reason" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable. If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)

\n

If we're "good enough" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.

\n

Also, somewhat aside to your question are the benefits of UV light to humans. We know that UVB allows us to synthesize Vitamin D, which is critical for survival. There are other possible benefits to UV light as well. It might well happen that we'll discover more concrete benefits.

\n

The question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.

\n", "answer_id": 115175, "answer_text": "I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.\n\n\n\n\n\n\n\nWhere is the error in my thinking?\n\n\n\n\n\n\n\nThe error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.\n\n\n\n\nEvolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable \"deficiencies\" in humans that make us \"imperfectly evolved\".\n\n\n\n\nThat we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any \"reason\" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable (https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/). If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)\n\n\n\n\nIf we're \"good enough\" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.\n\n\n\n\nAlso, somewhat aside to your question are the benefits of UV light to humans (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). We know that UVB allows us to synthesize Vitamin D, which is critical for survival. (https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d) There are other possible benefits to UV light as well (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). It might well happen that we'll discover more concrete benefits.\n\n\n\n\nThe question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.", "answer_url": "https://biology.stackexchange.com/a/115175", "author": "anongoodnurse", "author_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:19:48+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:19:48+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B27F09D5-F235-448E-AFF2-AD09B10346FA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B27F09D5-F235-448E-AFF2-AD09B10346FA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:27:18+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "D6BC325F-2058-42EC-A622-79DDDBAE9D28", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D6BC325F-2058-42EC-A622-79DDDBAE9D28/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:11:51+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "70F33937-681F-4BBB-90ED-DB3715ED6BF6", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/70F33937-681F-4BBB-90ED-DB3715ED6BF6/view-source"}], "score": 25, "updated_at": "2024-08-13T19:27:18+00:00"}, {"answer_html": "

Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is "good enough" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as "selective pressure" refers to selection for reproduction specifically.

\n

https://seer.cancer.gov/statfacts/html/melan.html

\n", "answer_id": 115176, "answer_text": "Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is \"good enough\" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as \"selective pressure\" refers to selection for reproduction specifically.\n\n\n\n\nhttps://seer.cancer.gov/statfacts/html/melan.html (https://seer.cancer.gov/statfacts/html/melan.html)", "answer_url": "https://biology.stackexchange.com/a/115176", "author": "Nuclear Hoagie", "author_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:41:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Nuclear Hoagie", "profile_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "user_type": "registered"}, "created_at": "2024-08-13T19:41:14+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E020D650-7DF7-42B4-A813-C07287A63A06", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E020D650-7DF7-42B4-A813-C07287A63A06/view-source"}], "score": 53, "updated_at": "2024-08-13T19:41:14+00:00"}, {"answer_html": "

Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.

\n
    \n

  • Melanin Production:

    \n

    Melanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.

    \n
    • \n

  • Epidermal Thickening:

    \n

    Another defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.

    \n
    • \n

  • DNA Repair Mechanisms:

    \n

    The human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.

    \n
    • \n

  • Inflammatory Response:

    \n

    The acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.

    \n
    • \n
\n", "answer_id": 115181, "answer_text": "Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.\n\n\n\n\n\n\n\nMelanin Production:\n\n\n\n\nMelanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.\n\n\n\n\n\n\n\n\n\nEpidermal Thickening:\n\n\n\n\nAnother defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.\n\n\n\n\n\n\n\n\n\nDNA Repair Mechanisms:\n\n\n\n\nThe human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase (https://en.wikipedia.org/wiki/Photolyase) repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.\n\n\n\n\n\n\n\n\n\nInflammatory Response:\n\n\n\n\nThe acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.", "answer_url": "https://biology.stackexchange.com/a/115181", "author": "Chris", "author_url": "https://biology.stackexchange.com/users/5144/chris", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T08:30:31+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-14T08:30:31+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "203DF798-60CE-4A5B-942C-F9066DA8BFEC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/203DF798-60CE-4A5B-942C-F9066DA8BFEC/view-source"}], "score": 12, "updated_at": "2024-08-14T08:30:31+00:00"}, {"answer_html": "

To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.

\n", "answer_id": 115184, "answer_text": "To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.", "answer_url": "https://biology.stackexchange.com/a/115184", "author": "Crazymoomin", "author_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T14:44:29+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:44:29+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "34124B84-4C54-404B-BD68-361FC0160072", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/34124B84-4C54-404B-BD68-361FC0160072/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:50:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "90C8EF4F-C093-46C8-845F-34F1CDBE3D76", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/90C8EF4F-C093-46C8-845F-34F1CDBE3D76/view-source"}], "score": 4, "updated_at": "2024-08-14T14:50:43+00:00"}, {"answer_html": "

There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia. It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.

\n

I recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...

\n", "answer_id": 115189, "answer_text": "There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia (https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/). It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.\n\n\n\n\nI recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...", "answer_url": "https://biology.stackexchange.com/a/115189", "author": "Simon Crase", "author_url": "https://biology.stackexchange.com/users/60999/simon-crase", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T06:47:00+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-15T06:47:00+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "06C3F178-4AC5-4566-87E9-1B7866F7776D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/06C3F178-4AC5-4566-87E9-1B7866F7776D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-16T00:56:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E63DE613-A666-4300-87F8-B4DFC7B8CA59", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E63DE613-A666-4300-87F8-B4DFC7B8CA59/view-source"}], "score": 5, "updated_at": "2024-08-16T00:56:43+00:00"}, {"answer_html": "

The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.

\n

Now if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.

\n

Also careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.

\n", "answer_id": 115195, "answer_text": "The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.\n\n\n\n\nNow if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.\n\n\n\n\nAlso careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.", "answer_url": "https://biology.stackexchange.com/a/115195", "author": "gnasher729", "author_url": "https://biology.stackexchange.com/users/10077/gnasher729", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T20:13:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gnasher729", "profile_url": "https://biology.stackexchange.com/users/10077/gnasher729", "user_type": "registered"}, "created_at": "2024-08-15T20:13:04+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B98FEE88-41D0-4F31-8B9A-0D171031B546", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B98FEE88-41D0-4F31-8B9A-0D171031B546/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:10:35+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "261F1C4D-1ECD-48FA-8442-CED29305E440", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/261F1C4D-1ECD-48FA-8442-CED29305E440/view-source"}], "score": 8, "updated_at": "2024-08-15T20:13:04+00:00"}, {"answer_html": "

Because cancer wasn't likely to be one's cause of death. Look at this comparison between 1900 and 2022:

\n

\"enter

\n

Cancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s:

\n
\n

Cancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’

\n
\n

Evolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:

\n
\n

Devil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.

\n

...

\n

In 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.

\n
\n", "answer_id": 115199, "answer_text": "Because cancer wasn't likely to be one's cause of death. Look at this comparison (https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/) between 1900 and 2022:\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/pzQsLWkf.png] (https://i.sstatic.net/pzQsLWkf.png)\n\n\n\n\nCancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/):\n\n\n\n\n\n\n\nCancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’\n\n\n\n\n\n\n\nEvolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence (https://en.wikipedia.org/wiki/Devil_facial_tumour_disease) from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:\n\n\n\n\n\n\n\nDevil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.\n\n\n\n\n...\n\n\n\n\nIn 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.", "answer_url": "https://biology.stackexchange.com/a/115199", "author": "MilkLife", "author_url": "https://biology.stackexchange.com/users/5492/milklife", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-16T23:47:16+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MilkLife", "profile_url": "https://biology.stackexchange.com/users/5492/milklife", "user_type": "registered"}, "created_at": "2024-08-16T23:47:16+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "FA30453C-1E93-40D2-9D07-DDC697CEF2EA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/FA30453C-1E93-40D2-9D07-DDC697CEF2EA/view-source"}], "score": 0, "updated_at": "2024-08-16T23:47:16+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/Devil_facial_tumour_disease", "https://en.wikipedia.org/wiki/Fitzpatrick_scale", "https://en.wikipedia.org/wiki/Photolyase", "https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/", "https://i.sstatic.net/pzQsLWkf.png", "https://seer.cancer.gov/statfacts/html/melan.html", "https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d", "https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/", "https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:05.762873+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/04ed2aa314c5d877c5d79e42620d1f80988a21de8d429a22d8c6af5280cfd6e8_0.json", "raw_sha256": "6dd355b99094bb9ba2c965ee7dd7b0e95f92a8078d3b2b85b64196fcb6cf717c", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=5&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "gaazkam", "question_author_url": "https://biology.stackexchange.com/users/15177/gaazkam", "question_author_user_type": "registered", "question_created_at": "2024-08-13T05:20:41+00:00", "question_html": "

Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.

\n

Especially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.

\n

Native to Europe are phototypes I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?

\n

So, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.

\n

Yet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.

\n

Where is the error in my thinking?

\n", "question_id": 115170, "question_license": "CC BY-SA 4.0", "question_score": 17, "question_text": "Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.\n\n\n\n\nEspecially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.\n\n\n\n\nNative to Europe are phototypes (https://en.wikipedia.org/wiki/Fitzpatrick_scale) I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?\n\n\n\n\nSo, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.\n\n\n\n\nYet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.\n\n\n\n\nWhere is the error in my thinking?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:20:41+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "828DB692-880A-4BBF-AD67-13CF3E06456A", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/828DB692-880A-4BBF-AD67-13CF3E06456A/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:26:09+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2024-08-14T08:31:47+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D/view-source"}, {"content_license": null, "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-15T13:36:46+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:12:55+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E7A91925-4841-42A6-89A7-24963075C01F", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/E7A91925-4841-42A6-89A7-24963075C01F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Basil Bourque", "profile_url": "https://biology.stackexchange.com/users/32521/basil-bourque", "user_type": "registered"}, "created_at": "2024-09-02T17:31:11+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "C86E2648-B494-446F-A6EC-EE52D185A1B7", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/C86E2648-B494-446F-A6EC-EE52D185A1B7/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/115170/why-did-evolution-fail-to-protect-humans-against-sun", "split": "test", "split_group": "503625bcfe466937a26431096aee38aeab3e6012cf849f4c5706c832b5d6195c", "tags": ["human-evolution", "skin", "melanin"], "thread_id": "biology:115170", "title": "Why did evolution fail to protect humans against sun?"}} {"citation_context": "auses-of-death-in-the-us/) between 1900 and 2022:\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/pzQsLWkf.png] (https://i.sstatic.net/pzQsLWkf.png)\n\n\n\n\nCancer used to be the cause of 5% of human deaths. Nowada", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://i.sstatic.net/pzQsLWkf.png", "kind": "external_url", "post_id": 115199, "post_url": "https://biology.stackexchange.com/a/115199", "product": "citations", "record_id": "Scientific-Citation-Graph:d43dc1423870e39b11037525", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.

\n
\n

Where is the error in my thinking?

\n
\n

The error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.

\n

Evolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable "deficiencies" in humans that make us "imperfectly evolved".

\n

That we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any "reason" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable. If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)

\n

If we're "good enough" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.

\n

Also, somewhat aside to your question are the benefits of UV light to humans. We know that UVB allows us to synthesize Vitamin D, which is critical for survival. There are other possible benefits to UV light as well. It might well happen that we'll discover more concrete benefits.

\n

The question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.

\n", "answer_id": 115175, "answer_text": "I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.\n\n\n\n\n\n\n\nWhere is the error in my thinking?\n\n\n\n\n\n\n\nThe error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.\n\n\n\n\nEvolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable \"deficiencies\" in humans that make us \"imperfectly evolved\".\n\n\n\n\nThat we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any \"reason\" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable (https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/). If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)\n\n\n\n\nIf we're \"good enough\" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.\n\n\n\n\nAlso, somewhat aside to your question are the benefits of UV light to humans (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). We know that UVB allows us to synthesize Vitamin D, which is critical for survival. (https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d) There are other possible benefits to UV light as well (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). It might well happen that we'll discover more concrete benefits.\n\n\n\n\nThe question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.", "answer_url": "https://biology.stackexchange.com/a/115175", "author": "anongoodnurse", "author_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:19:48+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:19:48+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B27F09D5-F235-448E-AFF2-AD09B10346FA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B27F09D5-F235-448E-AFF2-AD09B10346FA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:27:18+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "D6BC325F-2058-42EC-A622-79DDDBAE9D28", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D6BC325F-2058-42EC-A622-79DDDBAE9D28/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:11:51+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "70F33937-681F-4BBB-90ED-DB3715ED6BF6", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/70F33937-681F-4BBB-90ED-DB3715ED6BF6/view-source"}], "score": 25, "updated_at": "2024-08-13T19:27:18+00:00"}, {"answer_html": "

Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is "good enough" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as "selective pressure" refers to selection for reproduction specifically.

\n

https://seer.cancer.gov/statfacts/html/melan.html

\n", "answer_id": 115176, "answer_text": "Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is \"good enough\" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as \"selective pressure\" refers to selection for reproduction specifically.\n\n\n\n\nhttps://seer.cancer.gov/statfacts/html/melan.html (https://seer.cancer.gov/statfacts/html/melan.html)", "answer_url": "https://biology.stackexchange.com/a/115176", "author": "Nuclear Hoagie", "author_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:41:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Nuclear Hoagie", "profile_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "user_type": "registered"}, "created_at": "2024-08-13T19:41:14+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E020D650-7DF7-42B4-A813-C07287A63A06", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E020D650-7DF7-42B4-A813-C07287A63A06/view-source"}], "score": 53, "updated_at": "2024-08-13T19:41:14+00:00"}, {"answer_html": "

Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.

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    \n

  • Melanin Production:

    \n

    Melanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.

    \n
    • \n

  • Epidermal Thickening:

    \n

    Another defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.

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    • \n

  • DNA Repair Mechanisms:

    \n

    The human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.

    \n
    • \n

  • Inflammatory Response:

    \n

    The acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.

    \n
    • \n
\n", "answer_id": 115181, "answer_text": "Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.\n\n\n\n\n\n\n\nMelanin Production:\n\n\n\n\nMelanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.\n\n\n\n\n\n\n\n\n\nEpidermal Thickening:\n\n\n\n\nAnother defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.\n\n\n\n\n\n\n\n\n\nDNA Repair Mechanisms:\n\n\n\n\nThe human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase (https://en.wikipedia.org/wiki/Photolyase) repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.\n\n\n\n\n\n\n\n\n\nInflammatory Response:\n\n\n\n\nThe acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.", "answer_url": "https://biology.stackexchange.com/a/115181", "author": "Chris", "author_url": "https://biology.stackexchange.com/users/5144/chris", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T08:30:31+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-14T08:30:31+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "203DF798-60CE-4A5B-942C-F9066DA8BFEC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/203DF798-60CE-4A5B-942C-F9066DA8BFEC/view-source"}], "score": 12, "updated_at": "2024-08-14T08:30:31+00:00"}, {"answer_html": "

To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.

\n", "answer_id": 115184, "answer_text": "To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.", "answer_url": "https://biology.stackexchange.com/a/115184", "author": "Crazymoomin", "author_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T14:44:29+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:44:29+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "34124B84-4C54-404B-BD68-361FC0160072", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/34124B84-4C54-404B-BD68-361FC0160072/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:50:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "90C8EF4F-C093-46C8-845F-34F1CDBE3D76", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/90C8EF4F-C093-46C8-845F-34F1CDBE3D76/view-source"}], "score": 4, "updated_at": "2024-08-14T14:50:43+00:00"}, {"answer_html": "

There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia. It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.

\n

I recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...

\n", "answer_id": 115189, "answer_text": "There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia (https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/). It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.\n\n\n\n\nI recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...", "answer_url": "https://biology.stackexchange.com/a/115189", "author": "Simon Crase", "author_url": "https://biology.stackexchange.com/users/60999/simon-crase", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T06:47:00+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-15T06:47:00+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "06C3F178-4AC5-4566-87E9-1B7866F7776D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/06C3F178-4AC5-4566-87E9-1B7866F7776D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-16T00:56:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E63DE613-A666-4300-87F8-B4DFC7B8CA59", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E63DE613-A666-4300-87F8-B4DFC7B8CA59/view-source"}], "score": 5, "updated_at": "2024-08-16T00:56:43+00:00"}, {"answer_html": "

The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.

\n

Now if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.

\n

Also careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.

\n", "answer_id": 115195, "answer_text": "The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.\n\n\n\n\nNow if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.\n\n\n\n\nAlso careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.", "answer_url": "https://biology.stackexchange.com/a/115195", "author": "gnasher729", "author_url": "https://biology.stackexchange.com/users/10077/gnasher729", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T20:13:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gnasher729", "profile_url": "https://biology.stackexchange.com/users/10077/gnasher729", "user_type": "registered"}, "created_at": "2024-08-15T20:13:04+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B98FEE88-41D0-4F31-8B9A-0D171031B546", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B98FEE88-41D0-4F31-8B9A-0D171031B546/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:10:35+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "261F1C4D-1ECD-48FA-8442-CED29305E440", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/261F1C4D-1ECD-48FA-8442-CED29305E440/view-source"}], "score": 8, "updated_at": "2024-08-15T20:13:04+00:00"}, {"answer_html": "

Because cancer wasn't likely to be one's cause of death. Look at this comparison between 1900 and 2022:

\n

\"enter

\n

Cancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s:

\n
\n

Cancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’

\n
\n

Evolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:

\n
\n

Devil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.

\n

...

\n

In 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.

\n
\n", "answer_id": 115199, "answer_text": "Because cancer wasn't likely to be one's cause of death. Look at this comparison (https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/) between 1900 and 2022:\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/pzQsLWkf.png] (https://i.sstatic.net/pzQsLWkf.png)\n\n\n\n\nCancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/):\n\n\n\n\n\n\n\nCancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’\n\n\n\n\n\n\n\nEvolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence (https://en.wikipedia.org/wiki/Devil_facial_tumour_disease) from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:\n\n\n\n\n\n\n\nDevil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.\n\n\n\n\n...\n\n\n\n\nIn 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.", "answer_url": "https://biology.stackexchange.com/a/115199", "author": "MilkLife", "author_url": "https://biology.stackexchange.com/users/5492/milklife", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-16T23:47:16+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MilkLife", "profile_url": "https://biology.stackexchange.com/users/5492/milklife", "user_type": "registered"}, "created_at": "2024-08-16T23:47:16+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "FA30453C-1E93-40D2-9D07-DDC697CEF2EA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/FA30453C-1E93-40D2-9D07-DDC697CEF2EA/view-source"}], "score": 0, "updated_at": "2024-08-16T23:47:16+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/Devil_facial_tumour_disease", "https://en.wikipedia.org/wiki/Fitzpatrick_scale", "https://en.wikipedia.org/wiki/Photolyase", "https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/", "https://i.sstatic.net/pzQsLWkf.png", "https://seer.cancer.gov/statfacts/html/melan.html", "https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d", "https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/", "https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:05.762873+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/04ed2aa314c5d877c5d79e42620d1f80988a21de8d429a22d8c6af5280cfd6e8_0.json", "raw_sha256": "6dd355b99094bb9ba2c965ee7dd7b0e95f92a8078d3b2b85b64196fcb6cf717c", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=5&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "gaazkam", "question_author_url": "https://biology.stackexchange.com/users/15177/gaazkam", "question_author_user_type": "registered", "question_created_at": "2024-08-13T05:20:41+00:00", "question_html": "

Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.

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Especially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.

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Native to Europe are phototypes I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?

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So, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.

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Yet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.

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Where is the error in my thinking?

\n", "question_id": 115170, "question_license": "CC BY-SA 4.0", "question_score": 17, "question_text": "Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.\n\n\n\n\nEspecially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.\n\n\n\n\nNative to Europe are phototypes (https://en.wikipedia.org/wiki/Fitzpatrick_scale) I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?\n\n\n\n\nSo, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.\n\n\n\n\nYet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.\n\n\n\n\nWhere is the error in my thinking?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:20:41+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "828DB692-880A-4BBF-AD67-13CF3E06456A", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/828DB692-880A-4BBF-AD67-13CF3E06456A/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:26:09+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2024-08-14T08:31:47+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D/view-source"}, {"content_license": null, "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-15T13:36:46+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:12:55+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E7A91925-4841-42A6-89A7-24963075C01F", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/E7A91925-4841-42A6-89A7-24963075C01F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Basil Bourque", "profile_url": "https://biology.stackexchange.com/users/32521/basil-bourque", "user_type": "registered"}, "created_at": "2024-09-02T17:31:11+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "C86E2648-B494-446F-A6EC-EE52D185A1B7", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/C86E2648-B494-446F-A6EC-EE52D185A1B7/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/115170/why-did-evolution-fail-to-protect-humans-against-sun", "split": "test", "split_group": "503625bcfe466937a26431096aee38aeab3e6012cf849f4c5706c832b5d6195c", "tags": ["human-evolution", "skin", "melanin"], "thread_id": "biology:115170", "title": "Why did evolution fail to protect humans against sun?"}} {"citation_context": "uering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/):\n\n\n\n\n\n\n\nCancers were relatively rare. While the Victorians did not possess sophisticated diagnosti", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/", "kind": "external_url", "post_id": 115199, "post_url": "https://biology.stackexchange.com/a/115199", "product": "citations", "record_id": "Scientific-Citation-Graph:84bc23a5aa7579f67c5fcfe7", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.

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Where is the error in my thinking?

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The error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.

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Evolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable "deficiencies" in humans that make us "imperfectly evolved".

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That we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any "reason" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable. If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)

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If we're "good enough" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.

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Also, somewhat aside to your question are the benefits of UV light to humans. We know that UVB allows us to synthesize Vitamin D, which is critical for survival. There are other possible benefits to UV light as well. It might well happen that we'll discover more concrete benefits.

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The question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.

\n", "answer_id": 115175, "answer_text": "I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.\n\n\n\n\n\n\n\nWhere is the error in my thinking?\n\n\n\n\n\n\n\nThe error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.\n\n\n\n\nEvolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable \"deficiencies\" in humans that make us \"imperfectly evolved\".\n\n\n\n\nThat we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any \"reason\" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable (https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/). If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)\n\n\n\n\nIf we're \"good enough\" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.\n\n\n\n\nAlso, somewhat aside to your question are the benefits of UV light to humans (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). We know that UVB allows us to synthesize Vitamin D, which is critical for survival. (https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d) There are other possible benefits to UV light as well (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). It might well happen that we'll discover more concrete benefits.\n\n\n\n\nThe question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.", "answer_url": "https://biology.stackexchange.com/a/115175", "author": "anongoodnurse", "author_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:19:48+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:19:48+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B27F09D5-F235-448E-AFF2-AD09B10346FA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B27F09D5-F235-448E-AFF2-AD09B10346FA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:27:18+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "D6BC325F-2058-42EC-A622-79DDDBAE9D28", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D6BC325F-2058-42EC-A622-79DDDBAE9D28/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:11:51+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "70F33937-681F-4BBB-90ED-DB3715ED6BF6", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/70F33937-681F-4BBB-90ED-DB3715ED6BF6/view-source"}], "score": 25, "updated_at": "2024-08-13T19:27:18+00:00"}, {"answer_html": "

Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is "good enough" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as "selective pressure" refers to selection for reproduction specifically.

\n

https://seer.cancer.gov/statfacts/html/melan.html

\n", "answer_id": 115176, "answer_text": "Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is \"good enough\" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as \"selective pressure\" refers to selection for reproduction specifically.\n\n\n\n\nhttps://seer.cancer.gov/statfacts/html/melan.html (https://seer.cancer.gov/statfacts/html/melan.html)", "answer_url": "https://biology.stackexchange.com/a/115176", "author": "Nuclear Hoagie", "author_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:41:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Nuclear Hoagie", "profile_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "user_type": "registered"}, "created_at": "2024-08-13T19:41:14+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E020D650-7DF7-42B4-A813-C07287A63A06", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E020D650-7DF7-42B4-A813-C07287A63A06/view-source"}], "score": 53, "updated_at": "2024-08-13T19:41:14+00:00"}, {"answer_html": "

Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.

\n
    \n

  • Melanin Production:

    \n

    Melanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.

    \n
    • \n

  • Epidermal Thickening:

    \n

    Another defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.

    \n
    • \n

  • DNA Repair Mechanisms:

    \n

    The human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.

    \n
    • \n

  • Inflammatory Response:

    \n

    The acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.

    \n
    • \n
\n", "answer_id": 115181, "answer_text": "Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.\n\n\n\n\n\n\n\nMelanin Production:\n\n\n\n\nMelanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.\n\n\n\n\n\n\n\n\n\nEpidermal Thickening:\n\n\n\n\nAnother defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.\n\n\n\n\n\n\n\n\n\nDNA Repair Mechanisms:\n\n\n\n\nThe human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase (https://en.wikipedia.org/wiki/Photolyase) repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.\n\n\n\n\n\n\n\n\n\nInflammatory Response:\n\n\n\n\nThe acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.", "answer_url": "https://biology.stackexchange.com/a/115181", "author": "Chris", "author_url": "https://biology.stackexchange.com/users/5144/chris", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T08:30:31+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-14T08:30:31+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "203DF798-60CE-4A5B-942C-F9066DA8BFEC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/203DF798-60CE-4A5B-942C-F9066DA8BFEC/view-source"}], "score": 12, "updated_at": "2024-08-14T08:30:31+00:00"}, {"answer_html": "

To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.

\n", "answer_id": 115184, "answer_text": "To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.", "answer_url": "https://biology.stackexchange.com/a/115184", "author": "Crazymoomin", "author_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T14:44:29+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:44:29+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "34124B84-4C54-404B-BD68-361FC0160072", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/34124B84-4C54-404B-BD68-361FC0160072/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:50:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "90C8EF4F-C093-46C8-845F-34F1CDBE3D76", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/90C8EF4F-C093-46C8-845F-34F1CDBE3D76/view-source"}], "score": 4, "updated_at": "2024-08-14T14:50:43+00:00"}, {"answer_html": "

There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia. It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.

\n

I recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...

\n", "answer_id": 115189, "answer_text": "There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia (https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/). It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.\n\n\n\n\nI recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...", "answer_url": "https://biology.stackexchange.com/a/115189", "author": "Simon Crase", "author_url": "https://biology.stackexchange.com/users/60999/simon-crase", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T06:47:00+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-15T06:47:00+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "06C3F178-4AC5-4566-87E9-1B7866F7776D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/06C3F178-4AC5-4566-87E9-1B7866F7776D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-16T00:56:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E63DE613-A666-4300-87F8-B4DFC7B8CA59", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E63DE613-A666-4300-87F8-B4DFC7B8CA59/view-source"}], "score": 5, "updated_at": "2024-08-16T00:56:43+00:00"}, {"answer_html": "

The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.

\n

Now if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.

\n

Also careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.

\n", "answer_id": 115195, "answer_text": "The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.\n\n\n\n\nNow if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.\n\n\n\n\nAlso careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.", "answer_url": "https://biology.stackexchange.com/a/115195", "author": "gnasher729", "author_url": "https://biology.stackexchange.com/users/10077/gnasher729", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T20:13:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gnasher729", "profile_url": "https://biology.stackexchange.com/users/10077/gnasher729", "user_type": "registered"}, "created_at": "2024-08-15T20:13:04+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B98FEE88-41D0-4F31-8B9A-0D171031B546", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B98FEE88-41D0-4F31-8B9A-0D171031B546/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:10:35+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "261F1C4D-1ECD-48FA-8442-CED29305E440", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/261F1C4D-1ECD-48FA-8442-CED29305E440/view-source"}], "score": 8, "updated_at": "2024-08-15T20:13:04+00:00"}, {"answer_html": "

Because cancer wasn't likely to be one's cause of death. Look at this comparison between 1900 and 2022:

\n

\"enter

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Cancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s:

\n
\n

Cancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’

\n
\n

Evolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:

\n
\n

Devil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.

\n

...

\n

In 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.

\n
\n", "answer_id": 115199, "answer_text": "Because cancer wasn't likely to be one's cause of death. Look at this comparison (https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/) between 1900 and 2022:\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/pzQsLWkf.png] (https://i.sstatic.net/pzQsLWkf.png)\n\n\n\n\nCancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/):\n\n\n\n\n\n\n\nCancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’\n\n\n\n\n\n\n\nEvolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence (https://en.wikipedia.org/wiki/Devil_facial_tumour_disease) from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:\n\n\n\n\n\n\n\nDevil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.\n\n\n\n\n...\n\n\n\n\nIn 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.", "answer_url": "https://biology.stackexchange.com/a/115199", "author": "MilkLife", "author_url": "https://biology.stackexchange.com/users/5492/milklife", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-16T23:47:16+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MilkLife", "profile_url": "https://biology.stackexchange.com/users/5492/milklife", "user_type": "registered"}, "created_at": "2024-08-16T23:47:16+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "FA30453C-1E93-40D2-9D07-DDC697CEF2EA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/FA30453C-1E93-40D2-9D07-DDC697CEF2EA/view-source"}], "score": 0, "updated_at": "2024-08-16T23:47:16+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/Devil_facial_tumour_disease", "https://en.wikipedia.org/wiki/Fitzpatrick_scale", "https://en.wikipedia.org/wiki/Photolyase", "https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/", "https://i.sstatic.net/pzQsLWkf.png", "https://seer.cancer.gov/statfacts/html/melan.html", "https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d", "https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/", "https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:05.762873+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/04ed2aa314c5d877c5d79e42620d1f80988a21de8d429a22d8c6af5280cfd6e8_0.json", "raw_sha256": "6dd355b99094bb9ba2c965ee7dd7b0e95f92a8078d3b2b85b64196fcb6cf717c", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=5&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "gaazkam", "question_author_url": "https://biology.stackexchange.com/users/15177/gaazkam", "question_author_user_type": "registered", "question_created_at": "2024-08-13T05:20:41+00:00", "question_html": "

Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.

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Especially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.

\n

Native to Europe are phototypes I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?

\n

So, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.

\n

Yet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.

\n

Where is the error in my thinking?

\n", "question_id": 115170, "question_license": "CC BY-SA 4.0", "question_score": 17, "question_text": "Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.\n\n\n\n\nEspecially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.\n\n\n\n\nNative to Europe are phototypes (https://en.wikipedia.org/wiki/Fitzpatrick_scale) I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?\n\n\n\n\nSo, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.\n\n\n\n\nYet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.\n\n\n\n\nWhere is the error in my thinking?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:20:41+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "828DB692-880A-4BBF-AD67-13CF3E06456A", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/828DB692-880A-4BBF-AD67-13CF3E06456A/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:26:09+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2024-08-14T08:31:47+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D/view-source"}, {"content_license": null, "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-15T13:36:46+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:12:55+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E7A91925-4841-42A6-89A7-24963075C01F", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/E7A91925-4841-42A6-89A7-24963075C01F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Basil Bourque", "profile_url": "https://biology.stackexchange.com/users/32521/basil-bourque", "user_type": "registered"}, "created_at": "2024-09-02T17:31:11+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "C86E2648-B494-446F-A6EC-EE52D185A1B7", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/C86E2648-B494-446F-A6EC-EE52D185A1B7/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/115170/why-did-evolution-fail-to-protect-humans-against-sun", "split": "test", "split_group": "503625bcfe466937a26431096aee38aeab3e6012cf849f4c5706c832b5d6195c", "tags": ["human-evolution", "skin", "melanin"], "thread_id": "biology:115170", "title": "Why did evolution fail to protect humans against sun?"}} {"citation_context": "Because cancer wasn't likely to be one's cause of death. Look at this comparison (https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/) between 1900 and 2022:\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/pzQ", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/", "kind": "external_url", "post_id": 115199, "post_url": "https://biology.stackexchange.com/a/115199", "product": "citations", "record_id": "Scientific-Citation-Graph:72bf6df9f789784fbd1f5dd0", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.

\n
\n

Where is the error in my thinking?

\n
\n

The error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.

\n

Evolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable "deficiencies" in humans that make us "imperfectly evolved".

\n

That we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any "reason" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable. If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)

\n

If we're "good enough" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.

\n

Also, somewhat aside to your question are the benefits of UV light to humans. We know that UVB allows us to synthesize Vitamin D, which is critical for survival. There are other possible benefits to UV light as well. It might well happen that we'll discover more concrete benefits.

\n

The question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.

\n", "answer_id": 115175, "answer_text": "I find your question to be fine for this site, and you've provided the asked for sources, so it's fair to give you an answer.\n\n\n\n\n\n\n\nWhere is the error in my thinking?\n\n\n\n\n\n\n\nThe error is in thinking that evolution is somehow directed towards the greater good. It's not. It's the result of random mutations.\n\n\n\n\nEvolution doesn't make us perfect for the environment in which we evolved. We will never be perfect in any way, let alone every way. You're only addressing the risks of UV light, but people can come up with any number of imaginable \"deficiencies\" in humans that make us \"imperfectly evolved\".\n\n\n\n\nThat we're imperfect in no way means evolution has failed us somehow. Evolution doesn't occur to select for perfection. Evolution doesn't happen for any \"reason\" at all, in that it's not directed by a goal; evolution simply happens because DNA is mutable (https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/). If a mutation is harmless or beneficial in an environment, it will be passed on and likely persist. If it's harmful, depending on the degree to which it's detrimental, it will not be passed on. Sometimes in an particular environment, a mutation is both (e.g. sickle cell trait.)\n\n\n\n\nIf we're \"good enough\" overall to reproduce, if we're able to survive and pass on our genetic material, then that's what's going to happen, regardless of our perceived imperfections.\n\n\n\n\nAlso, somewhat aside to your question are the benefits of UV light to humans (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). We know that UVB allows us to synthesize Vitamin D, which is critical for survival. (https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d) There are other possible benefits to UV light as well (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/). It might well happen that we'll discover more concrete benefits.\n\n\n\n\nThe question which has been linked to as a duplicate discusses evolution in more detail (and more helpfully). This is only a fairly quick answer.", "answer_url": "https://biology.stackexchange.com/a/115175", "author": "anongoodnurse", "author_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:19:48+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:19:48+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B27F09D5-F235-448E-AFF2-AD09B10346FA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B27F09D5-F235-448E-AFF2-AD09B10346FA/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "anongoodnurse", "profile_url": "https://biology.stackexchange.com/users/5198/anongoodnurse", "user_type": "registered"}, "created_at": "2024-08-13T19:27:18+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "D6BC325F-2058-42EC-A622-79DDDBAE9D28", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D6BC325F-2058-42EC-A622-79DDDBAE9D28/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:11:51+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "70F33937-681F-4BBB-90ED-DB3715ED6BF6", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/70F33937-681F-4BBB-90ED-DB3715ED6BF6/view-source"}], "score": 25, "updated_at": "2024-08-13T19:27:18+00:00"}, {"answer_html": "

Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is "good enough" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as "selective pressure" refers to selection for reproduction specifically.

\n

https://seer.cancer.gov/statfacts/html/melan.html

\n", "answer_id": 115176, "answer_text": "Skin cancer typically results from a lifetime of sun exposure, and is usually seen in older individuals. 90% of new melanoma cases are diagnosed in people over 45. Nearly 95% of melanoma deaths are observed in people over 45. Simply put, humans' currently level of adaptation to the sun is \"good enough\" - the vast majority of people do not have their reproductive fitness affected in any way by how they handle sun exposure. There is little selective pressure that would result in someone with better sun adaptation being more likely to pass on their genes. Evolution won't typically operate on traits that are only meaningful after reproductive age, as \"selective pressure\" refers to selection for reproduction specifically.\n\n\n\n\nhttps://seer.cancer.gov/statfacts/html/melan.html (https://seer.cancer.gov/statfacts/html/melan.html)", "answer_url": "https://biology.stackexchange.com/a/115176", "author": "Nuclear Hoagie", "author_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-13T19:41:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Nuclear Hoagie", "profile_url": "https://biology.stackexchange.com/users/16849/nuclear-hoagie", "user_type": "registered"}, "created_at": "2024-08-13T19:41:14+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E020D650-7DF7-42B4-A813-C07287A63A06", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E020D650-7DF7-42B4-A813-C07287A63A06/view-source"}], "score": 53, "updated_at": "2024-08-13T19:41:14+00:00"}, {"answer_html": "

Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.

\n
    \n

  • Melanin Production:

    \n

    Melanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.

    \n
    • \n

  • Epidermal Thickening:

    \n

    Another defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.

    \n
    • \n

  • DNA Repair Mechanisms:

    \n

    The human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.

    \n
    • \n

  • Inflammatory Response:

    \n

    The acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.

    \n
    • \n
\n", "answer_id": 115181, "answer_text": "Besides the arguments already mentioned in the previous answers, the human body has developed numerous ways to protect itself from the harmful effects of sunlight and ultraviolet (UV) radiation.\n\n\n\n\n\n\n\nMelanin Production:\n\n\n\n\nMelanin is the main pigment in the skin that absorbs UV radiation to\nkeep it from damaging its structure. So, if the skin is exposed to UV\nrays, it is going to make more of this pigment, making the skin\ndarker, or tanned, which is a way of a protective response to the\ndeeper layers of the skin from getting damaged. This process helps absorb and dissipate UV radiation, reducing the risk of DNA damage that can lead to skin cancer.\n\n\n\n\n\n\n\n\n\nEpidermal Thickening:\n\n\n\n\nAnother defense mechanism is the thickening of the outermost skin layers (epidermis) in response to UV exposure. This thickening serves to attenuate UV penetration to deeper skin layers, thus providing an additional barrier against potential damage.\n\n\n\n\n\n\n\n\n\nDNA Repair Mechanisms:\n\n\n\n\nThe human skin protects its genetic material from being damaged by\nDNA repair. These mechanisms are the body's way of dealing\nwith and repairing UV-induced damage by the sun. This includes repair mechanisms like the photolyase (https://en.wikipedia.org/wiki/Photolyase) repair mechanism, which specifically repairs pyrimidine dimers of the DNA which are generated by UV exposure.\n\n\n\n\n\n\n\n\n\nInflammatory Response:\n\n\n\n\nThe acute response to excessive UV exposure is sunburn. This reaction is part of the body's inflammatory response, which serves to alert the immune system to potential damage and initiate repair processes.", "answer_url": "https://biology.stackexchange.com/a/115181", "author": "Chris", "author_url": "https://biology.stackexchange.com/users/5144/chris", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T08:30:31+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-14T08:30:31+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "203DF798-60CE-4A5B-942C-F9066DA8BFEC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/203DF798-60CE-4A5B-942C-F9066DA8BFEC/view-source"}], "score": 12, "updated_at": "2024-08-14T08:30:31+00:00"}, {"answer_html": "

To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.

\n", "answer_id": 115184, "answer_text": "To add to other answers, there have been behavioral changes in many societies with paler skin phototypes that have increased the risk of skin cancer. Laying on a beach or in a park to get a suntan is an activity that's only become common in recent decades, for centuries Europeans avoided working outside around the midday sun during summer (such as sleeping in the shade) and when working outside wore clothing that covered up most of the skin along with wide brimmed hats or other head covering (have a look at typical medieval peasant dress). That was enough to mitigate most of the risk of skin cancer, but not in more equatorial countries.", "answer_url": "https://biology.stackexchange.com/a/115184", "author": "Crazymoomin", "author_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-14T14:44:29+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:44:29+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "34124B84-4C54-404B-BD68-361FC0160072", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/34124B84-4C54-404B-BD68-361FC0160072/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Crazymoomin", "profile_url": "https://biology.stackexchange.com/users/77121/crazymoomin", "user_type": "registered"}, "created_at": "2024-08-14T14:50:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "90C8EF4F-C093-46C8-845F-34F1CDBE3D76", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/90C8EF4F-C093-46C8-845F-34F1CDBE3D76/view-source"}], "score": 4, "updated_at": "2024-08-14T14:50:43+00:00"}, {"answer_html": "

There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia. It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.

\n

I recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...

\n", "answer_id": 115189, "answer_text": "There are some excellent answers already referencing melanin. I used to live in the Solomon Islands, and noticed that the people from the West of the islands, and also in the East of PNG were much darker than the neighbours: in fact they were among the darkest people I ever encountered anywhere in the world. I found this article useful: The Case of Melanin in Melanesia (https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/). It includes a map showing ultra violet levels, and it is quite clear that the high UV levels are correlated with the regions where skins are very dark.\n\n\n\n\nI recall Tim Flannery writing (alas, the book was lost during a move) that there are reefs in that area of the Western Solomons with an abundance of seafood, but that the optimum time for harvesting was also the peak for UV, hence greater selection pressure for melanin...", "answer_url": "https://biology.stackexchange.com/a/115189", "author": "Simon Crase", "author_url": "https://biology.stackexchange.com/users/60999/simon-crase", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T06:47:00+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-15T06:47:00+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "06C3F178-4AC5-4566-87E9-1B7866F7776D", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/06C3F178-4AC5-4566-87E9-1B7866F7776D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Simon Crase", "profile_url": "https://biology.stackexchange.com/users/60999/simon-crase", "user_type": "registered"}, "created_at": "2024-08-16T00:56:43+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E63DE613-A666-4300-87F8-B4DFC7B8CA59", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E63DE613-A666-4300-87F8-B4DFC7B8CA59/view-source"}], "score": 5, "updated_at": "2024-08-16T00:56:43+00:00"}, {"answer_html": "

The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.

\n

Now if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.

\n

Also careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.

\n", "answer_id": 115195, "answer_text": "The best natural sun protection is melanin. But melanin makes it harder for the skin to produce vitamin D. In places with lots of UV radiation black skin is an evolutionary advantage, and the weaker vitamin D absorption is no big problem because there is so much UV radiation.\n\n\n\n\nNow if you live in northern areas, your sun protection isn’t as good as it could be, but lots of melanin would reduce vitamin d absorption too much, because there isn’t enough UV radiation around. So there is a balancing act: Better sun protection would hurt your health in different ways.\n\n\n\n\nAlso careless sun exposure was very much a thing say 1980 to 2000. Many people have wised up to the dangers and will avoid roasting themselves on the beach. So hopefully cases of cancer etc. will go down in the future. And health agencies are much more risk averse nowadays, and to some degree they have to because people get older and more survive to an age where skin cancer actually hits them.", "answer_url": "https://biology.stackexchange.com/a/115195", "author": "gnasher729", "author_url": "https://biology.stackexchange.com/users/10077/gnasher729", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-15T20:13:04+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gnasher729", "profile_url": "https://biology.stackexchange.com/users/10077/gnasher729", "user_type": "registered"}, "created_at": "2024-08-15T20:13:04+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "B98FEE88-41D0-4F31-8B9A-0D171031B546", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B98FEE88-41D0-4F31-8B9A-0D171031B546/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:10:35+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "261F1C4D-1ECD-48FA-8442-CED29305E440", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/261F1C4D-1ECD-48FA-8442-CED29305E440/view-source"}], "score": 8, "updated_at": "2024-08-15T20:13:04+00:00"}, {"answer_html": "

Because cancer wasn't likely to be one's cause of death. Look at this comparison between 1900 and 2022:

\n

\"enter

\n

Cancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s:

\n
\n

Cancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’

\n
\n

Evolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:

\n
\n

Devil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.

\n

...

\n

In 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.

\n
\n", "answer_id": 115199, "answer_text": "Because cancer wasn't likely to be one's cause of death. Look at this comparison (https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/) between 1900 and 2022:\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/pzQsLWkf.png] (https://i.sstatic.net/pzQsLWkf.png)\n\n\n\n\nCancer used to be the cause of 5% of human deaths. Nowadays its at 24% thanks to us conquering diseases like tuberculosis and influenza. Similar data is available for the UK in the 1850s (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/):\n\n\n\n\n\n\n\nCancers were relatively rare. While the Victorians did not possess sophisticated diagnostic or screening technology, they were as able to diagnose late stage cancer as we are today; but this was an uncommon finding. In that period, cancer carried none of the stigma that it has recently acquired, and was diagnosed without bias. For example, in 1869 the Physician to Charing Cross Hospital describes lung cancer as ‘… one of the rarer forms of a rare disease. You may probably pass the rest of your students life without seeing another example of it.’\n\n\n\n\n\n\n\nEvolution can't solve every problem all at once. Cancer was simply too far down the list of causes of mortality for it to enact sufficient evolutionary pressure. We also have evidence (https://en.wikipedia.org/wiki/Devil_facial_tumour_disease) from the Tasmanian Devil population showing that immunity to certain types of cancers can evolve very quickly if necessary:\n\n\n\n\n\n\n\nDevil facial tumour disease (DFTD) is an aggressive non-viral clonally transmissible cancer which affects Tasmanian devils, a marsupial native to the Australian island of Tasmania. The cancer manifests itself as lumps of soft and ulcerating tissue around the mouth, which may invade surrounding organs and metastasise to other parts of the body. Severe genetic abnormalities exist in cancer cells—for example, DFT2 cells are tetraploid, containing twice as much genetic material as normal cells. DFTD is most often spread by bites, when teeth come into contact with cancer cells; less important pathways of transmission are ingesting of infected carcasses and sharing of food. Adult Tasmanian devils who are otherwise the fittest are most susceptible to the disease. DFTD is estimated to have first developed in 1986.\n\n\n\n\n...\n\n\n\n\nIn 2016, devils are endangered as the localised populations were shown to have declined by 90 per cent and an overall species decline of more than 80 per cent in less than 20 years, with some models predicting extinction. Despite this, devil populations persist in disease-stricken areas. The devils have, in a way, fought back the extinction by developing the gene that is immune to face tumors. The genes have already existed in the Tasmanian devil as part of their immune system. They increased in frequency due to natural selection. That is, the individuals with particular forms of these genes (alleles) survived and reproduced disproportionately to those that lacked the specific variants when disease was present.", "answer_url": "https://biology.stackexchange.com/a/115199", "author": "MilkLife", "author_url": "https://biology.stackexchange.com/users/5492/milklife", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-08-16T23:47:16+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:25.304620+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/7fe0b66593eb4c0f175024453138b8bd50811f1580a079ffb990af38e09cd1cf_0.json", "raw_sha256": "b0a655f3b4c9626cf981180b3ac018a4a26330c5ab9b925b3df78bedd8169a84", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/115493;115490;115488;115483;115479;115477;115456;115453;115452;115447;115445;115444;115436;115431;115427;115413;115404;115403;115396;115391;115389;115388;115386;115383;115382;115379;115367;115365;115355;115340;115334;115328;115321;115314;115309;115304;115296;115295;115292;115283;115272;115270;115269;115265;115264;115260;115255;115252;115243;115235;115233;115225;115218;115215;115214;115213;115207;115204;115179;115177;115170;115167;115165;115164;115154;115149;115137;115131;115129;115115;115107;115099;115095;115094;115093;115085;115082;115081;115077;115076;115075;115074;115073;115072;115063;115044;115039;115035;115030;115025;115022;115019;115016;115012;115003;115002;114997;114993;114991;114987/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115170, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "MilkLife", "profile_url": "https://biology.stackexchange.com/users/5492/milklife", "user_type": "registered"}, "created_at": "2024-08-16T23:47:16+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "FA30453C-1E93-40D2-9D07-DDC697CEF2EA", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/FA30453C-1E93-40D2-9D07-DDC697CEF2EA/view-source"}], "score": 0, "updated_at": "2024-08-16T23:47:16+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/Devil_facial_tumour_disease", "https://en.wikipedia.org/wiki/Fitzpatrick_scale", "https://en.wikipedia.org/wiki/Photolyase", "https://garamut.wordpress.com/2009/08/10/the-case-of-melanin-in-melanesia/", "https://i.sstatic.net/pzQsLWkf.png", "https://seer.cancer.gov/statfacts/html/melan.html", "https://www.cuimc.columbia.edu/news/whats-deal-vitamin-d", "https://www.nature.com/scitable/topicpage/dna-is-constantly-changing-through-the-process-6524898/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2672390/", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3427189/", "https://www.statista.com/statistics/235703/major-causes-of-death-in-the-us/"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:05.762873+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/04ed2aa314c5d877c5d79e42620d1f80988a21de8d429a22d8c6af5280cfd6e8_0.json", "raw_sha256": "6dd355b99094bb9ba2c965ee7dd7b0e95f92a8078d3b2b85b64196fcb6cf717c", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=5&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "gaazkam", "question_author_url": "https://biology.stackexchange.com/users/15177/gaazkam", "question_author_user_type": "registered", "question_created_at": "2024-08-13T05:20:41+00:00", "question_html": "

Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.

\n

Especially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.

\n

Native to Europe are phototypes I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?

\n

So, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.

\n

Yet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.

\n

Where is the error in my thinking?

\n", "question_id": 115170, "question_license": "CC BY-SA 4.0", "question_score": 17, "question_text": "Experts recommend that people apply sunscreen every two hours throughout the year, even in winter.\n\n\n\n\nEspecially phototypes I - III are supposed to be most vulnerable to harmful UV radiation, so especially these phototypes should take care to keep applying sunscreen and to use at least SPF 50. This, at least, is what European health agencies tell us.\n\n\n\n\nNative to Europe are phototypes (https://en.wikipedia.org/wiki/Fitzpatrick_scale) I - III. This means that these phototypes evolved in these precise conditions. Isn't evolution suppose to lead to best adaptations to the precise conditions native to the area an organism evolved in?\n\n\n\n\nSo, by this line of argument, phototypes I - III should be well-adapted to the levels of Sun radiation present in Europe. They should not have to use sunscreen there. When traveling to areas that are significantly higher in Sun radiation, such as equatorial areas, they may have to start using sunscreen - but not in areas they are native to.\n\n\n\n\nYet European agencies keep telling us that especially phototypes I - III should use sunscreen while in Europe.\n\n\n\n\nWhere is the error in my thinking?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:20:41+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "828DB692-880A-4BBF-AD67-13CF3E06456A", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/828DB692-880A-4BBF-AD67-13CF3E06456A/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "gaazkam", "profile_url": "https://biology.stackexchange.com/users/15177/gaazkam", "user_type": "registered"}, "created_at": "2024-08-13T05:26:09+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E6AEDC3C-D874-42D3-A8D8-7210CFC2D8AB/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2024-08-14T08:31:47+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/BD6D1FEE-C8A1-4A4F-8BF6-62DE46F8A60D/view-source"}, {"content_license": null, "contributor": {"display_name": "Chris", "profile_url": "https://biology.stackexchange.com/users/5144/chris", "user_type": "moderator"}, "created_at": "2024-08-15T13:36:46+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/5FEC95C4-C66B-4A62-A8A4-C39F2EE4CA4E/view-source"}, {"content_license": null, "contributor": {"display_name": "AliceD", "profile_url": "https://biology.stackexchange.com/users/9943/aliced", "user_type": "registered"}, "created_at": "2024-08-16T08:12:55+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "E7A91925-4841-42A6-89A7-24963075C01F", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/E7A91925-4841-42A6-89A7-24963075C01F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Basil Bourque", "profile_url": "https://biology.stackexchange.com/users/32521/basil-bourque", "user_type": "registered"}, "created_at": "2024-09-02T17:31:11+00:00", "raw_file": "raw/codex_api_v1/920b7e5633cbad837bacc37f0887fd883044a5fce63b6e0fa3cc1504390bec54_1790824091899465600_0.json", "raw_sha256": "bac2cc1988c9b300f258cae319a9302dc73ac2617e76f7491908df2a0b939d11", "revision_guid": "C86E2648-B494-446F-A6EC-EE52D185A1B7", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/C86E2648-B494-446F-A6EC-EE52D185A1B7/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/115170/why-did-evolution-fail-to-protect-humans-against-sun", "split": "test", "split_group": "503625bcfe466937a26431096aee38aeab3e6012cf849f4c5706c832b5d6195c", "tags": ["human-evolution", "skin", "melanin"], "thread_id": "biology:115170", "title": "Why did evolution fail to protect humans against sun?"}} {"citation_context": "t partake in the Krebs cycle (https://en.wikipedia.org/wiki/Citric_acid_cycle), the citrate-malate (https://en.wikipedia.org/wiki/Citrate%E2%80%93malate_shuttle)/malate-aspartate (https://en.wikipedia.org/wiki/Malate%E2%80%93aspartate_shuttle) shuttles, and su", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Citrate%E2%80%93malate_shuttle", "kind": "external_url", "post_id": 113317, "post_url": "https://biology.stackexchange.com/questions/113317/can-humans-metabolize-d-malate", "product": "citations", "record_id": "Scientific-Citation-Graph:1c9d5b4cafb690718043d828", "split": "test", "thread": {"accepted_answer_id": 113370, "answers": [{"answer_html": "

I do not have specific proof, but I strongly suspect that the answer to this question is NO on the basis of the following arguments.

\n
    \n
  • The overwhelming majority of sugars, amino acids, carboxylic acids\nand other metabolites with and asymmetric carbon atom have been long\nknown to occur in only a single enantiomeric form within living\norganisms. This was established long before the nature of the enzymes that catalyse their reactions were characterized.
    • \n
  • Since the 1950s and 1960s we have understood that the stereo-specificity of enzymic reactions reflects the weak but binding of (co-)substrates to specific chemical groups of amino acid residues in the active site, and the subsequent flow of electrons between the bound components (often including the amino acid residues). The overall three-dimensional structure of the interactions that allow such catalysis only occur with one form of the enantiomeric metabolite.
    • \n
  • The fact that malate (e.g. in fruit such as apples) only occurs in the L-form indicates that the reactions which involve it (predominantly malate dehydrogenase and fumarase) conform to the principle just expounded.
    • \n
  • Although racemases (enzymes that interconvert enantiomers) exist for certain compounds in certain species, malate racemases have only been reported in obscure bacteria. They are not known to be present in man.
    • \n
\n

The problem is that this is so well established that studies with D-malate of relevance to the question are hard to find. One thing to do would be to examine the three-dimensional structure of malate dehydrogenase with a suitable malate analogue bound and model the enantiomer. This requires some work — a cursory trawl shows that usually the enzyme is crystalized with the product, oxaloacetate bound.

\n

I have not looked at the mitochondrial transport system involved in the shuttle: something else for the poster to try. Nor can I find information on whether D-malate is taken up by the gut, and what its fate is if it is.

\n", "answer_id": 113370, "answer_text": "I do not have specific proof, but I strongly suspect that the answer to this question is NO on the basis of the following arguments.\n\n\n\n\n\nThe overwhelming majority of sugars, amino acids, carboxylic acids\nand other metabolites with and asymmetric carbon atom have been long\nknown to occur in only a single enantiomeric form within living\norganisms. This was established long before the nature of the enzymes that catalyse their reactions were characterized.\n\n\n\n\nSince the 1950s and 1960s we have understood that the stereo-specificity of enzymic reactions reflects the weak but binding of (co-)substrates to specific chemical groups of amino acid residues in the active site, and the subsequent flow of electrons between the bound components (often including the amino acid residues). The overall three-dimensional structure of the interactions that allow such catalysis only occur with one form of the enantiomeric metabolite.\n\n\n\n\nThe fact that malate (e.g. in fruit such as apples) only occurs in the L-form indicates that the reactions which involve it (predominantly malate dehydrogenase and fumarase) conform to the principle just expounded.\n\n\n\n\nAlthough racemases (enzymes that interconvert enantiomers) exist for certain compounds in certain species, malate racemases have only been reported in obscure bacteria. They are not known to be present in man.\n\n\n\n\n\nThe problem is that this is so well established that studies with D-malate of relevance to the question are hard to find. One thing to do would be to examine the three-dimensional structure of malate dehydrogenase with a suitable malate analogue bound and model the enantiomer. This requires some work — a cursory trawl shows that usually the enzyme is crystalized with the product, oxaloacetate bound.\n\n\n\n\nI have not looked at the mitochondrial transport system involved in the shuttle: something else for the poster to try. Nor can I find information on whether D-malate is taken up by the gut, and what its fate is if it is.", "answer_url": "https://biology.stackexchange.com/a/113370", "author": "David", "author_url": "https://biology.stackexchange.com/users/22057/david", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2023-10-31T13:53:25+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:36.208962+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/ce9de3cf6525f1e283f75a76c7c279c0bd53024cf8e6597abc34f072e18cfbf7_0.json", "raw_sha256": "c65c49a81e92972be3758d3b220c036300d85c38ce4d9079a6203d2eeac0d96d", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/113468;113465;113459;113453;113451;113449;113442;113437;113425;113421;113416;113415;113413;113406;113400;113398;113386;113378;113364;113363;113347;113340;113333;113324;113317;113315;113310;113303;113307;113299;113293;113291;113284;113282;113279;113277;113275;113274;113263;113253;113252;113243;113239;113235;113231;113229;113223;113221;113218;113216;113210;113198;113191;113183;113180;113175;113164;113158;113153;113146;113141;113118;113116;113115;113113;113110;113109;113106;113104;113101;113095;113089;113086;113081;113080;113077;113076;113075;113070;113067;113064;113053;113046;113043;113039;113031;113030;113028;113027;113024;113017;113016;113015;113014;113009;113008;113007;113005;112998;112984/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 113317, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2023-10-31T13:53:25+00:00", "raw_file": "raw/codex_api_v1/90c6546608151c55782a98b278e0bff1131c56a003319717b96f8124b5cd81ad_1790824039302420800_0.json", "raw_sha256": "9f60f0aa014afb8146c20434cb45e9daca2b9f5585a871678859e9e68314a991", "revision_guid": "E6DFB790-51F0-4849-A29E-FC3EDAF06762", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E6DFB790-51F0-4849-A29E-FC3EDAF06762/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2023-10-31T15:57:12+00:00", "raw_file": "raw/codex_api_v1/90c6546608151c55782a98b278e0bff1131c56a003319717b96f8124b5cd81ad_1790824039302420800_0.json", "raw_sha256": "9f60f0aa014afb8146c20434cb45e9daca2b9f5585a871678859e9e68314a991", "revision_guid": "77EB4357-0724-41A6-BD79-26171B406BF9", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/77EB4357-0724-41A6-BD79-26171B406BF9/view-source"}], "score": 2, "updated_at": "2023-10-31T15:57:12+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/Citrate%E2%80%93malate_shuttle", "https://en.wikipedia.org/wiki/Citric_acid_cycle", "https://en.wikipedia.org/wiki/Malate%E2%80%93aspartate_shuttle", "https://en.wikipedia.org/wiki/Malic_acid#Biochemistry"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:11.333206+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/3e71d6afdfe444c721dbb1321f43c14066813d2fd740fb255123cf87e737d071_0.json", "raw_sha256": "84992ad678a40907dca3af99f849ee653142b680281a54e02542dc7f47d30773", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=9&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "ManRow", "question_author_url": "https://biology.stackexchange.com/users/30343/manrow", "question_author_user_type": "registered", "question_created_at": "2023-10-24T21:51:28+00:00", "question_html": "

Only the L-isomer is produced naturally, while racemic mixtures are produced synthetically and used commercially as food additives and energy supplements.

\n

So what happens when we consume D-malate? Does it just partake in the Krebs cycle, the citrate-malate/malate-aspartate shuttles, and such like the L-isomer?

\n

Or, does it just bioaccumulate and/or inhibit these processes? Until it gets excreted out?

\n", "question_id": 113317, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "Only the L-isomer is produced naturally (https://en.wikipedia.org/wiki/Malic_acid#Biochemistry), while racemic mixtures are produced synthetically and used commercially as food additives and energy supplements.\n\n\n\n\nSo what happens when we consume D-malate? Does it just partake in the Krebs cycle (https://en.wikipedia.org/wiki/Citric_acid_cycle), the citrate-malate (https://en.wikipedia.org/wiki/Citrate%E2%80%93malate_shuttle)/malate-aspartate (https://en.wikipedia.org/wiki/Malate%E2%80%93aspartate_shuttle) shuttles, and such like the L-isomer?\n\n\n\n\nOr, does it just bioaccumulate and/or inhibit these processes? 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"https://biology.stackexchange.com/revisions/CD98ED0B-3000-49D4-86BD-273F51989EF8/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/113317/can-humans-metabolize-d-malate", "split": "test", "split_group": "ba2318c8960a94cea2c57e423dca3e293dd15130d8d2f39cf4dcf3fbeeaa0250", "tags": ["human-biology", "biochemistry", "molecular-biology", "metabolism", "enzymes"], "thread_id": "biology:113317", "title": "Can humans metabolize D-malate?"}} {"citation_context": "supplements.\n\n\n\n\nSo what happens when we consume D-malate? Does it just partake in the Krebs cycle (https://en.wikipedia.org/wiki/Citric_acid_cycle), the citrate-malate (https://en.wikipedia.org/wiki/Citrate%E2%80%93malate_shuttle)/malate-aspartat", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Citric_acid_cycle", "kind": "external_url", "post_id": 113317, "post_url": "https://biology.stackexchange.com/questions/113317/can-humans-metabolize-d-malate", "product": "citations", "record_id": "Scientific-Citation-Graph:b240a7bd1a197f438aae95cb", "split": "test", "thread": {"accepted_answer_id": 113370, "answers": [{"answer_html": "

I do not have specific proof, but I strongly suspect that the answer to this question is NO on the basis of the following arguments.

\n
    \n
  • The overwhelming majority of sugars, amino acids, carboxylic acids\nand other metabolites with and asymmetric carbon atom have been long\nknown to occur in only a single enantiomeric form within living\norganisms. This was established long before the nature of the enzymes that catalyse their reactions were characterized.
    • \n
  • Since the 1950s and 1960s we have understood that the stereo-specificity of enzymic reactions reflects the weak but binding of (co-)substrates to specific chemical groups of amino acid residues in the active site, and the subsequent flow of electrons between the bound components (often including the amino acid residues). The overall three-dimensional structure of the interactions that allow such catalysis only occur with one form of the enantiomeric metabolite.
    • \n
  • The fact that malate (e.g. in fruit such as apples) only occurs in the L-form indicates that the reactions which involve it (predominantly malate dehydrogenase and fumarase) conform to the principle just expounded.
    • \n
  • Although racemases (enzymes that interconvert enantiomers) exist for certain compounds in certain species, malate racemases have only been reported in obscure bacteria. They are not known to be present in man.
    • \n
\n

The problem is that this is so well established that studies with D-malate of relevance to the question are hard to find. One thing to do would be to examine the three-dimensional structure of malate dehydrogenase with a suitable malate analogue bound and model the enantiomer. This requires some work — a cursory trawl shows that usually the enzyme is crystalized with the product, oxaloacetate bound.

\n

I have not looked at the mitochondrial transport system involved in the shuttle: something else for the poster to try. Nor can I find information on whether D-malate is taken up by the gut, and what its fate is if it is.

\n", "answer_id": 113370, "answer_text": "I do not have specific proof, but I strongly suspect that the answer to this question is NO on the basis of the following arguments.\n\n\n\n\n\nThe overwhelming majority of sugars, amino acids, carboxylic acids\nand other metabolites with and asymmetric carbon atom have been long\nknown to occur in only a single enantiomeric form within living\norganisms. This was established long before the nature of the enzymes that catalyse their reactions were characterized.\n\n\n\n\nSince the 1950s and 1960s we have understood that the stereo-specificity of enzymic reactions reflects the weak but binding of (co-)substrates to specific chemical groups of amino acid residues in the active site, and the subsequent flow of electrons between the bound components (often including the amino acid residues). The overall three-dimensional structure of the interactions that allow such catalysis only occur with one form of the enantiomeric metabolite.\n\n\n\n\nThe fact that malate (e.g. in fruit such as apples) only occurs in the L-form indicates that the reactions which involve it (predominantly malate dehydrogenase and fumarase) conform to the principle just expounded.\n\n\n\n\nAlthough racemases (enzymes that interconvert enantiomers) exist for certain compounds in certain species, malate racemases have only been reported in obscure bacteria. They are not known to be present in man.\n\n\n\n\n\nThe problem is that this is so well established that studies with D-malate of relevance to the question are hard to find. One thing to do would be to examine the three-dimensional structure of malate dehydrogenase with a suitable malate analogue bound and model the enantiomer. This requires some work — a cursory trawl shows that usually the enzyme is crystalized with the product, oxaloacetate bound.\n\n\n\n\nI have not looked at the mitochondrial transport system involved in the shuttle: something else for the poster to try. Nor can I find information on whether D-malate is taken up by the gut, and what its fate is if it is.", "answer_url": "https://biology.stackexchange.com/a/113370", "author": "David", "author_url": "https://biology.stackexchange.com/users/22057/david", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2023-10-31T13:53:25+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:36.208962+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/ce9de3cf6525f1e283f75a76c7c279c0bd53024cf8e6597abc34f072e18cfbf7_0.json", "raw_sha256": "c65c49a81e92972be3758d3b220c036300d85c38ce4d9079a6203d2eeac0d96d", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/113468;113465;113459;113453;113451;113449;113442;113437;113425;113421;113416;113415;113413;113406;113400;113398;113386;113378;113364;113363;113347;113340;113333;113324;113317;113315;113310;113303;113307;113299;113293;113291;113284;113282;113279;113277;113275;113274;113263;113253;113252;113243;113239;113235;113231;113229;113223;113221;113218;113216;113210;113198;113191;113183;113180;113175;113164;113158;113153;113146;113141;113118;113116;113115;113113;113110;113109;113106;113104;113101;113095;113089;113086;113081;113080;113077;113076;113075;113070;113067;113064;113053;113046;113043;113039;113031;113030;113028;113027;113024;113017;113016;113015;113014;113009;113008;113007;113005;112998;112984/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 113317, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2023-10-31T13:53:25+00:00", "raw_file": "raw/codex_api_v1/90c6546608151c55782a98b278e0bff1131c56a003319717b96f8124b5cd81ad_1790824039302420800_0.json", "raw_sha256": "9f60f0aa014afb8146c20434cb45e9daca2b9f5585a871678859e9e68314a991", "revision_guid": "E6DFB790-51F0-4849-A29E-FC3EDAF06762", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E6DFB790-51F0-4849-A29E-FC3EDAF06762/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2023-10-31T15:57:12+00:00", "raw_file": "raw/codex_api_v1/90c6546608151c55782a98b278e0bff1131c56a003319717b96f8124b5cd81ad_1790824039302420800_0.json", "raw_sha256": "9f60f0aa014afb8146c20434cb45e9daca2b9f5585a871678859e9e68314a991", "revision_guid": "77EB4357-0724-41A6-BD79-26171B406BF9", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/77EB4357-0724-41A6-BD79-26171B406BF9/view-source"}], "score": 2, "updated_at": "2023-10-31T15:57:12+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/Citrate%E2%80%93malate_shuttle", "https://en.wikipedia.org/wiki/Citric_acid_cycle", "https://en.wikipedia.org/wiki/Malate%E2%80%93aspartate_shuttle", "https://en.wikipedia.org/wiki/Malic_acid#Biochemistry"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:11.333206+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/3e71d6afdfe444c721dbb1321f43c14066813d2fd740fb255123cf87e737d071_0.json", "raw_sha256": "84992ad678a40907dca3af99f849ee653142b680281a54e02542dc7f47d30773", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=9&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "ManRow", "question_author_url": "https://biology.stackexchange.com/users/30343/manrow", "question_author_user_type": "registered", "question_created_at": "2023-10-24T21:51:28+00:00", "question_html": "

Only the L-isomer is produced naturally, while racemic mixtures are produced synthetically and used commercially as food additives and energy supplements.

\n

So what happens when we consume D-malate? Does it just partake in the Krebs cycle, the citrate-malate/malate-aspartate shuttles, and such like the L-isomer?

\n

Or, does it just bioaccumulate and/or inhibit these processes? Until it gets excreted out?

\n", "question_id": 113317, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "Only the L-isomer is produced naturally (https://en.wikipedia.org/wiki/Malic_acid#Biochemistry), while racemic mixtures are produced synthetically and used commercially as food additives and energy supplements.\n\n\n\n\nSo what happens when we consume D-malate? Does it just partake in the Krebs cycle (https://en.wikipedia.org/wiki/Citric_acid_cycle), the citrate-malate (https://en.wikipedia.org/wiki/Citrate%E2%80%93malate_shuttle)/malate-aspartate (https://en.wikipedia.org/wiki/Malate%E2%80%93aspartate_shuttle) shuttles, and such like the L-isomer?\n\n\n\n\nOr, does it just bioaccumulate and/or inhibit these processes? Until it gets excreted out?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "ManRow", "profile_url": "https://biology.stackexchange.com/users/30343/manrow", "user_type": "registered"}, "created_at": "2023-10-24T21:51:28+00:00", "raw_file": "raw/codex_api_v1/05c310a2e43a25cef557efc8abb78d08e3282613971fb1f949f4d401e11807fa_1790824041474830100_0.json", "raw_sha256": "06275f053755243837bd950c2a032e528759a141759c26078d708e55d401af9b", "revision_guid": "8EEA12C7-3334-40ED-8EA7-3C3C6EA0DFBC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/8EEA12C7-3334-40ED-8EA7-3C3C6EA0DFBC/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "ManRow", "profile_url": "https://biology.stackexchange.com/users/30343/manrow", "user_type": "registered"}, "created_at": "2023-10-24T22:01:20+00:00", "raw_file": 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I do not have specific proof, but I strongly suspect that the answer to this question is NO on the basis of the following arguments.

\n
    \n
  • The overwhelming majority of sugars, amino acids, carboxylic acids\nand other metabolites with and asymmetric carbon atom have been long\nknown to occur in only a single enantiomeric form within living\norganisms. This was established long before the nature of the enzymes that catalyse their reactions were characterized.
    • \n
  • Since the 1950s and 1960s we have understood that the stereo-specificity of enzymic reactions reflects the weak but binding of (co-)substrates to specific chemical groups of amino acid residues in the active site, and the subsequent flow of electrons between the bound components (often including the amino acid residues). The overall three-dimensional structure of the interactions that allow such catalysis only occur with one form of the enantiomeric metabolite.
    • \n
  • The fact that malate (e.g. in fruit such as apples) only occurs in the L-form indicates that the reactions which involve it (predominantly malate dehydrogenase and fumarase) conform to the principle just expounded.
    • \n
  • Although racemases (enzymes that interconvert enantiomers) exist for certain compounds in certain species, malate racemases have only been reported in obscure bacteria. They are not known to be present in man.
    • \n
\n

The problem is that this is so well established that studies with D-malate of relevance to the question are hard to find. One thing to do would be to examine the three-dimensional structure of malate dehydrogenase with a suitable malate analogue bound and model the enantiomer. This requires some work — a cursory trawl shows that usually the enzyme is crystalized with the product, oxaloacetate bound.

\n

I have not looked at the mitochondrial transport system involved in the shuttle: something else for the poster to try. Nor can I find information on whether D-malate is taken up by the gut, and what its fate is if it is.

\n", "answer_id": 113370, "answer_text": "I do not have specific proof, but I strongly suspect that the answer to this question is NO on the basis of the following arguments.\n\n\n\n\n\nThe overwhelming majority of sugars, amino acids, carboxylic acids\nand other metabolites with and asymmetric carbon atom have been long\nknown to occur in only a single enantiomeric form within living\norganisms. This was established long before the nature of the enzymes that catalyse their reactions were characterized.\n\n\n\n\nSince the 1950s and 1960s we have understood that the stereo-specificity of enzymic reactions reflects the weak but binding of (co-)substrates to specific chemical groups of amino acid residues in the active site, and the subsequent flow of electrons between the bound components (often including the amino acid residues). The overall three-dimensional structure of the interactions that allow such catalysis only occur with one form of the enantiomeric metabolite.\n\n\n\n\nThe fact that malate (e.g. in fruit such as apples) only occurs in the L-form indicates that the reactions which involve it (predominantly malate dehydrogenase and fumarase) conform to the principle just expounded.\n\n\n\n\nAlthough racemases (enzymes that interconvert enantiomers) exist for certain compounds in certain species, malate racemases have only been reported in obscure bacteria. They are not known to be present in man.\n\n\n\n\n\nThe problem is that this is so well established that studies with D-malate of relevance to the question are hard to find. One thing to do would be to examine the three-dimensional structure of malate dehydrogenase with a suitable malate analogue bound and model the enantiomer. This requires some work — a cursory trawl shows that usually the enzyme is crystalized with the product, oxaloacetate bound.\n\n\n\n\nI have not looked at the mitochondrial transport system involved in the shuttle: something else for the poster to try. Nor can I find information on whether D-malate is taken up by the gut, and what its fate is if it is.", "answer_url": "https://biology.stackexchange.com/a/113370", "author": "David", "author_url": "https://biology.stackexchange.com/users/22057/david", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2023-10-31T13:53:25+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:36.208962+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/ce9de3cf6525f1e283f75a76c7c279c0bd53024cf8e6597abc34f072e18cfbf7_0.json", "raw_sha256": "c65c49a81e92972be3758d3b220c036300d85c38ce4d9079a6203d2eeac0d96d", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/113468;113465;113459;113453;113451;113449;113442;113437;113425;113421;113416;113415;113413;113406;113400;113398;113386;113378;113364;113363;113347;113340;113333;113324;113317;113315;113310;113303;113307;113299;113293;113291;113284;113282;113279;113277;113275;113274;113263;113253;113252;113243;113239;113235;113231;113229;113223;113221;113218;113216;113210;113198;113191;113183;113180;113175;113164;113158;113153;113146;113141;113118;113116;113115;113113;113110;113109;113106;113104;113101;113095;113089;113086;113081;113080;113077;113076;113075;113070;113067;113064;113053;113046;113043;113039;113031;113030;113028;113027;113024;113017;113016;113015;113014;113009;113008;113007;113005;112998;112984/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 113317, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2023-10-31T13:53:25+00:00", "raw_file": "raw/codex_api_v1/90c6546608151c55782a98b278e0bff1131c56a003319717b96f8124b5cd81ad_1790824039302420800_0.json", "raw_sha256": "9f60f0aa014afb8146c20434cb45e9daca2b9f5585a871678859e9e68314a991", "revision_guid": "E6DFB790-51F0-4849-A29E-FC3EDAF06762", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E6DFB790-51F0-4849-A29E-FC3EDAF06762/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2023-10-31T15:57:12+00:00", "raw_file": "raw/codex_api_v1/90c6546608151c55782a98b278e0bff1131c56a003319717b96f8124b5cd81ad_1790824039302420800_0.json", "raw_sha256": "9f60f0aa014afb8146c20434cb45e9daca2b9f5585a871678859e9e68314a991", "revision_guid": "77EB4357-0724-41A6-BD79-26171B406BF9", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/77EB4357-0724-41A6-BD79-26171B406BF9/view-source"}], "score": 2, "updated_at": "2023-10-31T15:57:12+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/Citrate%E2%80%93malate_shuttle", "https://en.wikipedia.org/wiki/Citric_acid_cycle", "https://en.wikipedia.org/wiki/Malate%E2%80%93aspartate_shuttle", "https://en.wikipedia.org/wiki/Malic_acid#Biochemistry"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:11.333206+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/3e71d6afdfe444c721dbb1321f43c14066813d2fd740fb255123cf87e737d071_0.json", "raw_sha256": "84992ad678a40907dca3af99f849ee653142b680281a54e02542dc7f47d30773", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=9&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "ManRow", "question_author_url": "https://biology.stackexchange.com/users/30343/manrow", "question_author_user_type": "registered", "question_created_at": "2023-10-24T21:51:28+00:00", "question_html": "

Only the L-isomer is produced naturally, while racemic mixtures are produced synthetically and used commercially as food additives and energy supplements.

\n

So what happens when we consume D-malate? Does it just partake in the Krebs cycle, the citrate-malate/malate-aspartate shuttles, and such like the L-isomer?

\n

Or, does it just bioaccumulate and/or inhibit these processes? Until it gets excreted out?

\n", "question_id": 113317, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "Only the L-isomer is produced naturally (https://en.wikipedia.org/wiki/Malic_acid#Biochemistry), while racemic mixtures are produced synthetically and used commercially as food additives and energy supplements.\n\n\n\n\nSo what happens when we consume D-malate? Does it just partake in the Krebs cycle (https://en.wikipedia.org/wiki/Citric_acid_cycle), the citrate-malate (https://en.wikipedia.org/wiki/Citrate%E2%80%93malate_shuttle)/malate-aspartate (https://en.wikipedia.org/wiki/Malate%E2%80%93aspartate_shuttle) shuttles, and such like the L-isomer?\n\n\n\n\nOr, does it just bioaccumulate and/or inhibit these processes? 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I do not have specific proof, but I strongly suspect that the answer to this question is NO on the basis of the following arguments.

\n
    \n
  • The overwhelming majority of sugars, amino acids, carboxylic acids\nand other metabolites with and asymmetric carbon atom have been long\nknown to occur in only a single enantiomeric form within living\norganisms. This was established long before the nature of the enzymes that catalyse their reactions were characterized.
    • \n
  • Since the 1950s and 1960s we have understood that the stereo-specificity of enzymic reactions reflects the weak but binding of (co-)substrates to specific chemical groups of amino acid residues in the active site, and the subsequent flow of electrons between the bound components (often including the amino acid residues). The overall three-dimensional structure of the interactions that allow such catalysis only occur with one form of the enantiomeric metabolite.
    • \n
  • The fact that malate (e.g. in fruit such as apples) only occurs in the L-form indicates that the reactions which involve it (predominantly malate dehydrogenase and fumarase) conform to the principle just expounded.
    • \n
  • Although racemases (enzymes that interconvert enantiomers) exist for certain compounds in certain species, malate racemases have only been reported in obscure bacteria. They are not known to be present in man.
    • \n
\n

The problem is that this is so well established that studies with D-malate of relevance to the question are hard to find. One thing to do would be to examine the three-dimensional structure of malate dehydrogenase with a suitable malate analogue bound and model the enantiomer. This requires some work — a cursory trawl shows that usually the enzyme is crystalized with the product, oxaloacetate bound.

\n

I have not looked at the mitochondrial transport system involved in the shuttle: something else for the poster to try. Nor can I find information on whether D-malate is taken up by the gut, and what its fate is if it is.

\n", "answer_id": 113370, "answer_text": "I do not have specific proof, but I strongly suspect that the answer to this question is NO on the basis of the following arguments.\n\n\n\n\n\nThe overwhelming majority of sugars, amino acids, carboxylic acids\nand other metabolites with and asymmetric carbon atom have been long\nknown to occur in only a single enantiomeric form within living\norganisms. This was established long before the nature of the enzymes that catalyse their reactions were characterized.\n\n\n\n\nSince the 1950s and 1960s we have understood that the stereo-specificity of enzymic reactions reflects the weak but binding of (co-)substrates to specific chemical groups of amino acid residues in the active site, and the subsequent flow of electrons between the bound components (often including the amino acid residues). The overall three-dimensional structure of the interactions that allow such catalysis only occur with one form of the enantiomeric metabolite.\n\n\n\n\nThe fact that malate (e.g. in fruit such as apples) only occurs in the L-form indicates that the reactions which involve it (predominantly malate dehydrogenase and fumarase) conform to the principle just expounded.\n\n\n\n\nAlthough racemases (enzymes that interconvert enantiomers) exist for certain compounds in certain species, malate racemases have only been reported in obscure bacteria. They are not known to be present in man.\n\n\n\n\n\nThe problem is that this is so well established that studies with D-malate of relevance to the question are hard to find. One thing to do would be to examine the three-dimensional structure of malate dehydrogenase with a suitable malate analogue bound and model the enantiomer. This requires some work — a cursory trawl shows that usually the enzyme is crystalized with the product, oxaloacetate bound.\n\n\n\n\nI have not looked at the mitochondrial transport system involved in the shuttle: something else for the poster to try. Nor can I find information on whether D-malate is taken up by the gut, and what its fate is if it is.", "answer_url": "https://biology.stackexchange.com/a/113370", "author": "David", "author_url": "https://biology.stackexchange.com/users/22057/david", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2023-10-31T13:53:25+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:36.208962+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/ce9de3cf6525f1e283f75a76c7c279c0bd53024cf8e6597abc34f072e18cfbf7_0.json", "raw_sha256": "c65c49a81e92972be3758d3b220c036300d85c38ce4d9079a6203d2eeac0d96d", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/113468;113465;113459;113453;113451;113449;113442;113437;113425;113421;113416;113415;113413;113406;113400;113398;113386;113378;113364;113363;113347;113340;113333;113324;113317;113315;113310;113303;113307;113299;113293;113291;113284;113282;113279;113277;113275;113274;113263;113253;113252;113243;113239;113235;113231;113229;113223;113221;113218;113216;113210;113198;113191;113183;113180;113175;113164;113158;113153;113146;113141;113118;113116;113115;113113;113110;113109;113106;113104;113101;113095;113089;113086;113081;113080;113077;113076;113075;113070;113067;113064;113053;113046;113043;113039;113031;113030;113028;113027;113024;113017;113016;113015;113014;113009;113008;113007;113005;112998;112984/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 113317, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2023-10-31T13:53:25+00:00", "raw_file": "raw/codex_api_v1/90c6546608151c55782a98b278e0bff1131c56a003319717b96f8124b5cd81ad_1790824039302420800_0.json", "raw_sha256": "9f60f0aa014afb8146c20434cb45e9daca2b9f5585a871678859e9e68314a991", "revision_guid": "E6DFB790-51F0-4849-A29E-FC3EDAF06762", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E6DFB790-51F0-4849-A29E-FC3EDAF06762/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2023-10-31T15:57:12+00:00", "raw_file": "raw/codex_api_v1/90c6546608151c55782a98b278e0bff1131c56a003319717b96f8124b5cd81ad_1790824039302420800_0.json", "raw_sha256": "9f60f0aa014afb8146c20434cb45e9daca2b9f5585a871678859e9e68314a991", "revision_guid": "77EB4357-0724-41A6-BD79-26171B406BF9", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/77EB4357-0724-41A6-BD79-26171B406BF9/view-source"}], "score": 2, "updated_at": "2023-10-31T15:57:12+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/Citrate%E2%80%93malate_shuttle", "https://en.wikipedia.org/wiki/Citric_acid_cycle", "https://en.wikipedia.org/wiki/Malate%E2%80%93aspartate_shuttle", "https://en.wikipedia.org/wiki/Malic_acid#Biochemistry"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:11.333206+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/3e71d6afdfe444c721dbb1321f43c14066813d2fd740fb255123cf87e737d071_0.json", "raw_sha256": "84992ad678a40907dca3af99f849ee653142b680281a54e02542dc7f47d30773", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=9&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "ManRow", "question_author_url": "https://biology.stackexchange.com/users/30343/manrow", "question_author_user_type": "registered", "question_created_at": "2023-10-24T21:51:28+00:00", "question_html": "

Only the L-isomer is produced naturally, while racemic mixtures are produced synthetically and used commercially as food additives and energy supplements.

\n

So what happens when we consume D-malate? Does it just partake in the Krebs cycle, the citrate-malate/malate-aspartate shuttles, and such like the L-isomer?

\n

Or, does it just bioaccumulate and/or inhibit these processes? Until it gets excreted out?

\n", "question_id": 113317, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "Only the L-isomer is produced naturally (https://en.wikipedia.org/wiki/Malic_acid#Biochemistry), while racemic mixtures are produced synthetically and used commercially as food additives and energy supplements.\n\n\n\n\nSo what happens when we consume D-malate? Does it just partake in the Krebs cycle (https://en.wikipedia.org/wiki/Citric_acid_cycle), the citrate-malate (https://en.wikipedia.org/wiki/Citrate%E2%80%93malate_shuttle)/malate-aspartate (https://en.wikipedia.org/wiki/Malate%E2%80%93aspartate_shuttle) shuttles, and such like the L-isomer?\n\n\n\n\nOr, does it just bioaccumulate and/or inhibit these processes? Until it gets excreted out?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "ManRow", "profile_url": "https://biology.stackexchange.com/users/30343/manrow", "user_type": "registered"}, "created_at": "2023-10-24T21:51:28+00:00", "raw_file": "raw/codex_api_v1/05c310a2e43a25cef557efc8abb78d08e3282613971fb1f949f4d401e11807fa_1790824041474830100_0.json", "raw_sha256": "06275f053755243837bd950c2a032e528759a141759c26078d708e55d401af9b", "revision_guid": "8EEA12C7-3334-40ED-8EA7-3C3C6EA0DFBC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/8EEA12C7-3334-40ED-8EA7-3C3C6EA0DFBC/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "ManRow", "profile_url": "https://biology.stackexchange.com/users/30343/manrow", "user_type": "registered"}, "created_at": "2023-10-24T22:01:20+00:00", "raw_file": 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It should work fine, isn't it?[image: Meselson and Stahl experiment; source: https://i.sstatic.net/vuVq2Oo7.jpg] (https://i.sstatic.net/vuVq2Oo7.jpg) Image source (https://www.mun.ca/biology/scarr/Meselson_StahL", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://i.sstatic.net/vuVq2Oo7.jpg", "kind": "external_url", "post_id": 117990, "post_url": "https://biology.stackexchange.com/questions/117990/use-of-n-15-in-meselson-and-stahl-experiment", "product": "citations", "record_id": "Scientific-Citation-Graph:bd2c78d72a3d896fd2eb740f", "split": "test", "thread": {"accepted_answer_id": 118024, "answers": [{"answer_html": "

The vast majority of nitrogen is $\\ce{^{14}N}$, see e.g. https://en.m.wikipedia.org/wiki/Isotopes_of_nitrogen

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So, they're starting with the experimental manipulation and then showing how their manipulated $\\ce{^{15}N}$ follows cell divisions.

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Imagine you wanted to follow some water, so you add a dye to it and see where the dyed water goes. That's fairly easy, and you can probably even spot by eye places where the dye is diluted to 1% the concentration you added. Alternatively, you could dye everything in the system, and then add some pure water and follow that through. Some areas will then be diluted with that pure water and have just 99% of the original concentration of dye. However, it's a lot harder to tell the difference between "lots of dye vs slightly less due" than it is "very little dye vs background of zero". If you had a bit less sample volume (say, 1% less) you'd easily have the same "change" as your target (say, 98% to 100%), whereas if you're looking for the 1% dye, a volume change of 1% would give you 1.01% to 0.99%.

\n

You're right, hypothetically you could keep everything in an $\\ce{^{15}N}$ world after starting with $\\ce{^{14}N}$, except you'd have to make sure to supply every nitrogenous reagent chemical needed in the experiment as $\\ce{^{15}N}$, and the world isn't perfect and there could be other plausible explanations of how $\\ce{^{14}N}$ entered the experiment accidentally.

\n

For the experiment with $\\ce{^{15}N}$, it's pretty clear that any substantial $\\ce{^{15}N}$ came from the original organism.

\n", "answer_id": 117991, "answer_text": "The vast majority of nitrogen is $\\ce{^{14}N}$, see e.g. https://en.m.wikipedia.org/wiki/Isotopes_of_nitrogen (https://en.m.wikipedia.org/wiki/Isotopes_of_nitrogen)\n\n\n\n\nSo, they're starting with the experimental manipulation and then showing how their manipulated $\\ce{^{15}N}$ follows cell divisions.\n\n\n\n\nImagine you wanted to follow some water, so you add a dye to it and see where the dyed water goes. That's fairly easy, and you can probably even spot by eye places where the dye is diluted to 1% the concentration you added. Alternatively, you could dye everything in the system, and then add some pure water and follow that through. Some areas will then be diluted with that pure water and have just 99% of the original concentration of dye. However, it's a lot harder to tell the difference between \"lots of dye vs slightly less due\" than it is \"very little dye vs background of zero\". If you had a bit less sample volume (say, 1% less) you'd easily have the same \"change\" as your target (say, 98% to 100%), whereas if you're looking for the 1% dye, a volume change of 1% would give you 1.01% to 0.99%.\n\n\n\n\nYou're right, hypothetically you could keep everything in an $\\ce{^{15}N}$ world after starting with $\\ce{^{14}N}$, except you'd have to make sure to supply every nitrogenous reagent chemical needed in the experiment as $\\ce{^{15}N}$, and the world isn't perfect and there could be other plausible explanations of how $\\ce{^{14}N}$ entered the experiment accidentally.\n\n\n\n\nFor the experiment with $\\ce{^{15}N}$, it's pretty clear that any substantial $\\ce{^{15}N}$ came from the original organism.", "answer_url": "https://biology.stackexchange.com/a/117991", "author": "Bryan Krause", "author_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2025-09-29T18:25:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:16.948131+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/46a41fae37d5c2c243f9abcbf6829a0045f46a51c624fbba2b897c320cdcba71_0.json", "raw_sha256": "e039e310d0106dc61f992ee05bbb0b0b57ded1c5092f97df2c52989edd5eaf68", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/118153;118142;118137;118126;118122;118117;118113;118102;118099;118097;118094;118081;118076;118072;118069;118065;118059;118056;118043;118039;118036;118030;118029;118025;118022;118018;117994;117992;117990;117987;117983;117981;117975;117971;117956;117953;117951;117945;117943;117941;117934;117926;117924;117920;117916;117914;117907;117892;117889;117887;117883;117876;117872;117867;117861;117860;117856;117855;117850;117849;117844;117840;117833;117821;117819;117817;117815;117814;117805;117794;117782;117774;117771;117767;117766;117761;117759;117756;117747;117732;117726;117724;117709;117701;117694;117693;117681;117680;117677;117671;117668;117664;117662;117659;117651;117641;117632;117624;117623;117607/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 117990, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Bryan Krause", "profile_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "user_type": "moderator"}, "created_at": "2025-09-29T18:25:14+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "E994CA32-9A11-48E2-B6FD-6D289F8FD806", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E994CA32-9A11-48E2-B6FD-6D289F8FD806/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Bryan Krause", "profile_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "user_type": "moderator"}, "created_at": "2025-09-29T18:35:46+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "453C4C81-3BE3-4FC8-BB22-F413055A48EC", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/453C4C81-3BE3-4FC8-BB22-F413055A48EC/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Bryan Krause", "profile_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "user_type": "moderator"}, "created_at": "2025-09-30T21:25:07+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "3B2CC543-8C81-41B8-8ACE-C8124F5764FF", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/3B2CC543-8C81-41B8-8ACE-C8124F5764FF/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-10-16T03:37:06+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "815A1F6B-17DF-427A-8B18-545B12FDFCFF", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/815A1F6B-17DF-427A-8B18-545B12FDFCFF/view-source"}], "score": 4, "updated_at": "2025-10-16T03:37:06+00:00"}, {"answer_html": "

The experiment was "actually" performed in both directions simultaneously because the order of the switch does not change the fundamental result—it simply provides double the confirmation. Whether you start with bacteria grown in a "heavy" medium and switch them to a "light" one, or start with "light" and switch to "heavy," the biological mechanism remains identical: the DNA strands separate, and each old strand pairs with a new strand built from whatever resources are currently available. In both cases, the first generation of new DNA ends up having an intermediate or "hybrid" density. Therefore, the direction of the experiment doesn't matter for the validity of the theory; doing it both ways merely served as a rigorous check to prove that the "hybrid" result was consistent and not caused by experimental error or contamination.

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Here's an extract from Google books, pg 308. A pic of it is added below.\"Holme's

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Image transcript:

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[...]Stahl had to leave for Missouri for a job interview. Too eager to wait for Stahl's return, Meselson decided to perform the experiment by himself. Before Stahl's departure Meselson suggested that it would be good to run the experiment in two directions - one beginning in heavy medium and switched to normal, the other beginning in normal and switched to heavy. Stahl cautioned him not to try to do both at once, because there was too much risk that he would mix up the samples.

\n

After Stahl had gone, Meselson decided that he could color-code the tubes in which he placed the samples and carry out a double experiment without confusion. To be absolutely thorough, he may even have added one or two control experiments in which he switched cul-tures from one heavy to another heavy medium, and from one light to another light medium.[...]

\n
\n", "answer_id": 118024, "answer_text": "The experiment was \"actually\" performed in both directions simultaneously because the order of the switch does not change the fundamental result—it simply provides double the confirmation. Whether you start with bacteria grown in a \"heavy\" medium and switch them to a \"light\" one, or start with \"light\" and switch to \"heavy,\" the biological mechanism remains identical: the DNA strands separate, and each old strand pairs with a new strand built from whatever resources are currently available. In both cases, the first generation of new DNA ends up having an intermediate or \"hybrid\" density. Therefore, the direction of the experiment doesn't matter for the validity of the theory; doing it both ways merely served as a rigorous check to prove that the \"hybrid\" result was consistent and not caused by experimental error or contamination.\n\n\n\n\n\n\n\nHere's an extract from Google books, pg 308 (https://books.google.co.in/books?redir_esc=y&id=g4DGSXAqReoC&q=Missouri#v=snippet&q=Missouri&f=false). A pic of it is added below.[image: Holme's book: The Most Beautiful Experiment in Biology; source: https://i.sstatic.net/eACU4P4v.png] (https://i.sstatic.net/eACU4P4v.png)\n\n\n\n\n\n\n\nImage transcript:\n\n\n\n\n\n\n\n[...]Stahl had to leave for Missouri for a job interview. Too eager to wait for Stahl's return, Meselson decided to perform the experiment by himself. Before Stahl's departure Meselson suggested that it would be good to run the experiment in two directions - one beginning in heavy medium and switched to normal, the other beginning in normal and switched to heavy. Stahl cautioned him not to try to do both at once, because there was too much risk that he would mix up the samples.\n\n\n\n\nAfter Stahl had gone, Meselson decided that he could color-code the tubes in which he placed the samples and carry out a double experiment without confusion. To be absolutely thorough, he may even have added one or two control experiments in which he switched cul-tures from one heavy to another heavy medium, and from one light to another light medium.[...]", "answer_url": "https://biology.stackexchange.com/a/118024", "author": "Shayan", "author_url": "https://biology.stackexchange.com/users/114723/shayan", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-10-16T04:51:37+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:16.948131+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/46a41fae37d5c2c243f9abcbf6829a0045f46a51c624fbba2b897c320cdcba71_0.json", "raw_sha256": "e039e310d0106dc61f992ee05bbb0b0b57ded1c5092f97df2c52989edd5eaf68", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/118153;118142;118137;118126;118122;118117;118113;118102;118099;118097;118094;118081;118076;118072;118069;118065;118059;118056;118043;118039;118036;118030;118029;118025;118022;118018;117994;117992;117990;117987;117983;117981;117975;117971;117956;117953;117951;117945;117943;117941;117934;117926;117924;117920;117916;117914;117907;117892;117889;117887;117883;117876;117872;117867;117861;117860;117856;117855;117850;117849;117844;117840;117833;117821;117819;117817;117815;117814;117805;117794;117782;117774;117771;117767;117766;117761;117759;117756;117747;117732;117726;117724;117709;117701;117694;117693;117681;117680;117677;117671;117668;117664;117662;117659;117651;117641;117632;117624;117623;117607/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; 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In Meselson and Stahl's experiment, why do we start with bacteria having $\\ce{^{15}N}$ incorporated into its DNA? I think if we start with $\\ce{^{14}N}$ then we would get light band first, hybrid in the next and hybrid and heavy from the next generation onwards. It should work fine, isn't it?\"Meselson Image source

\n", "question_id": 117990, "question_license": "CC BY-SA 4.0", "question_score": 4, "question_text": "In Meselson and Stahl's experiment, why do we start with bacteria having $\\ce{^{15}N}$ incorporated into its DNA? I think if we start with $\\ce{^{14}N}$ then we would get light band first, hybrid in the next and hybrid and heavy from the next generation onwards. It should work fine, isn't it?[image: Meselson and Stahl experiment; source: https://i.sstatic.net/vuVq2Oo7.jpg] (https://i.sstatic.net/vuVq2Oo7.jpg) Image source (https://www.mun.ca/biology/scarr/Meselson_StahL_experiment.html)", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-09-29T16:10:54+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "0618FB11-12EF-4A73-BC04-5CFE3B943C44", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/0618FB11-12EF-4A73-BC04-5CFE3B943C44/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-09-29T17:13:40+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "24B29716-9C7C-4D69-8D85-A449B5CE28D8", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/24B29716-9C7C-4D69-8D85-A449B5CE28D8/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-09-30T13:17:34+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "BBE9B6D5-8133-4A15-8BC2-8DDAA329AD85", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/BBE9B6D5-8133-4A15-8BC2-8DDAA329AD85/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-10-16T02:41:12+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "D0367674-BA27-48CA-A3F2-5558BFB7DE9E", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D0367674-BA27-48CA-A3F2-5558BFB7DE9E/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-12-27T18:32:11+00:00", "raw_file": "raw/codex_api_v1/24d8c4344fb56e0a47a9b0522e7fa13631e62cee2987c8bebddae0c2fd26f9ef_1790824157688070000_0.json", "raw_sha256": "4317829c6b2c1d1874a8b88f2daa4b8fa8bda8b06cf0c252f9adce0558f8183c", "revision_guid": "55602E3D-3D72-4021-B2AF-12ADD4EBEACD", "revision_number": 5, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/55602E3D-3D72-4021-B2AF-12ADD4EBEACD/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/117990/use-of-n-15-in-meselson-and-stahl-experiment", "split": "test", "split_group": "a57f57c46250c0d0ff15c0b1f14644ee9ff3241fce1bebc62ee9475b0c5d4ead", "tags": ["dna-replication"], "thread_id": "biology:117990", "title": "Use of N-15 in Meselson and Stahl experiment"}} {"citation_context": "ent; source: https://i.sstatic.net/vuVq2Oo7.jpg] (https://i.sstatic.net/vuVq2Oo7.jpg) Image source (https://www.mun.ca/biology/scarr/Meselson_StahL_experiment.html)", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.mun.ca/biology/scarr/Meselson_StahL_experiment.html", "kind": "external_url", "post_id": 117990, "post_url": "https://biology.stackexchange.com/questions/117990/use-of-n-15-in-meselson-and-stahl-experiment", "product": "citations", "record_id": "Scientific-Citation-Graph:385421b00fd77300679f7c0f", "split": "test", "thread": {"accepted_answer_id": 118024, "answers": [{"answer_html": "

The vast majority of nitrogen is $\\ce{^{14}N}$, see e.g. https://en.m.wikipedia.org/wiki/Isotopes_of_nitrogen

\n

So, they're starting with the experimental manipulation and then showing how their manipulated $\\ce{^{15}N}$ follows cell divisions.

\n

Imagine you wanted to follow some water, so you add a dye to it and see where the dyed water goes. That's fairly easy, and you can probably even spot by eye places where the dye is diluted to 1% the concentration you added. Alternatively, you could dye everything in the system, and then add some pure water and follow that through. Some areas will then be diluted with that pure water and have just 99% of the original concentration of dye. However, it's a lot harder to tell the difference between "lots of dye vs slightly less due" than it is "very little dye vs background of zero". If you had a bit less sample volume (say, 1% less) you'd easily have the same "change" as your target (say, 98% to 100%), whereas if you're looking for the 1% dye, a volume change of 1% would give you 1.01% to 0.99%.

\n

You're right, hypothetically you could keep everything in an $\\ce{^{15}N}$ world after starting with $\\ce{^{14}N}$, except you'd have to make sure to supply every nitrogenous reagent chemical needed in the experiment as $\\ce{^{15}N}$, and the world isn't perfect and there could be other plausible explanations of how $\\ce{^{14}N}$ entered the experiment accidentally.

\n

For the experiment with $\\ce{^{15}N}$, it's pretty clear that any substantial $\\ce{^{15}N}$ came from the original organism.

\n", "answer_id": 117991, "answer_text": "The vast majority of nitrogen is $\\ce{^{14}N}$, see e.g. https://en.m.wikipedia.org/wiki/Isotopes_of_nitrogen (https://en.m.wikipedia.org/wiki/Isotopes_of_nitrogen)\n\n\n\n\nSo, they're starting with the experimental manipulation and then showing how their manipulated $\\ce{^{15}N}$ follows cell divisions.\n\n\n\n\nImagine you wanted to follow some water, so you add a dye to it and see where the dyed water goes. That's fairly easy, and you can probably even spot by eye places where the dye is diluted to 1% the concentration you added. Alternatively, you could dye everything in the system, and then add some pure water and follow that through. Some areas will then be diluted with that pure water and have just 99% of the original concentration of dye. However, it's a lot harder to tell the difference between \"lots of dye vs slightly less due\" than it is \"very little dye vs background of zero\". If you had a bit less sample volume (say, 1% less) you'd easily have the same \"change\" as your target (say, 98% to 100%), whereas if you're looking for the 1% dye, a volume change of 1% would give you 1.01% to 0.99%.\n\n\n\n\nYou're right, hypothetically you could keep everything in an $\\ce{^{15}N}$ world after starting with $\\ce{^{14}N}$, except you'd have to make sure to supply every nitrogenous reagent chemical needed in the experiment as $\\ce{^{15}N}$, and the world isn't perfect and there could be other plausible explanations of how $\\ce{^{14}N}$ entered the experiment accidentally.\n\n\n\n\nFor the experiment with $\\ce{^{15}N}$, it's pretty clear that any substantial $\\ce{^{15}N}$ came from the original organism.", "answer_url": "https://biology.stackexchange.com/a/117991", "author": "Bryan Krause", "author_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2025-09-29T18:25:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:16.948131+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/46a41fae37d5c2c243f9abcbf6829a0045f46a51c624fbba2b897c320cdcba71_0.json", "raw_sha256": "e039e310d0106dc61f992ee05bbb0b0b57ded1c5092f97df2c52989edd5eaf68", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/118153;118142;118137;118126;118122;118117;118113;118102;118099;118097;118094;118081;118076;118072;118069;118065;118059;118056;118043;118039;118036;118030;118029;118025;118022;118018;117994;117992;117990;117987;117983;117981;117975;117971;117956;117953;117951;117945;117943;117941;117934;117926;117924;117920;117916;117914;117907;117892;117889;117887;117883;117876;117872;117867;117861;117860;117856;117855;117850;117849;117844;117840;117833;117821;117819;117817;117815;117814;117805;117794;117782;117774;117771;117767;117766;117761;117759;117756;117747;117732;117726;117724;117709;117701;117694;117693;117681;117680;117677;117671;117668;117664;117662;117659;117651;117641;117632;117624;117623;117607/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; 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The experiment was "actually" performed in both directions simultaneously because the order of the switch does not change the fundamental result—it simply provides double the confirmation. Whether you start with bacteria grown in a "heavy" medium and switch them to a "light" one, or start with "light" and switch to "heavy," the biological mechanism remains identical: the DNA strands separate, and each old strand pairs with a new strand built from whatever resources are currently available. In both cases, the first generation of new DNA ends up having an intermediate or "hybrid" density. Therefore, the direction of the experiment doesn't matter for the validity of the theory; doing it both ways merely served as a rigorous check to prove that the "hybrid" result was consistent and not caused by experimental error or contamination.

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Here's an extract from Google books, pg 308. A pic of it is added below.\"Holme's

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Image transcript:

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[...]Stahl had to leave for Missouri for a job interview. Too eager to wait for Stahl's return, Meselson decided to perform the experiment by himself. Before Stahl's departure Meselson suggested that it would be good to run the experiment in two directions - one beginning in heavy medium and switched to normal, the other beginning in normal and switched to heavy. Stahl cautioned him not to try to do both at once, because there was too much risk that he would mix up the samples.

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After Stahl had gone, Meselson decided that he could color-code the tubes in which he placed the samples and carry out a double experiment without confusion. To be absolutely thorough, he may even have added one or two control experiments in which he switched cul-tures from one heavy to another heavy medium, and from one light to another light medium.[...]

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\n", "answer_id": 118024, "answer_text": "The experiment was \"actually\" performed in both directions simultaneously because the order of the switch does not change the fundamental result—it simply provides double the confirmation. Whether you start with bacteria grown in a \"heavy\" medium and switch them to a \"light\" one, or start with \"light\" and switch to \"heavy,\" the biological mechanism remains identical: the DNA strands separate, and each old strand pairs with a new strand built from whatever resources are currently available. In both cases, the first generation of new DNA ends up having an intermediate or \"hybrid\" density. Therefore, the direction of the experiment doesn't matter for the validity of the theory; doing it both ways merely served as a rigorous check to prove that the \"hybrid\" result was consistent and not caused by experimental error or contamination.\n\n\n\n\n\n\n\nHere's an extract from Google books, pg 308 (https://books.google.co.in/books?redir_esc=y&id=g4DGSXAqReoC&q=Missouri#v=snippet&q=Missouri&f=false). A pic of it is added below.[image: Holme's book: The Most Beautiful Experiment in Biology; source: https://i.sstatic.net/eACU4P4v.png] (https://i.sstatic.net/eACU4P4v.png)\n\n\n\n\n\n\n\nImage transcript:\n\n\n\n\n\n\n\n[...]Stahl had to leave for Missouri for a job interview. Too eager to wait for Stahl's return, Meselson decided to perform the experiment by himself. Before Stahl's departure Meselson suggested that it would be good to run the experiment in two directions - one beginning in heavy medium and switched to normal, the other beginning in normal and switched to heavy. Stahl cautioned him not to try to do both at once, because there was too much risk that he would mix up the samples.\n\n\n\n\nAfter Stahl had gone, Meselson decided that he could color-code the tubes in which he placed the samples and carry out a double experiment without confusion. To be absolutely thorough, he may even have added one or two control experiments in which he switched cul-tures from one heavy to another heavy medium, and from one light to another light medium.[...]", "answer_url": "https://biology.stackexchange.com/a/118024", "author": "Shayan", "author_url": "https://biology.stackexchange.com/users/114723/shayan", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-10-16T04:51:37+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:16.948131+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/46a41fae37d5c2c243f9abcbf6829a0045f46a51c624fbba2b897c320cdcba71_0.json", "raw_sha256": "e039e310d0106dc61f992ee05bbb0b0b57ded1c5092f97df2c52989edd5eaf68", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/118153;118142;118137;118126;118122;118117;118113;118102;118099;118097;118094;118081;118076;118072;118069;118065;118059;118056;118043;118039;118036;118030;118029;118025;118022;118018;117994;117992;117990;117987;117983;117981;117975;117971;117956;117953;117951;117945;117943;117941;117934;117926;117924;117920;117916;117914;117907;117892;117889;117887;117883;117876;117872;117867;117861;117860;117856;117855;117850;117849;117844;117840;117833;117821;117819;117817;117815;117814;117805;117794;117782;117774;117771;117767;117766;117761;117759;117756;117747;117732;117726;117724;117709;117701;117694;117693;117681;117680;117677;117671;117668;117664;117662;117659;117651;117641;117632;117624;117623;117607/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; 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In Meselson and Stahl's experiment, why do we start with bacteria having $\\ce{^{15}N}$ incorporated into its DNA? I think if we start with $\\ce{^{14}N}$ then we would get light band first, hybrid in the next and hybrid and heavy from the next generation onwards. It should work fine, isn't it?\"Meselson Image source

\n", "question_id": 117990, "question_license": "CC BY-SA 4.0", "question_score": 4, "question_text": "In Meselson and Stahl's experiment, why do we start with bacteria having $\\ce{^{15}N}$ incorporated into its DNA? I think if we start with $\\ce{^{14}N}$ then we would get light band first, hybrid in the next and hybrid and heavy from the next generation onwards. It should work fine, isn't it?[image: Meselson and Stahl experiment; source: https://i.sstatic.net/vuVq2Oo7.jpg] (https://i.sstatic.net/vuVq2Oo7.jpg) Image source (https://www.mun.ca/biology/scarr/Meselson_StahL_experiment.html)", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-09-29T16:10:54+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "0618FB11-12EF-4A73-BC04-5CFE3B943C44", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/0618FB11-12EF-4A73-BC04-5CFE3B943C44/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-09-29T17:13:40+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "24B29716-9C7C-4D69-8D85-A449B5CE28D8", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/24B29716-9C7C-4D69-8D85-A449B5CE28D8/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-09-30T13:17:34+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "BBE9B6D5-8133-4A15-8BC2-8DDAA329AD85", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/BBE9B6D5-8133-4A15-8BC2-8DDAA329AD85/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-10-16T02:41:12+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "D0367674-BA27-48CA-A3F2-5558BFB7DE9E", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D0367674-BA27-48CA-A3F2-5558BFB7DE9E/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-12-27T18:32:11+00:00", "raw_file": "raw/codex_api_v1/24d8c4344fb56e0a47a9b0522e7fa13631e62cee2987c8bebddae0c2fd26f9ef_1790824157688070000_0.json", "raw_sha256": "4317829c6b2c1d1874a8b88f2daa4b8fa8bda8b06cf0c252f9adce0558f8183c", "revision_guid": "55602E3D-3D72-4021-B2AF-12ADD4EBEACD", "revision_number": 5, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/55602E3D-3D72-4021-B2AF-12ADD4EBEACD/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/117990/use-of-n-15-in-meselson-and-stahl-experiment", "split": "test", "split_group": "a57f57c46250c0d0ff15c0b1f14644ee9ff3241fce1bebc62ee9475b0c5d4ead", "tags": ["dna-replication"], "thread_id": "biology:117990", "title": "Use of N-15 in Meselson and Stahl experiment"}} {"citation_context": "The vast majority of nitrogen is $\\ce{^{14}N}$, see e.g. https://en.m.wikipedia.org/wiki/Isotopes_of_nitrogen (https://en.m.wikipedia.org/wiki/Isotopes_of_nitrogen)\n\n\n\n\nSo, they're starting with the experiment", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.m.wikipedia.org/wiki/Isotopes_of_nitrogen", "kind": "external_url", "post_id": 117991, "post_url": "https://biology.stackexchange.com/a/117991", "product": "citations", "record_id": "Scientific-Citation-Graph:f86fe70e9f7adfe6a41696e2", "split": "test", "thread": {"accepted_answer_id": 118024, "answers": [{"answer_html": "

The vast majority of nitrogen is $\\ce{^{14}N}$, see e.g. https://en.m.wikipedia.org/wiki/Isotopes_of_nitrogen

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So, they're starting with the experimental manipulation and then showing how their manipulated $\\ce{^{15}N}$ follows cell divisions.

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Imagine you wanted to follow some water, so you add a dye to it and see where the dyed water goes. That's fairly easy, and you can probably even spot by eye places where the dye is diluted to 1% the concentration you added. Alternatively, you could dye everything in the system, and then add some pure water and follow that through. Some areas will then be diluted with that pure water and have just 99% of the original concentration of dye. However, it's a lot harder to tell the difference between "lots of dye vs slightly less due" than it is "very little dye vs background of zero". If you had a bit less sample volume (say, 1% less) you'd easily have the same "change" as your target (say, 98% to 100%), whereas if you're looking for the 1% dye, a volume change of 1% would give you 1.01% to 0.99%.

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You're right, hypothetically you could keep everything in an $\\ce{^{15}N}$ world after starting with $\\ce{^{14}N}$, except you'd have to make sure to supply every nitrogenous reagent chemical needed in the experiment as $\\ce{^{15}N}$, and the world isn't perfect and there could be other plausible explanations of how $\\ce{^{14}N}$ entered the experiment accidentally.

\n

For the experiment with $\\ce{^{15}N}$, it's pretty clear that any substantial $\\ce{^{15}N}$ came from the original organism.

\n", "answer_id": 117991, "answer_text": "The vast majority of nitrogen is $\\ce{^{14}N}$, see e.g. https://en.m.wikipedia.org/wiki/Isotopes_of_nitrogen (https://en.m.wikipedia.org/wiki/Isotopes_of_nitrogen)\n\n\n\n\nSo, they're starting with the experimental manipulation and then showing how their manipulated $\\ce{^{15}N}$ follows cell divisions.\n\n\n\n\nImagine you wanted to follow some water, so you add a dye to it and see where the dyed water goes. That's fairly easy, and you can probably even spot by eye places where the dye is diluted to 1% the concentration you added. Alternatively, you could dye everything in the system, and then add some pure water and follow that through. Some areas will then be diluted with that pure water and have just 99% of the original concentration of dye. However, it's a lot harder to tell the difference between \"lots of dye vs slightly less due\" than it is \"very little dye vs background of zero\". If you had a bit less sample volume (say, 1% less) you'd easily have the same \"change\" as your target (say, 98% to 100%), whereas if you're looking for the 1% dye, a volume change of 1% would give you 1.01% to 0.99%.\n\n\n\n\nYou're right, hypothetically you could keep everything in an $\\ce{^{15}N}$ world after starting with $\\ce{^{14}N}$, except you'd have to make sure to supply every nitrogenous reagent chemical needed in the experiment as $\\ce{^{15}N}$, and the world isn't perfect and there could be other plausible explanations of how $\\ce{^{14}N}$ entered the experiment accidentally.\n\n\n\n\nFor the experiment with $\\ce{^{15}N}$, it's pretty clear that any substantial $\\ce{^{15}N}$ came from the original organism.", "answer_url": "https://biology.stackexchange.com/a/117991", "author": "Bryan Krause", "author_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2025-09-29T18:25:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:16.948131+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/46a41fae37d5c2c243f9abcbf6829a0045f46a51c624fbba2b897c320cdcba71_0.json", "raw_sha256": "e039e310d0106dc61f992ee05bbb0b0b57ded1c5092f97df2c52989edd5eaf68", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/118153;118142;118137;118126;118122;118117;118113;118102;118099;118097;118094;118081;118076;118072;118069;118065;118059;118056;118043;118039;118036;118030;118029;118025;118022;118018;117994;117992;117990;117987;117983;117981;117975;117971;117956;117953;117951;117945;117943;117941;117934;117926;117924;117920;117916;117914;117907;117892;117889;117887;117883;117876;117872;117867;117861;117860;117856;117855;117850;117849;117844;117840;117833;117821;117819;117817;117815;117814;117805;117794;117782;117774;117771;117767;117766;117761;117759;117756;117747;117732;117726;117724;117709;117701;117694;117693;117681;117680;117677;117671;117668;117664;117662;117659;117651;117641;117632;117624;117623;117607/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 117990, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Bryan Krause", "profile_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "user_type": "moderator"}, "created_at": "2025-09-29T18:25:14+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "E994CA32-9A11-48E2-B6FD-6D289F8FD806", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E994CA32-9A11-48E2-B6FD-6D289F8FD806/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Bryan Krause", "profile_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "user_type": "moderator"}, "created_at": "2025-09-29T18:35:46+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "453C4C81-3BE3-4FC8-BB22-F413055A48EC", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/453C4C81-3BE3-4FC8-BB22-F413055A48EC/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Bryan Krause", "profile_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "user_type": "moderator"}, "created_at": "2025-09-30T21:25:07+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "3B2CC543-8C81-41B8-8ACE-C8124F5764FF", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/3B2CC543-8C81-41B8-8ACE-C8124F5764FF/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-10-16T03:37:06+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "815A1F6B-17DF-427A-8B18-545B12FDFCFF", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/815A1F6B-17DF-427A-8B18-545B12FDFCFF/view-source"}], "score": 4, "updated_at": "2025-10-16T03:37:06+00:00"}, {"answer_html": "

The experiment was "actually" performed in both directions simultaneously because the order of the switch does not change the fundamental result—it simply provides double the confirmation. Whether you start with bacteria grown in a "heavy" medium and switch them to a "light" one, or start with "light" and switch to "heavy," the biological mechanism remains identical: the DNA strands separate, and each old strand pairs with a new strand built from whatever resources are currently available. In both cases, the first generation of new DNA ends up having an intermediate or "hybrid" density. Therefore, the direction of the experiment doesn't matter for the validity of the theory; doing it both ways merely served as a rigorous check to prove that the "hybrid" result was consistent and not caused by experimental error or contamination.

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Here's an extract from Google books, pg 308. A pic of it is added below.\"Holme's

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Image transcript:

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[...]Stahl had to leave for Missouri for a job interview. Too eager to wait for Stahl's return, Meselson decided to perform the experiment by himself. Before Stahl's departure Meselson suggested that it would be good to run the experiment in two directions - one beginning in heavy medium and switched to normal, the other beginning in normal and switched to heavy. Stahl cautioned him not to try to do both at once, because there was too much risk that he would mix up the samples.

\n

After Stahl had gone, Meselson decided that he could color-code the tubes in which he placed the samples and carry out a double experiment without confusion. To be absolutely thorough, he may even have added one or two control experiments in which he switched cul-tures from one heavy to another heavy medium, and from one light to another light medium.[...]

\n
\n", "answer_id": 118024, "answer_text": "The experiment was \"actually\" performed in both directions simultaneously because the order of the switch does not change the fundamental result—it simply provides double the confirmation. Whether you start with bacteria grown in a \"heavy\" medium and switch them to a \"light\" one, or start with \"light\" and switch to \"heavy,\" the biological mechanism remains identical: the DNA strands separate, and each old strand pairs with a new strand built from whatever resources are currently available. In both cases, the first generation of new DNA ends up having an intermediate or \"hybrid\" density. Therefore, the direction of the experiment doesn't matter for the validity of the theory; doing it both ways merely served as a rigorous check to prove that the \"hybrid\" result was consistent and not caused by experimental error or contamination.\n\n\n\n\n\n\n\nHere's an extract from Google books, pg 308 (https://books.google.co.in/books?redir_esc=y&id=g4DGSXAqReoC&q=Missouri#v=snippet&q=Missouri&f=false). A pic of it is added below.[image: Holme's book: The Most Beautiful Experiment in Biology; source: https://i.sstatic.net/eACU4P4v.png] (https://i.sstatic.net/eACU4P4v.png)\n\n\n\n\n\n\n\nImage transcript:\n\n\n\n\n\n\n\n[...]Stahl had to leave for Missouri for a job interview. Too eager to wait for Stahl's return, Meselson decided to perform the experiment by himself. Before Stahl's departure Meselson suggested that it would be good to run the experiment in two directions - one beginning in heavy medium and switched to normal, the other beginning in normal and switched to heavy. Stahl cautioned him not to try to do both at once, because there was too much risk that he would mix up the samples.\n\n\n\n\nAfter Stahl had gone, Meselson decided that he could color-code the tubes in which he placed the samples and carry out a double experiment without confusion. To be absolutely thorough, he may even have added one or two control experiments in which he switched cul-tures from one heavy to another heavy medium, and from one light to another light medium.[...]", "answer_url": "https://biology.stackexchange.com/a/118024", "author": "Shayan", "author_url": "https://biology.stackexchange.com/users/114723/shayan", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-10-16T04:51:37+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:16.948131+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/46a41fae37d5c2c243f9abcbf6829a0045f46a51c624fbba2b897c320cdcba71_0.json", "raw_sha256": "e039e310d0106dc61f992ee05bbb0b0b57ded1c5092f97df2c52989edd5eaf68", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/118153;118142;118137;118126;118122;118117;118113;118102;118099;118097;118094;118081;118076;118072;118069;118065;118059;118056;118043;118039;118036;118030;118029;118025;118022;118018;117994;117992;117990;117987;117983;117981;117975;117971;117956;117953;117951;117945;117943;117941;117934;117926;117924;117920;117916;117914;117907;117892;117889;117887;117883;117876;117872;117867;117861;117860;117856;117855;117850;117849;117844;117840;117833;117821;117819;117817;117815;117814;117805;117794;117782;117774;117771;117767;117766;117761;117759;117756;117747;117732;117726;117724;117709;117701;117694;117693;117681;117680;117677;117671;117668;117664;117662;117659;117651;117641;117632;117624;117623;117607/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; 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mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Shayan", "question_author_url": "https://biology.stackexchange.com/users/114723/shayan", "question_author_user_type": "registered", "question_created_at": "2025-09-29T16:10:54+00:00", "question_html": "

In Meselson and Stahl's experiment, why do we start with bacteria having $\\ce{^{15}N}$ incorporated into its DNA? I think if we start with $\\ce{^{14}N}$ then we would get light band first, hybrid in the next and hybrid and heavy from the next generation onwards. It should work fine, isn't it?\"Meselson Image source

\n", "question_id": 117990, "question_license": "CC BY-SA 4.0", "question_score": 4, "question_text": "In Meselson and Stahl's experiment, why do we start with bacteria having $\\ce{^{15}N}$ incorporated into its DNA? I think if we start with $\\ce{^{14}N}$ then we would get light band first, hybrid in the next and hybrid and heavy from the next generation onwards. It should work fine, isn't it?[image: Meselson and Stahl experiment; source: https://i.sstatic.net/vuVq2Oo7.jpg] (https://i.sstatic.net/vuVq2Oo7.jpg) Image source (https://www.mun.ca/biology/scarr/Meselson_StahL_experiment.html)", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-09-29T16:10:54+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "0618FB11-12EF-4A73-BC04-5CFE3B943C44", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/0618FB11-12EF-4A73-BC04-5CFE3B943C44/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-09-29T17:13:40+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "24B29716-9C7C-4D69-8D85-A449B5CE28D8", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/24B29716-9C7C-4D69-8D85-A449B5CE28D8/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-09-30T13:17:34+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "BBE9B6D5-8133-4A15-8BC2-8DDAA329AD85", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/BBE9B6D5-8133-4A15-8BC2-8DDAA329AD85/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-10-16T02:41:12+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "D0367674-BA27-48CA-A3F2-5558BFB7DE9E", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D0367674-BA27-48CA-A3F2-5558BFB7DE9E/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-12-27T18:32:11+00:00", "raw_file": "raw/codex_api_v1/24d8c4344fb56e0a47a9b0522e7fa13631e62cee2987c8bebddae0c2fd26f9ef_1790824157688070000_0.json", "raw_sha256": "4317829c6b2c1d1874a8b88f2daa4b8fa8bda8b06cf0c252f9adce0558f8183c", "revision_guid": "55602E3D-3D72-4021-B2AF-12ADD4EBEACD", "revision_number": 5, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/55602E3D-3D72-4021-B2AF-12ADD4EBEACD/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/117990/use-of-n-15-in-meselson-and-stahl-experiment", "split": "test", "split_group": "a57f57c46250c0d0ff15c0b1f14644ee9ff3241fce1bebc62ee9475b0c5d4ead", "tags": ["dna-replication"], "thread_id": "biology:117990", "title": "Use of N-15 in Meselson and Stahl experiment"}} {"citation_context": " caused by experimental error or contamination.\n\n\n\n\n\n\n\nHere's an extract from Google books, pg 308 (https://books.google.co.in/books?redir_esc=y&id=g4DGSXAqReoC&q=Missouri#v=snippet&q=Missouri&f=false). A pic of it is added below.[image: Holme's book: The Most Beautiful Experiment in Biology; source", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://books.google.co.in/books?redir_esc=y&id=g4DGSXAqReoC&q=Missouri#v=snippet&q=Missouri&f=false", "kind": "external_url", "post_id": 118024, "post_url": "https://biology.stackexchange.com/a/118024", "product": "citations", "record_id": "Scientific-Citation-Graph:a416410a49df83085d478f4d", "split": "test", "thread": {"accepted_answer_id": 118024, "answers": [{"answer_html": "

The vast majority of nitrogen is $\\ce{^{14}N}$, see e.g. https://en.m.wikipedia.org/wiki/Isotopes_of_nitrogen

\n

So, they're starting with the experimental manipulation and then showing how their manipulated $\\ce{^{15}N}$ follows cell divisions.

\n

Imagine you wanted to follow some water, so you add a dye to it and see where the dyed water goes. That's fairly easy, and you can probably even spot by eye places where the dye is diluted to 1% the concentration you added. Alternatively, you could dye everything in the system, and then add some pure water and follow that through. Some areas will then be diluted with that pure water and have just 99% of the original concentration of dye. However, it's a lot harder to tell the difference between "lots of dye vs slightly less due" than it is "very little dye vs background of zero". If you had a bit less sample volume (say, 1% less) you'd easily have the same "change" as your target (say, 98% to 100%), whereas if you're looking for the 1% dye, a volume change of 1% would give you 1.01% to 0.99%.

\n

You're right, hypothetically you could keep everything in an $\\ce{^{15}N}$ world after starting with $\\ce{^{14}N}$, except you'd have to make sure to supply every nitrogenous reagent chemical needed in the experiment as $\\ce{^{15}N}$, and the world isn't perfect and there could be other plausible explanations of how $\\ce{^{14}N}$ entered the experiment accidentally.

\n

For the experiment with $\\ce{^{15}N}$, it's pretty clear that any substantial $\\ce{^{15}N}$ came from the original organism.

\n", "answer_id": 117991, "answer_text": "The vast majority of nitrogen is $\\ce{^{14}N}$, see e.g. https://en.m.wikipedia.org/wiki/Isotopes_of_nitrogen (https://en.m.wikipedia.org/wiki/Isotopes_of_nitrogen)\n\n\n\n\nSo, they're starting with the experimental manipulation and then showing how their manipulated $\\ce{^{15}N}$ follows cell divisions.\n\n\n\n\nImagine you wanted to follow some water, so you add a dye to it and see where the dyed water goes. That's fairly easy, and you can probably even spot by eye places where the dye is diluted to 1% the concentration you added. Alternatively, you could dye everything in the system, and then add some pure water and follow that through. Some areas will then be diluted with that pure water and have just 99% of the original concentration of dye. However, it's a lot harder to tell the difference between \"lots of dye vs slightly less due\" than it is \"very little dye vs background of zero\". If you had a bit less sample volume (say, 1% less) you'd easily have the same \"change\" as your target (say, 98% to 100%), whereas if you're looking for the 1% dye, a volume change of 1% would give you 1.01% to 0.99%.\n\n\n\n\nYou're right, hypothetically you could keep everything in an $\\ce{^{15}N}$ world after starting with $\\ce{^{14}N}$, except you'd have to make sure to supply every nitrogenous reagent chemical needed in the experiment as $\\ce{^{15}N}$, and the world isn't perfect and there could be other plausible explanations of how $\\ce{^{14}N}$ entered the experiment accidentally.\n\n\n\n\nFor the experiment with $\\ce{^{15}N}$, it's pretty clear that any substantial $\\ce{^{15}N}$ came from the original organism.", "answer_url": "https://biology.stackexchange.com/a/117991", "author": "Bryan Krause", "author_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2025-09-29T18:25:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:16.948131+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/46a41fae37d5c2c243f9abcbf6829a0045f46a51c624fbba2b897c320cdcba71_0.json", "raw_sha256": "e039e310d0106dc61f992ee05bbb0b0b57ded1c5092f97df2c52989edd5eaf68", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/118153;118142;118137;118126;118122;118117;118113;118102;118099;118097;118094;118081;118076;118072;118069;118065;118059;118056;118043;118039;118036;118030;118029;118025;118022;118018;117994;117992;117990;117987;117983;117981;117975;117971;117956;117953;117951;117945;117943;117941;117934;117926;117924;117920;117916;117914;117907;117892;117889;117887;117883;117876;117872;117867;117861;117860;117856;117855;117850;117849;117844;117840;117833;117821;117819;117817;117815;117814;117805;117794;117782;117774;117771;117767;117766;117761;117759;117756;117747;117732;117726;117724;117709;117701;117694;117693;117681;117680;117677;117671;117668;117664;117662;117659;117651;117641;117632;117624;117623;117607/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; 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The experiment was "actually" performed in both directions simultaneously because the order of the switch does not change the fundamental result—it simply provides double the confirmation. Whether you start with bacteria grown in a "heavy" medium and switch them to a "light" one, or start with "light" and switch to "heavy," the biological mechanism remains identical: the DNA strands separate, and each old strand pairs with a new strand built from whatever resources are currently available. In both cases, the first generation of new DNA ends up having an intermediate or "hybrid" density. Therefore, the direction of the experiment doesn't matter for the validity of the theory; doing it both ways merely served as a rigorous check to prove that the "hybrid" result was consistent and not caused by experimental error or contamination.

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Here's an extract from Google books, pg 308. A pic of it is added below.\"Holme's

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Image transcript:

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[...]Stahl had to leave for Missouri for a job interview. Too eager to wait for Stahl's return, Meselson decided to perform the experiment by himself. Before Stahl's departure Meselson suggested that it would be good to run the experiment in two directions - one beginning in heavy medium and switched to normal, the other beginning in normal and switched to heavy. Stahl cautioned him not to try to do both at once, because there was too much risk that he would mix up the samples.

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After Stahl had gone, Meselson decided that he could color-code the tubes in which he placed the samples and carry out a double experiment without confusion. To be absolutely thorough, he may even have added one or two control experiments in which he switched cul-tures from one heavy to another heavy medium, and from one light to another light medium.[...]

\n
\n", "answer_id": 118024, "answer_text": "The experiment was \"actually\" performed in both directions simultaneously because the order of the switch does not change the fundamental result—it simply provides double the confirmation. Whether you start with bacteria grown in a \"heavy\" medium and switch them to a \"light\" one, or start with \"light\" and switch to \"heavy,\" the biological mechanism remains identical: the DNA strands separate, and each old strand pairs with a new strand built from whatever resources are currently available. In both cases, the first generation of new DNA ends up having an intermediate or \"hybrid\" density. Therefore, the direction of the experiment doesn't matter for the validity of the theory; doing it both ways merely served as a rigorous check to prove that the \"hybrid\" result was consistent and not caused by experimental error or contamination.\n\n\n\n\n\n\n\nHere's an extract from Google books, pg 308 (https://books.google.co.in/books?redir_esc=y&id=g4DGSXAqReoC&q=Missouri#v=snippet&q=Missouri&f=false). A pic of it is added below.[image: Holme's book: The Most Beautiful Experiment in Biology; source: https://i.sstatic.net/eACU4P4v.png] (https://i.sstatic.net/eACU4P4v.png)\n\n\n\n\n\n\n\nImage transcript:\n\n\n\n\n\n\n\n[...]Stahl had to leave for Missouri for a job interview. Too eager to wait for Stahl's return, Meselson decided to perform the experiment by himself. Before Stahl's departure Meselson suggested that it would be good to run the experiment in two directions - one beginning in heavy medium and switched to normal, the other beginning in normal and switched to heavy. Stahl cautioned him not to try to do both at once, because there was too much risk that he would mix up the samples.\n\n\n\n\nAfter Stahl had gone, Meselson decided that he could color-code the tubes in which he placed the samples and carry out a double experiment without confusion. To be absolutely thorough, he may even have added one or two control experiments in which he switched cul-tures from one heavy to another heavy medium, and from one light to another light medium.[...]", "answer_url": "https://biology.stackexchange.com/a/118024", "author": "Shayan", "author_url": "https://biology.stackexchange.com/users/114723/shayan", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-10-16T04:51:37+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:16.948131+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/46a41fae37d5c2c243f9abcbf6829a0045f46a51c624fbba2b897c320cdcba71_0.json", "raw_sha256": "e039e310d0106dc61f992ee05bbb0b0b57ded1c5092f97df2c52989edd5eaf68", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/118153;118142;118137;118126;118122;118117;118113;118102;118099;118097;118094;118081;118076;118072;118069;118065;118059;118056;118043;118039;118036;118030;118029;118025;118022;118018;117994;117992;117990;117987;117983;117981;117975;117971;117956;117953;117951;117945;117943;117941;117934;117926;117924;117920;117916;117914;117907;117892;117889;117887;117883;117876;117872;117867;117861;117860;117856;117855;117850;117849;117844;117840;117833;117821;117819;117817;117815;117814;117805;117794;117782;117774;117771;117767;117766;117761;117759;117756;117747;117732;117726;117724;117709;117701;117694;117693;117681;117680;117677;117671;117668;117664;117662;117659;117651;117641;117632;117624;117623;117607/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; 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mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Shayan", "question_author_url": "https://biology.stackexchange.com/users/114723/shayan", "question_author_user_type": "registered", "question_created_at": "2025-09-29T16:10:54+00:00", "question_html": "

In Meselson and Stahl's experiment, why do we start with bacteria having $\\ce{^{15}N}$ incorporated into its DNA? I think if we start with $\\ce{^{14}N}$ then we would get light band first, hybrid in the next and hybrid and heavy from the next generation onwards. It should work fine, isn't it?\"Meselson Image source

\n", "question_id": 117990, "question_license": "CC BY-SA 4.0", "question_score": 4, "question_text": "In Meselson and Stahl's experiment, why do we start with bacteria having $\\ce{^{15}N}$ incorporated into its DNA? I think if we start with $\\ce{^{14}N}$ then we would get light band first, hybrid in the next and hybrid and heavy from the next generation onwards. It should work fine, isn't it?[image: Meselson and Stahl experiment; source: https://i.sstatic.net/vuVq2Oo7.jpg] (https://i.sstatic.net/vuVq2Oo7.jpg) Image source (https://www.mun.ca/biology/scarr/Meselson_StahL_experiment.html)", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-09-29T16:10:54+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "0618FB11-12EF-4A73-BC04-5CFE3B943C44", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/0618FB11-12EF-4A73-BC04-5CFE3B943C44/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-09-29T17:13:40+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "24B29716-9C7C-4D69-8D85-A449B5CE28D8", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/24B29716-9C7C-4D69-8D85-A449B5CE28D8/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-09-30T13:17:34+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "BBE9B6D5-8133-4A15-8BC2-8DDAA329AD85", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/BBE9B6D5-8133-4A15-8BC2-8DDAA329AD85/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-10-16T02:41:12+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "D0367674-BA27-48CA-A3F2-5558BFB7DE9E", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D0367674-BA27-48CA-A3F2-5558BFB7DE9E/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-12-27T18:32:11+00:00", "raw_file": "raw/codex_api_v1/24d8c4344fb56e0a47a9b0522e7fa13631e62cee2987c8bebddae0c2fd26f9ef_1790824157688070000_0.json", "raw_sha256": "4317829c6b2c1d1874a8b88f2daa4b8fa8bda8b06cf0c252f9adce0558f8183c", "revision_guid": "55602E3D-3D72-4021-B2AF-12ADD4EBEACD", "revision_number": 5, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/55602E3D-3D72-4021-B2AF-12ADD4EBEACD/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/117990/use-of-n-15-in-meselson-and-stahl-experiment", "split": "test", "split_group": "a57f57c46250c0d0ff15c0b1f14644ee9ff3241fce1bebc62ee9475b0c5d4ead", "tags": ["dna-replication"], "thread_id": "biology:117990", "title": "Use of N-15 in Meselson and Stahl experiment"}} {"citation_context": " A pic of it is added below.[image: Holme's book: The Most Beautiful Experiment in Biology; source: https://i.sstatic.net/eACU4P4v.png] (https://i.sstatic.net/eACU4P4v.png)\n\n\n\n\n\n\n\nImage transcript:\n\n\n\n\n\n\n\n[...]Stahl had to leave for M", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://i.sstatic.net/eACU4P4v.png", "kind": "external_url", "post_id": 118024, "post_url": "https://biology.stackexchange.com/a/118024", "product": "citations", "record_id": "Scientific-Citation-Graph:d841df67c78ba1d8d413f9f2", "split": "test", "thread": {"accepted_answer_id": 118024, "answers": [{"answer_html": "

The vast majority of nitrogen is $\\ce{^{14}N}$, see e.g. https://en.m.wikipedia.org/wiki/Isotopes_of_nitrogen

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So, they're starting with the experimental manipulation and then showing how their manipulated $\\ce{^{15}N}$ follows cell divisions.

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Imagine you wanted to follow some water, so you add a dye to it and see where the dyed water goes. That's fairly easy, and you can probably even spot by eye places where the dye is diluted to 1% the concentration you added. Alternatively, you could dye everything in the system, and then add some pure water and follow that through. Some areas will then be diluted with that pure water and have just 99% of the original concentration of dye. However, it's a lot harder to tell the difference between "lots of dye vs slightly less due" than it is "very little dye vs background of zero". If you had a bit less sample volume (say, 1% less) you'd easily have the same "change" as your target (say, 98% to 100%), whereas if you're looking for the 1% dye, a volume change of 1% would give you 1.01% to 0.99%.

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You're right, hypothetically you could keep everything in an $\\ce{^{15}N}$ world after starting with $\\ce{^{14}N}$, except you'd have to make sure to supply every nitrogenous reagent chemical needed in the experiment as $\\ce{^{15}N}$, and the world isn't perfect and there could be other plausible explanations of how $\\ce{^{14}N}$ entered the experiment accidentally.

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For the experiment with $\\ce{^{15}N}$, it's pretty clear that any substantial $\\ce{^{15}N}$ came from the original organism.

\n", "answer_id": 117991, "answer_text": "The vast majority of nitrogen is $\\ce{^{14}N}$, see e.g. https://en.m.wikipedia.org/wiki/Isotopes_of_nitrogen (https://en.m.wikipedia.org/wiki/Isotopes_of_nitrogen)\n\n\n\n\nSo, they're starting with the experimental manipulation and then showing how their manipulated $\\ce{^{15}N}$ follows cell divisions.\n\n\n\n\nImagine you wanted to follow some water, so you add a dye to it and see where the dyed water goes. That's fairly easy, and you can probably even spot by eye places where the dye is diluted to 1% the concentration you added. Alternatively, you could dye everything in the system, and then add some pure water and follow that through. Some areas will then be diluted with that pure water and have just 99% of the original concentration of dye. However, it's a lot harder to tell the difference between \"lots of dye vs slightly less due\" than it is \"very little dye vs background of zero\". If you had a bit less sample volume (say, 1% less) you'd easily have the same \"change\" as your target (say, 98% to 100%), whereas if you're looking for the 1% dye, a volume change of 1% would give you 1.01% to 0.99%.\n\n\n\n\nYou're right, hypothetically you could keep everything in an $\\ce{^{15}N}$ world after starting with $\\ce{^{14}N}$, except you'd have to make sure to supply every nitrogenous reagent chemical needed in the experiment as $\\ce{^{15}N}$, and the world isn't perfect and there could be other plausible explanations of how $\\ce{^{14}N}$ entered the experiment accidentally.\n\n\n\n\nFor the experiment with $\\ce{^{15}N}$, it's pretty clear that any substantial $\\ce{^{15}N}$ came from the original organism.", "answer_url": "https://biology.stackexchange.com/a/117991", "author": "Bryan Krause", "author_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2025-09-29T18:25:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:16.948131+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/46a41fae37d5c2c243f9abcbf6829a0045f46a51c624fbba2b897c320cdcba71_0.json", "raw_sha256": "e039e310d0106dc61f992ee05bbb0b0b57ded1c5092f97df2c52989edd5eaf68", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/118153;118142;118137;118126;118122;118117;118113;118102;118099;118097;118094;118081;118076;118072;118069;118065;118059;118056;118043;118039;118036;118030;118029;118025;118022;118018;117994;117992;117990;117987;117983;117981;117975;117971;117956;117953;117951;117945;117943;117941;117934;117926;117924;117920;117916;117914;117907;117892;117889;117887;117883;117876;117872;117867;117861;117860;117856;117855;117850;117849;117844;117840;117833;117821;117819;117817;117815;117814;117805;117794;117782;117774;117771;117767;117766;117761;117759;117756;117747;117732;117726;117724;117709;117701;117694;117693;117681;117680;117677;117671;117668;117664;117662;117659;117651;117641;117632;117624;117623;117607/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 117990, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Bryan Krause", "profile_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "user_type": "moderator"}, "created_at": "2025-09-29T18:25:14+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "E994CA32-9A11-48E2-B6FD-6D289F8FD806", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E994CA32-9A11-48E2-B6FD-6D289F8FD806/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Bryan Krause", "profile_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "user_type": "moderator"}, "created_at": "2025-09-29T18:35:46+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "453C4C81-3BE3-4FC8-BB22-F413055A48EC", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/453C4C81-3BE3-4FC8-BB22-F413055A48EC/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Bryan Krause", "profile_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "user_type": "moderator"}, "created_at": "2025-09-30T21:25:07+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "3B2CC543-8C81-41B8-8ACE-C8124F5764FF", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/3B2CC543-8C81-41B8-8ACE-C8124F5764FF/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-10-16T03:37:06+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "815A1F6B-17DF-427A-8B18-545B12FDFCFF", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/815A1F6B-17DF-427A-8B18-545B12FDFCFF/view-source"}], "score": 4, "updated_at": "2025-10-16T03:37:06+00:00"}, {"answer_html": "

The experiment was "actually" performed in both directions simultaneously because the order of the switch does not change the fundamental result—it simply provides double the confirmation. Whether you start with bacteria grown in a "heavy" medium and switch them to a "light" one, or start with "light" and switch to "heavy," the biological mechanism remains identical: the DNA strands separate, and each old strand pairs with a new strand built from whatever resources are currently available. In both cases, the first generation of new DNA ends up having an intermediate or "hybrid" density. Therefore, the direction of the experiment doesn't matter for the validity of the theory; doing it both ways merely served as a rigorous check to prove that the "hybrid" result was consistent and not caused by experimental error or contamination.

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Here's an extract from Google books, pg 308. A pic of it is added below.\"Holme's

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Image transcript:

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[...]Stahl had to leave for Missouri for a job interview. Too eager to wait for Stahl's return, Meselson decided to perform the experiment by himself. Before Stahl's departure Meselson suggested that it would be good to run the experiment in two directions - one beginning in heavy medium and switched to normal, the other beginning in normal and switched to heavy. Stahl cautioned him not to try to do both at once, because there was too much risk that he would mix up the samples.

\n

After Stahl had gone, Meselson decided that he could color-code the tubes in which he placed the samples and carry out a double experiment without confusion. To be absolutely thorough, he may even have added one or two control experiments in which he switched cul-tures from one heavy to another heavy medium, and from one light to another light medium.[...]

\n
\n", "answer_id": 118024, "answer_text": "The experiment was \"actually\" performed in both directions simultaneously because the order of the switch does not change the fundamental result—it simply provides double the confirmation. Whether you start with bacteria grown in a \"heavy\" medium and switch them to a \"light\" one, or start with \"light\" and switch to \"heavy,\" the biological mechanism remains identical: the DNA strands separate, and each old strand pairs with a new strand built from whatever resources are currently available. In both cases, the first generation of new DNA ends up having an intermediate or \"hybrid\" density. Therefore, the direction of the experiment doesn't matter for the validity of the theory; doing it both ways merely served as a rigorous check to prove that the \"hybrid\" result was consistent and not caused by experimental error or contamination.\n\n\n\n\n\n\n\nHere's an extract from Google books, pg 308 (https://books.google.co.in/books?redir_esc=y&id=g4DGSXAqReoC&q=Missouri#v=snippet&q=Missouri&f=false). A pic of it is added below.[image: Holme's book: The Most Beautiful Experiment in Biology; source: https://i.sstatic.net/eACU4P4v.png] (https://i.sstatic.net/eACU4P4v.png)\n\n\n\n\n\n\n\nImage transcript:\n\n\n\n\n\n\n\n[...]Stahl had to leave for Missouri for a job interview. Too eager to wait for Stahl's return, Meselson decided to perform the experiment by himself. Before Stahl's departure Meselson suggested that it would be good to run the experiment in two directions - one beginning in heavy medium and switched to normal, the other beginning in normal and switched to heavy. Stahl cautioned him not to try to do both at once, because there was too much risk that he would mix up the samples.\n\n\n\n\nAfter Stahl had gone, Meselson decided that he could color-code the tubes in which he placed the samples and carry out a double experiment without confusion. To be absolutely thorough, he may even have added one or two control experiments in which he switched cul-tures from one heavy to another heavy medium, and from one light to another light medium.[...]", "answer_url": "https://biology.stackexchange.com/a/118024", "author": "Shayan", "author_url": "https://biology.stackexchange.com/users/114723/shayan", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2025-10-16T04:51:37+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:16.948131+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/46a41fae37d5c2c243f9abcbf6829a0045f46a51c624fbba2b897c320cdcba71_0.json", "raw_sha256": "e039e310d0106dc61f992ee05bbb0b0b57ded1c5092f97df2c52989edd5eaf68", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/118153;118142;118137;118126;118122;118117;118113;118102;118099;118097;118094;118081;118076;118072;118069;118065;118059;118056;118043;118039;118036;118030;118029;118025;118022;118018;117994;117992;117990;117987;117983;117981;117975;117971;117956;117953;117951;117945;117943;117941;117934;117926;117924;117920;117916;117914;117907;117892;117889;117887;117883;117876;117872;117867;117861;117860;117856;117855;117850;117849;117844;117840;117833;117821;117819;117817;117815;117814;117805;117794;117782;117774;117771;117767;117766;117761;117759;117756;117747;117732;117726;117724;117709;117701;117694;117693;117681;117680;117677;117671;117668;117664;117662;117659;117651;117641;117632;117624;117623;117607/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; 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In Meselson and Stahl's experiment, why do we start with bacteria having $\\ce{^{15}N}$ incorporated into its DNA? I think if we start with $\\ce{^{14}N}$ then we would get light band first, hybrid in the next and hybrid and heavy from the next generation onwards. It should work fine, isn't it?\"Meselson Image source

\n", "question_id": 117990, "question_license": "CC BY-SA 4.0", "question_score": 4, "question_text": "In Meselson and Stahl's experiment, why do we start with bacteria having $\\ce{^{15}N}$ incorporated into its DNA? I think if we start with $\\ce{^{14}N}$ then we would get light band first, hybrid in the next and hybrid and heavy from the next generation onwards. It should work fine, isn't it?[image: Meselson and Stahl experiment; source: https://i.sstatic.net/vuVq2Oo7.jpg] (https://i.sstatic.net/vuVq2Oo7.jpg) Image source (https://www.mun.ca/biology/scarr/Meselson_StahL_experiment.html)", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-09-29T16:10:54+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "0618FB11-12EF-4A73-BC04-5CFE3B943C44", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/0618FB11-12EF-4A73-BC04-5CFE3B943C44/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-09-29T17:13:40+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "24B29716-9C7C-4D69-8D85-A449B5CE28D8", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/24B29716-9C7C-4D69-8D85-A449B5CE28D8/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-09-30T13:17:34+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "BBE9B6D5-8133-4A15-8BC2-8DDAA329AD85", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/BBE9B6D5-8133-4A15-8BC2-8DDAA329AD85/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-10-16T02:41:12+00:00", "raw_file": "raw/codex_api_v1/e6c4101e2e357aa8c5379bd547ec537e2ae9d3a66d32b72c727e9d2ad82690d6_1790824162028580600_0.json", "raw_sha256": "cba09186cd183cf1116bbe2f874d16b08a8bc537baa01c33e34f5c3821229cc5", "revision_guid": "D0367674-BA27-48CA-A3F2-5558BFB7DE9E", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D0367674-BA27-48CA-A3F2-5558BFB7DE9E/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2025-12-27T18:32:11+00:00", "raw_file": "raw/codex_api_v1/24d8c4344fb56e0a47a9b0522e7fa13631e62cee2987c8bebddae0c2fd26f9ef_1790824157688070000_0.json", "raw_sha256": "4317829c6b2c1d1874a8b88f2daa4b8fa8bda8b06cf0c252f9adce0558f8183c", "revision_guid": "55602E3D-3D72-4021-B2AF-12ADD4EBEACD", "revision_number": 5, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/55602E3D-3D72-4021-B2AF-12ADD4EBEACD/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/117990/use-of-n-15-in-meselson-and-stahl-experiment", "split": "test", "split_group": "a57f57c46250c0d0ff15c0b1f14644ee9ff3241fce1bebc62ee9475b0c5d4ead", "tags": ["dna-replication"], "thread_id": "biology:117990", "title": "Use of N-15 in Meselson and Stahl experiment"}} {"citation_context": "In this paper (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8831796/), the authors say:\n\n\n\n\n\n\n\nWe demonstrate that for a considerable number of eplets, the\nantibody-ver", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8831796/", "kind": "external_url", "post_id": 113415, "post_url": "https://biology.stackexchange.com/questions/113415/monoclonal-antibodies", "product": "citations", "record_id": "Scientific-Citation-Graph:c4d68cfa53479891648418c4", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

Update

\n

It was pointed out by OP in a comment that the sequences/structures provided in the db are not antibody but antigen sequences, which I overlooked. Therefore, no clear sequences of the antibodies are provided directly in the db.

\n

Original answer

\n

Your confusion is warranted, given that the authors of the paper simply do not describe how they obtained the antibodies (as far as I can tell, though I only skimmed a few sections).

\n

However, I'll note that many researchers would respond to reasonable request for reagents- specifically if it were publicly reported in a database somewhere, which is not too different from publication (peer review not being necessarily any particular mark of distinction; and presumably there is some minimal vetting before database inclusion).

\n

Furthermore, it does appear that for at least many of the antibodies in that database, either full sequence information is available, or the antibodies can be directly ordered commercially.

\n

In such cases, obtaining antibodies would not be an obstacle (though possibly expensive).

\n", "answer_id": 113419, "answer_text": "Update\n\n\n\n\nIt was pointed out by OP in a comment that the sequences/structures provided in the db are not antibody but antigen sequences, which I overlooked. Therefore, no clear sequences of the antibodies are provided directly in the db.\n\n\n\n\nOriginal answer\n\n\n\n\nYour confusion is warranted, given that the authors of the paper simply do not describe how they obtained the antibodies (as far as I can tell, though I only skimmed a few sections).\n\n\n\n\nHowever, I'll note that many researchers would respond to reasonable request for reagents- specifically if it were publicly reported in a database somewhere, which is not too different from publication (peer review not being necessarily any particular mark of distinction (https://researchintegrityjournal.biomedcentral.com/articles/10.1186/s41073-020-00092-1); and presumably there is some minimal vetting before database inclusion).\n\n\n\n\nFurthermore, it does appear that for at least many of the antibodies in that database, either full sequence information is available (https://www.phla3d.com.br/alleles/view/C*12:03/1?display=A:1,A:), or the antibodies can be directly ordered commercially (https://www.epregistry.com.br/index/databases/database/DQ).\n\n\n\n\nIn such cases, obtaining antibodies would not be an obstacle (though possibly expensive).", "answer_url": "https://biology.stackexchange.com/a/113419", "author": "Maximilian Press", "author_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2023-11-06T13:28:06+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:36.208962+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/ce9de3cf6525f1e283f75a76c7c279c0bd53024cf8e6597abc34f072e18cfbf7_0.json", "raw_sha256": "c65c49a81e92972be3758d3b220c036300d85c38ce4d9079a6203d2eeac0d96d", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/113468;113465;113459;113453;113451;113449;113442;113437;113425;113421;113416;113415;113413;113406;113400;113398;113386;113378;113364;113363;113347;113340;113333;113324;113317;113315;113310;113303;113307;113299;113293;113291;113284;113282;113279;113277;113275;113274;113263;113253;113252;113243;113239;113235;113231;113229;113223;113221;113218;113216;113210;113198;113191;113183;113180;113175;113164;113158;113153;113146;113141;113118;113116;113115;113113;113110;113109;113106;113104;113101;113095;113089;113086;113081;113080;113077;113076;113075;113070;113067;113064;113053;113046;113043;113039;113031;113030;113028;113027;113024;113017;113016;113015;113014;113009;113008;113007;113005;112998;112984/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; 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mechanical HTML-to-text; no LLM rewriting"}, "question_author": "FluidMechanics Potential Flows", "question_author_url": "https://biology.stackexchange.com/users/71819/fluidmechanics-potential-flows", "question_author_user_type": "registered", "question_created_at": "2023-11-06T09:41:01+00:00", "question_html": "

In this paper, the authors say:

\n
\n

We demonstrate that for a considerable number of eplets, the\nantibody-verified status is solely based on polyclonal serum\nreactivity of multiparous women or on reactivity of murine mAbs.\nFurthermore, we noted that a substantial proportion of patient sera\nanalyses and human mAb data presented in the HLA Epitope Registry\nDatabase has never been published in a peer-reviewed journal.\nTherefore, we tested several unpublished human HLA-specific mAbs by\nluminex single antigen beads assay to analyze their HLA reactivity for\neplet antibody verification. Although the majority of analyzed mAbs\nindeed verified their assigned eplets, this was not the case for a\nnumber of eplets.

\n
\n

I don't understand how did they have access to the monoclonal antibodies that were published but not in peer-reviewed journal. Surely those authors of non peer-reviewed journals did not ship the antibodies to the authors of this article, right?\nIs there something I'm not understanding?

\n", "question_id": 113415, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "In this paper (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8831796/), the authors say:\n\n\n\n\n\n\n\nWe demonstrate that for a considerable number of eplets, the\nantibody-verified status is solely based on polyclonal serum\nreactivity of multiparous women or on reactivity of murine mAbs.\nFurthermore, we noted that a substantial proportion of patient sera\nanalyses and human mAb data presented in the HLA Epitope Registry\nDatabase has never been published in a peer-reviewed journal.\nTherefore, we tested several unpublished human HLA-specific mAbs by\nluminex single antigen beads assay to analyze their HLA reactivity for\neplet antibody verification. Although the majority of analyzed mAbs\nindeed verified their assigned eplets, this was not the case for a\nnumber of eplets.\n\n\n\n\n\n\n\nI don't understand how did they have access to the monoclonal antibodies that were published but not in peer-reviewed journal. Surely those authors of non peer-reviewed journals did not ship the antibodies to the authors of this article, right?\nIs there something I'm not understanding?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "FluidMechanics Potential Flows", "profile_url": "https://biology.stackexchange.com/users/71819/fluidmechanics-potential-flows", "user_type": "registered"}, "created_at": "2023-11-06T09:41:01+00:00", "raw_file": "raw/codex_api_v1/90c6546608151c55782a98b278e0bff1131c56a003319717b96f8124b5cd81ad_1790824039302420800_0.json", "raw_sha256": "9f60f0aa014afb8146c20434cb45e9daca2b9f5585a871678859e9e68314a991", "revision_guid": "B63BC758-3D14-4540-B540-62067DEB8155", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B63BC758-3D14-4540-B540-62067DEB8155/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/113415/monoclonal-antibodies", "split": "test", "split_group": "b309e610317fb0fe5547f86b6c109e2b86705a16e2cdc97913698e43036df427", "tags": ["immunology", "antibody", "mhc"], "thread_id": "biology:113415", "title": "Monoclonal Antibodies"}} {"citation_context": "o different from publication (peer review not being necessarily any particular mark of distinction (https://researchintegrityjournal.biomedcentral.com/articles/10.1186/s41073-020-00092-1); and presumably there is some minimal vetting before database inclusion).\n\n\n\n\nFurthermore, it does", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": "10.1186/s41073-020-00092-1", "external_url": "https://researchintegrityjournal.biomedcentral.com/articles/10.1186/s41073-020-00092-1", "kind": "doi_url", "post_id": 113419, "post_url": "https://biology.stackexchange.com/a/113419", "product": "citations", "record_id": "Scientific-Citation-Graph:f5320f3c5d9e01f26d71257f", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

Update

\n

It was pointed out by OP in a comment that the sequences/structures provided in the db are not antibody but antigen sequences, which I overlooked. Therefore, no clear sequences of the antibodies are provided directly in the db.

\n

Original answer

\n

Your confusion is warranted, given that the authors of the paper simply do not describe how they obtained the antibodies (as far as I can tell, though I only skimmed a few sections).

\n

However, I'll note that many researchers would respond to reasonable request for reagents- specifically if it were publicly reported in a database somewhere, which is not too different from publication (peer review not being necessarily any particular mark of distinction; and presumably there is some minimal vetting before database inclusion).

\n

Furthermore, it does appear that for at least many of the antibodies in that database, either full sequence information is available, or the antibodies can be directly ordered commercially.

\n

In such cases, obtaining antibodies would not be an obstacle (though possibly expensive).

\n", "answer_id": 113419, "answer_text": "Update\n\n\n\n\nIt was pointed out by OP in a comment that the sequences/structures provided in the db are not antibody but antigen sequences, which I overlooked. Therefore, no clear sequences of the antibodies are provided directly in the db.\n\n\n\n\nOriginal answer\n\n\n\n\nYour confusion is warranted, given that the authors of the paper simply do not describe how they obtained the antibodies (as far as I can tell, though I only skimmed a few sections).\n\n\n\n\nHowever, I'll note that many researchers would respond to reasonable request for reagents- specifically if it were publicly reported in a database somewhere, which is not too different from publication (peer review not being necessarily any particular mark of distinction (https://researchintegrityjournal.biomedcentral.com/articles/10.1186/s41073-020-00092-1); and presumably there is some minimal vetting before database inclusion).\n\n\n\n\nFurthermore, it does appear that for at least many of the antibodies in that database, either full sequence information is available (https://www.phla3d.com.br/alleles/view/C*12:03/1?display=A:1,A:), or the antibodies can be directly ordered commercially (https://www.epregistry.com.br/index/databases/database/DQ).\n\n\n\n\nIn such cases, obtaining antibodies would not be an obstacle (though possibly expensive).", "answer_url": "https://biology.stackexchange.com/a/113419", "author": "Maximilian Press", "author_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2023-11-06T13:28:06+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:36.208962+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/ce9de3cf6525f1e283f75a76c7c279c0bd53024cf8e6597abc34f072e18cfbf7_0.json", "raw_sha256": "c65c49a81e92972be3758d3b220c036300d85c38ce4d9079a6203d2eeac0d96d", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/113468;113465;113459;113453;113451;113449;113442;113437;113425;113421;113416;113415;113413;113406;113400;113398;113386;113378;113364;113363;113347;113340;113333;113324;113317;113315;113310;113303;113307;113299;113293;113291;113284;113282;113279;113277;113275;113274;113263;113253;113252;113243;113239;113235;113231;113229;113223;113221;113218;113216;113210;113198;113191;113183;113180;113175;113164;113158;113153;113146;113141;113118;113116;113115;113113;113110;113109;113106;113104;113101;113095;113089;113086;113081;113080;113077;113076;113075;113070;113067;113064;113053;113046;113043;113039;113031;113030;113028;113027;113024;113017;113016;113015;113014;113009;113008;113007;113005;112998;112984/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 113415, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2023-11-06T13:28:06+00:00", "raw_file": "raw/codex_api_v1/90c6546608151c55782a98b278e0bff1131c56a003319717b96f8124b5cd81ad_1790824039302420800_0.json", "raw_sha256": "9f60f0aa014afb8146c20434cb45e9daca2b9f5585a871678859e9e68314a991", "revision_guid": "D1AC98FE-E9A9-42A6-A3C3-B6B25929F08B", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D1AC98FE-E9A9-42A6-A3C3-B6B25929F08B/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2023-11-08T17:23:58+00:00", "raw_file": "raw/codex_api_v1/90c6546608151c55782a98b278e0bff1131c56a003319717b96f8124b5cd81ad_1790824039302420800_0.json", "raw_sha256": "9f60f0aa014afb8146c20434cb45e9daca2b9f5585a871678859e9e68314a991", "revision_guid": "958C1B3D-FCD9-4120-84BF-8D1A13F915F3", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/958C1B3D-FCD9-4120-84BF-8D1A13F915F3/view-source"}], "score": 1, "updated_at": "2023-11-08T17:23:58+00:00"}], "domain": "biology", "external_links": ["https://researchintegrityjournal.biomedcentral.com/articles/10.1186/s41073-020-00092-1", "https://www.epregistry.com.br/index/databases/database/DQ", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8831796/", "https://www.phla3d.com.br/alleles/view/C*12:03/1?display=A:1,A:"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:11.333206+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/3e71d6afdfe444c721dbb1321f43c14066813d2fd740fb255123cf87e737d071_0.json", "raw_sha256": "84992ad678a40907dca3af99f849ee653142b680281a54e02542dc7f47d30773", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=9&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "FluidMechanics Potential Flows", "question_author_url": "https://biology.stackexchange.com/users/71819/fluidmechanics-potential-flows", "question_author_user_type": "registered", "question_created_at": "2023-11-06T09:41:01+00:00", "question_html": "

In this paper, the authors say:

\n
\n

We demonstrate that for a considerable number of eplets, the\nantibody-verified status is solely based on polyclonal serum\nreactivity of multiparous women or on reactivity of murine mAbs.\nFurthermore, we noted that a substantial proportion of patient sera\nanalyses and human mAb data presented in the HLA Epitope Registry\nDatabase has never been published in a peer-reviewed journal.\nTherefore, we tested several unpublished human HLA-specific mAbs by\nluminex single antigen beads assay to analyze their HLA reactivity for\neplet antibody verification. Although the majority of analyzed mAbs\nindeed verified their assigned eplets, this was not the case for a\nnumber of eplets.

\n
\n

I don't understand how did they have access to the monoclonal antibodies that were published but not in peer-reviewed journal. Surely those authors of non peer-reviewed journals did not ship the antibodies to the authors of this article, right?\nIs there something I'm not understanding?

\n", "question_id": 113415, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "In this paper (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8831796/), the authors say:\n\n\n\n\n\n\n\nWe demonstrate that for a considerable number of eplets, the\nantibody-verified status is solely based on polyclonal serum\nreactivity of multiparous women or on reactivity of murine mAbs.\nFurthermore, we noted that a substantial proportion of patient sera\nanalyses and human mAb data presented in the HLA Epitope Registry\nDatabase has never been published in a peer-reviewed journal.\nTherefore, we tested several unpublished human HLA-specific mAbs by\nluminex single antigen beads assay to analyze their HLA reactivity for\neplet antibody verification. Although the majority of analyzed mAbs\nindeed verified their assigned eplets, this was not the case for a\nnumber of eplets.\n\n\n\n\n\n\n\nI don't understand how did they have access to the monoclonal antibodies that were published but not in peer-reviewed journal. Surely those authors of non peer-reviewed journals did not ship the antibodies to the authors of this article, right?\nIs there something I'm not understanding?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "FluidMechanics Potential Flows", "profile_url": "https://biology.stackexchange.com/users/71819/fluidmechanics-potential-flows", "user_type": "registered"}, "created_at": "2023-11-06T09:41:01+00:00", "raw_file": "raw/codex_api_v1/90c6546608151c55782a98b278e0bff1131c56a003319717b96f8124b5cd81ad_1790824039302420800_0.json", "raw_sha256": "9f60f0aa014afb8146c20434cb45e9daca2b9f5585a871678859e9e68314a991", "revision_guid": "B63BC758-3D14-4540-B540-62067DEB8155", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B63BC758-3D14-4540-B540-62067DEB8155/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/113415/monoclonal-antibodies", "split": "test", "split_group": "b309e610317fb0fe5547f86b6c109e2b86705a16e2cdc97913698e43036df427", "tags": ["immunology", "antibody", "mhc"], "thread_id": "biology:113415", "title": "Monoclonal Antibodies"}} {"citation_context": ".br/alleles/view/C*12:03/1?display=A:1,A:), or the antibodies can be directly ordered commercially (https://www.epregistry.com.br/index/databases/database/DQ).\n\n\n\n\nIn such cases, obtaining antibodies would not be an obstacle (though possibly expensive).", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.epregistry.com.br/index/databases/database/DQ", "kind": "external_url", "post_id": 113419, "post_url": "https://biology.stackexchange.com/a/113419", "product": "citations", "record_id": "Scientific-Citation-Graph:66cf70b76fb62226c4447ef7", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

Update

\n

It was pointed out by OP in a comment that the sequences/structures provided in the db are not antibody but antigen sequences, which I overlooked. Therefore, no clear sequences of the antibodies are provided directly in the db.

\n

Original answer

\n

Your confusion is warranted, given that the authors of the paper simply do not describe how they obtained the antibodies (as far as I can tell, though I only skimmed a few sections).

\n

However, I'll note that many researchers would respond to reasonable request for reagents- specifically if it were publicly reported in a database somewhere, which is not too different from publication (peer review not being necessarily any particular mark of distinction; and presumably there is some minimal vetting before database inclusion).

\n

Furthermore, it does appear that for at least many of the antibodies in that database, either full sequence information is available, or the antibodies can be directly ordered commercially.

\n

In such cases, obtaining antibodies would not be an obstacle (though possibly expensive).

\n", "answer_id": 113419, "answer_text": "Update\n\n\n\n\nIt was pointed out by OP in a comment that the sequences/structures provided in the db are not antibody but antigen sequences, which I overlooked. Therefore, no clear sequences of the antibodies are provided directly in the db.\n\n\n\n\nOriginal answer\n\n\n\n\nYour confusion is warranted, given that the authors of the paper simply do not describe how they obtained the antibodies (as far as I can tell, though I only skimmed a few sections).\n\n\n\n\nHowever, I'll note that many researchers would respond to reasonable request for reagents- specifically if it were publicly reported in a database somewhere, which is not too different from publication (peer review not being necessarily any particular mark of distinction (https://researchintegrityjournal.biomedcentral.com/articles/10.1186/s41073-020-00092-1); and presumably there is some minimal vetting before database inclusion).\n\n\n\n\nFurthermore, it does appear that for at least many of the antibodies in that database, either full sequence information is available (https://www.phla3d.com.br/alleles/view/C*12:03/1?display=A:1,A:), or the antibodies can be directly ordered commercially (https://www.epregistry.com.br/index/databases/database/DQ).\n\n\n\n\nIn such cases, obtaining antibodies would not be an obstacle (though possibly expensive).", "answer_url": "https://biology.stackexchange.com/a/113419", "author": "Maximilian Press", "author_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2023-11-06T13:28:06+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:36.208962+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/ce9de3cf6525f1e283f75a76c7c279c0bd53024cf8e6597abc34f072e18cfbf7_0.json", "raw_sha256": "c65c49a81e92972be3758d3b220c036300d85c38ce4d9079a6203d2eeac0d96d", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/113468;113465;113459;113453;113451;113449;113442;113437;113425;113421;113416;113415;113413;113406;113400;113398;113386;113378;113364;113363;113347;113340;113333;113324;113317;113315;113310;113303;113307;113299;113293;113291;113284;113282;113279;113277;113275;113274;113263;113253;113252;113243;113239;113235;113231;113229;113223;113221;113218;113216;113210;113198;113191;113183;113180;113175;113164;113158;113153;113146;113141;113118;113116;113115;113113;113110;113109;113106;113104;113101;113095;113089;113086;113081;113080;113077;113076;113075;113070;113067;113064;113053;113046;113043;113039;113031;113030;113028;113027;113024;113017;113016;113015;113014;113009;113008;113007;113005;112998;112984/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 113415, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2023-11-06T13:28:06+00:00", "raw_file": "raw/codex_api_v1/90c6546608151c55782a98b278e0bff1131c56a003319717b96f8124b5cd81ad_1790824039302420800_0.json", "raw_sha256": "9f60f0aa014afb8146c20434cb45e9daca2b9f5585a871678859e9e68314a991", "revision_guid": "D1AC98FE-E9A9-42A6-A3C3-B6B25929F08B", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D1AC98FE-E9A9-42A6-A3C3-B6B25929F08B/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2023-11-08T17:23:58+00:00", "raw_file": "raw/codex_api_v1/90c6546608151c55782a98b278e0bff1131c56a003319717b96f8124b5cd81ad_1790824039302420800_0.json", "raw_sha256": "9f60f0aa014afb8146c20434cb45e9daca2b9f5585a871678859e9e68314a991", "revision_guid": "958C1B3D-FCD9-4120-84BF-8D1A13F915F3", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/958C1B3D-FCD9-4120-84BF-8D1A13F915F3/view-source"}], "score": 1, "updated_at": "2023-11-08T17:23:58+00:00"}], "domain": "biology", "external_links": ["https://researchintegrityjournal.biomedcentral.com/articles/10.1186/s41073-020-00092-1", "https://www.epregistry.com.br/index/databases/database/DQ", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8831796/", "https://www.phla3d.com.br/alleles/view/C*12:03/1?display=A:1,A:"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:11.333206+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/3e71d6afdfe444c721dbb1321f43c14066813d2fd740fb255123cf87e737d071_0.json", "raw_sha256": "84992ad678a40907dca3af99f849ee653142b680281a54e02542dc7f47d30773", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=9&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "FluidMechanics Potential Flows", "question_author_url": "https://biology.stackexchange.com/users/71819/fluidmechanics-potential-flows", "question_author_user_type": "registered", "question_created_at": "2023-11-06T09:41:01+00:00", "question_html": "

In this paper, the authors say:

\n
\n

We demonstrate that for a considerable number of eplets, the\nantibody-verified status is solely based on polyclonal serum\nreactivity of multiparous women or on reactivity of murine mAbs.\nFurthermore, we noted that a substantial proportion of patient sera\nanalyses and human mAb data presented in the HLA Epitope Registry\nDatabase has never been published in a peer-reviewed journal.\nTherefore, we tested several unpublished human HLA-specific mAbs by\nluminex single antigen beads assay to analyze their HLA reactivity for\neplet antibody verification. Although the majority of analyzed mAbs\nindeed verified their assigned eplets, this was not the case for a\nnumber of eplets.

\n
\n

I don't understand how did they have access to the monoclonal antibodies that were published but not in peer-reviewed journal. Surely those authors of non peer-reviewed journals did not ship the antibodies to the authors of this article, right?\nIs there something I'm not understanding?

\n", "question_id": 113415, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "In this paper (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8831796/), the authors say:\n\n\n\n\n\n\n\nWe demonstrate that for a considerable number of eplets, the\nantibody-verified status is solely based on polyclonal serum\nreactivity of multiparous women or on reactivity of murine mAbs.\nFurthermore, we noted that a substantial proportion of patient sera\nanalyses and human mAb data presented in the HLA Epitope Registry\nDatabase has never been published in a peer-reviewed journal.\nTherefore, we tested several unpublished human HLA-specific mAbs by\nluminex single antigen beads assay to analyze their HLA reactivity for\neplet antibody verification. Although the majority of analyzed mAbs\nindeed verified their assigned eplets, this was not the case for a\nnumber of eplets.\n\n\n\n\n\n\n\nI don't understand how did they have access to the monoclonal antibodies that were published but not in peer-reviewed journal. Surely those authors of non peer-reviewed journals did not ship the antibodies to the authors of this article, right?\nIs there something I'm not understanding?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "FluidMechanics Potential Flows", "profile_url": "https://biology.stackexchange.com/users/71819/fluidmechanics-potential-flows", "user_type": "registered"}, "created_at": "2023-11-06T09:41:01+00:00", "raw_file": "raw/codex_api_v1/90c6546608151c55782a98b278e0bff1131c56a003319717b96f8124b5cd81ad_1790824039302420800_0.json", "raw_sha256": "9f60f0aa014afb8146c20434cb45e9daca2b9f5585a871678859e9e68314a991", "revision_guid": "B63BC758-3D14-4540-B540-62067DEB8155", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B63BC758-3D14-4540-B540-62067DEB8155/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/113415/monoclonal-antibodies", "split": "test", "split_group": "b309e610317fb0fe5547f86b6c109e2b86705a16e2cdc97913698e43036df427", "tags": ["immunology", "antibody", "mhc"], "thread_id": "biology:113415", "title": "Monoclonal Antibodies"}} {"citation_context": "or at least many of the antibodies in that database, either full sequence information is available (https://www.phla3d.com.br/alleles/view/C*12:03/1?display=A:1,A:), or the antibodies can be directly ordered commercially (https://www.epregistry.com.br/index/datab", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.phla3d.com.br/alleles/view/C*12:03/1?display=A:1,A:", "kind": "external_url", "post_id": 113419, "post_url": "https://biology.stackexchange.com/a/113419", "product": "citations", "record_id": "Scientific-Citation-Graph:4357de4f8204a7e578e7c586", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

Update

\n

It was pointed out by OP in a comment that the sequences/structures provided in the db are not antibody but antigen sequences, which I overlooked. Therefore, no clear sequences of the antibodies are provided directly in the db.

\n

Original answer

\n

Your confusion is warranted, given that the authors of the paper simply do not describe how they obtained the antibodies (as far as I can tell, though I only skimmed a few sections).

\n

However, I'll note that many researchers would respond to reasonable request for reagents- specifically if it were publicly reported in a database somewhere, which is not too different from publication (peer review not being necessarily any particular mark of distinction; and presumably there is some minimal vetting before database inclusion).

\n

Furthermore, it does appear that for at least many of the antibodies in that database, either full sequence information is available, or the antibodies can be directly ordered commercially.

\n

In such cases, obtaining antibodies would not be an obstacle (though possibly expensive).

\n", "answer_id": 113419, "answer_text": "Update\n\n\n\n\nIt was pointed out by OP in a comment that the sequences/structures provided in the db are not antibody but antigen sequences, which I overlooked. Therefore, no clear sequences of the antibodies are provided directly in the db.\n\n\n\n\nOriginal answer\n\n\n\n\nYour confusion is warranted, given that the authors of the paper simply do not describe how they obtained the antibodies (as far as I can tell, though I only skimmed a few sections).\n\n\n\n\nHowever, I'll note that many researchers would respond to reasonable request for reagents- specifically if it were publicly reported in a database somewhere, which is not too different from publication (peer review not being necessarily any particular mark of distinction (https://researchintegrityjournal.biomedcentral.com/articles/10.1186/s41073-020-00092-1); and presumably there is some minimal vetting before database inclusion).\n\n\n\n\nFurthermore, it does appear that for at least many of the antibodies in that database, either full sequence information is available (https://www.phla3d.com.br/alleles/view/C*12:03/1?display=A:1,A:), or the antibodies can be directly ordered commercially (https://www.epregistry.com.br/index/databases/database/DQ).\n\n\n\n\nIn such cases, obtaining antibodies would not be an obstacle (though possibly expensive).", "answer_url": "https://biology.stackexchange.com/a/113419", "author": "Maximilian Press", "author_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2023-11-06T13:28:06+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:36.208962+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/ce9de3cf6525f1e283f75a76c7c279c0bd53024cf8e6597abc34f072e18cfbf7_0.json", "raw_sha256": "c65c49a81e92972be3758d3b220c036300d85c38ce4d9079a6203d2eeac0d96d", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/113468;113465;113459;113453;113451;113449;113442;113437;113425;113421;113416;113415;113413;113406;113400;113398;113386;113378;113364;113363;113347;113340;113333;113324;113317;113315;113310;113303;113307;113299;113293;113291;113284;113282;113279;113277;113275;113274;113263;113253;113252;113243;113239;113235;113231;113229;113223;113221;113218;113216;113210;113198;113191;113183;113180;113175;113164;113158;113153;113146;113141;113118;113116;113115;113113;113110;113109;113106;113104;113101;113095;113089;113086;113081;113080;113077;113076;113075;113070;113067;113064;113053;113046;113043;113039;113031;113030;113028;113027;113024;113017;113016;113015;113014;113009;113008;113007;113005;112998;112984/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 113415, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2023-11-06T13:28:06+00:00", "raw_file": "raw/codex_api_v1/90c6546608151c55782a98b278e0bff1131c56a003319717b96f8124b5cd81ad_1790824039302420800_0.json", "raw_sha256": "9f60f0aa014afb8146c20434cb45e9daca2b9f5585a871678859e9e68314a991", "revision_guid": "D1AC98FE-E9A9-42A6-A3C3-B6B25929F08B", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/D1AC98FE-E9A9-42A6-A3C3-B6B25929F08B/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Maximilian Press", "profile_url": "https://biology.stackexchange.com/users/22392/maximilian-press", "user_type": "registered"}, "created_at": "2023-11-08T17:23:58+00:00", "raw_file": "raw/codex_api_v1/90c6546608151c55782a98b278e0bff1131c56a003319717b96f8124b5cd81ad_1790824039302420800_0.json", "raw_sha256": "9f60f0aa014afb8146c20434cb45e9daca2b9f5585a871678859e9e68314a991", "revision_guid": "958C1B3D-FCD9-4120-84BF-8D1A13F915F3", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/958C1B3D-FCD9-4120-84BF-8D1A13F915F3/view-source"}], "score": 1, "updated_at": "2023-11-08T17:23:58+00:00"}], "domain": "biology", "external_links": ["https://researchintegrityjournal.biomedcentral.com/articles/10.1186/s41073-020-00092-1", "https://www.epregistry.com.br/index/databases/database/DQ", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8831796/", "https://www.phla3d.com.br/alleles/view/C*12:03/1?display=A:1,A:"], "medical_sensitive": true, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:11.333206+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/3e71d6afdfe444c721dbb1321f43c14066813d2fd740fb255123cf87e737d071_0.json", "raw_sha256": "84992ad678a40907dca3af99f849ee653142b680281a54e02542dc7f47d30773", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=9&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "FluidMechanics Potential Flows", "question_author_url": "https://biology.stackexchange.com/users/71819/fluidmechanics-potential-flows", "question_author_user_type": "registered", "question_created_at": "2023-11-06T09:41:01+00:00", "question_html": "

In this paper, the authors say:

\n
\n

We demonstrate that for a considerable number of eplets, the\nantibody-verified status is solely based on polyclonal serum\nreactivity of multiparous women or on reactivity of murine mAbs.\nFurthermore, we noted that a substantial proportion of patient sera\nanalyses and human mAb data presented in the HLA Epitope Registry\nDatabase has never been published in a peer-reviewed journal.\nTherefore, we tested several unpublished human HLA-specific mAbs by\nluminex single antigen beads assay to analyze their HLA reactivity for\neplet antibody verification. Although the majority of analyzed mAbs\nindeed verified their assigned eplets, this was not the case for a\nnumber of eplets.

\n
\n

I don't understand how did they have access to the monoclonal antibodies that were published but not in peer-reviewed journal. Surely those authors of non peer-reviewed journals did not ship the antibodies to the authors of this article, right?\nIs there something I'm not understanding?

\n", "question_id": 113415, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "In this paper (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8831796/), the authors say:\n\n\n\n\n\n\n\nWe demonstrate that for a considerable number of eplets, the\nantibody-verified status is solely based on polyclonal serum\nreactivity of multiparous women or on reactivity of murine mAbs.\nFurthermore, we noted that a substantial proportion of patient sera\nanalyses and human mAb data presented in the HLA Epitope Registry\nDatabase has never been published in a peer-reviewed journal.\nTherefore, we tested several unpublished human HLA-specific mAbs by\nluminex single antigen beads assay to analyze their HLA reactivity for\neplet antibody verification. Although the majority of analyzed mAbs\nindeed verified their assigned eplets, this was not the case for a\nnumber of eplets.\n\n\n\n\n\n\n\nI don't understand how did they have access to the monoclonal antibodies that were published but not in peer-reviewed journal. Surely those authors of non peer-reviewed journals did not ship the antibodies to the authors of this article, right?\nIs there something I'm not understanding?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "FluidMechanics Potential Flows", "profile_url": "https://biology.stackexchange.com/users/71819/fluidmechanics-potential-flows", "user_type": "registered"}, "created_at": "2023-11-06T09:41:01+00:00", "raw_file": "raw/codex_api_v1/90c6546608151c55782a98b278e0bff1131c56a003319717b96f8124b5cd81ad_1790824039302420800_0.json", "raw_sha256": "9f60f0aa014afb8146c20434cb45e9daca2b9f5585a871678859e9e68314a991", "revision_guid": "B63BC758-3D14-4540-B540-62067DEB8155", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/B63BC758-3D14-4540-B540-62067DEB8155/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/113415/monoclonal-antibodies", "split": "test", "split_group": "b309e610317fb0fe5547f86b6c109e2b86705a16e2cdc97913698e43036df427", "tags": ["immunology", "antibody", "mhc"], "thread_id": "biology:113415", "title": "Monoclonal Antibodies"}} {"citation_context": " protect you, and give you confidence that you can reclaim your garden.\n\n\n\n\n1/ research dissuasion (https://www.google.com/search?q=how+to+dissuade+%22ground+hornets%22) of ground hornets.\n\n\n\n\n2/ put together some protective clothing, in case you have to spray a bioco", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.google.com/search?q=how+to+dissuade+%22ground+hornets%22", "kind": "external_url", "post_id": 114033, "post_url": "https://biology.stackexchange.com/a/114033", "product": "citations", "record_id": "Scientific-Citation-Graph:6b590169f03c34bd61f1c3ae", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

Yes, they are likely to return to the same zone and garden if it is a good habitat for them.

\n

Knowledge of them will protect you, and give you confidence that you can reclaim your garden.

\n

1/ research dissuasion of ground hornets.

\n

2/ put together some protective clothing, in case you have to spray a biocontrol agent or another deterrent. I don't know what your budget is, but you could get by with a hat protected by netting, from some instructions online, and some gloves, they won't swarm you in great hives.

\n

3/ Invest in a lot of diligent research, to know what month they start burrowing, what day temperature they prefer to wake up to, how to protect yourself physically if you have to approach an active nesting hornet, if it's ok to keep a good long-handle net near the porch and intercept them when they venture too close in the evening. Read stories of others who have had the same adventure.

\n

I am an experienced zoologist I have been stung by wasps many times, and fortunately not a hornet.

\n

I climbed a tree with 20 in nest just above me and climbed down again, and many other encounters.

\n

The biggest danger is that a wasp or bee falls in a cola when someone is briefly distracted.

\n

Folk should know to be conscious of not mouth-breathing when running near them, and what to do if your friend is stung inside the throat on a hike far from help and breathing becomes difficult.

\n

With this knowledge, I am became confident to let wasps and bees forage and walk on my hands and face which can be annoying after a minute or if they insist on foraging over an eyelid or a nostril, however it is better than startling them, I know how to tell the difference between more and less aggressive lookalikes based on their flying patterns, leg length in flight and other markers, It's a good thing to teach children. I became confident to stay very calm near a hornet nest and try to avoid it, to immediately suck a wasp sting and very fast put cola, or vinegar is better, on a sting, to greatly diminish its effect, and run fast if a nest is disturbed so they go into an aggressive mode.

\n

Good luck.

\n", "answer_id": 114033, "answer_text": "Yes, they are likely to return to the same zone and garden if it is a good habitat for them.\n\n\n\n\nKnowledge of them will protect you, and give you confidence that you can reclaim your garden.\n\n\n\n\n1/ research dissuasion (https://www.google.com/search?q=how+to+dissuade+%22ground+hornets%22) of ground hornets.\n\n\n\n\n2/ put together some protective clothing, in case you have to spray a biocontrol agent or another deterrent. I don't know what your budget is, but you could get by with a hat protected by netting, from some instructions online, and some gloves, they won't swarm you in great hives.\n\n\n\n\n3/ Invest in a lot of diligent research, to know what month they start burrowing, what day temperature they prefer to wake up to, how to protect yourself physically if you have to approach an active nesting hornet, if it's ok to keep a good long-handle net near the porch and intercept them when they venture too close in the evening. Read stories of others who have had the same adventure.\n\n\n\n\nI am an experienced zoologist I have been stung by wasps many times, and fortunately not a hornet.\n\n\n\n\nI climbed a tree with 20 in nest just above me and climbed down again, and many other encounters.\n\n\n\n\nThe biggest danger is that a wasp or bee falls in a cola when someone is briefly distracted.\n\n\n\n\nFolk should know to be conscious of not mouth-breathing when running near them, and what to do if your friend is stung inside the throat on a hike far from help and breathing becomes difficult.\n\n\n\n\nWith this knowledge, I am became confident to let wasps and bees forage and walk on my hands and face which can be annoying after a minute or if they insist on foraging over an eyelid or a nostril, however it is better than startling them, I know how to tell the difference between more and less aggressive lookalikes based on their flying patterns, leg length in flight and other markers, It's a good thing to teach children. I became confident to stay very calm near a hornet nest and try to avoid it, to immediately suck a wasp sting and very fast put cola, or vinegar is better, on a sting, to greatly diminish its effect, and run fast if a nest is disturbed so they go into an aggressive mode.\n\n\n\n\nGood luck.", "answer_url": "https://biology.stackexchange.com/a/114033", "author": "bandybabboon", "author_url": "https://biology.stackexchange.com/users/8952/bandybabboon", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-02-05T01:05:50+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:30.839943+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/2139ae0ecb1bf62b149af3f8e91d7ce461ad269d38020aaf05922333eabb51a1_0.json", "raw_sha256": "2610bc07f1691b2794681a23d0459bba24822de1f31c7b48d79495b29b0b1285", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/114428;114427;114412;114410;114399;114395;114391;114386;114385;114381;114378;114377;114376;114374;114372;114371;114370;114361;114354;114353;114348;114342;114331;114329;114324;114321;114319;114307;114305;114304;114299;114298;114295;114290;114281;114277;114273;114266;114256;114239;114238;114222;114216;114213;114211;114207;114197;114192;114185;114180;114178;114175;114174;114173;114172;114169;114161;114156;114155;114148;114145;114144;114139;114136;114135;114127;114119;114117;114114;114111;114110;114103;114098;114096;114094;114089;114085;114078;114076;114069;114067;114065;114058;114055;114048;114045;114038;114031;114028;114027;114025;114021;114020;114012;114006;113998;113997;113988;113986;113983/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 114031, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "bandybabboon", "profile_url": "https://biology.stackexchange.com/users/8952/bandybabboon", "user_type": "registered"}, "created_at": "2024-02-05T01:05:50+00:00", "raw_file": "raw/codex_api_v1/4aa156cabb1f3edbc4e0a74ff84deb30f9cd06be13c7d021adab58e209db850d_1790824057164545000_0.json", "raw_sha256": "42ee08c1af6f231bf4bd10a51fd8384910e076e5d887f51c6dd79384012b46ec", "revision_guid": "A1FCB338-A6F0-4A68-A2F2-AEE3D08548F7", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/A1FCB338-A6F0-4A68-A2F2-AEE3D08548F7/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "bandybabboon", "profile_url": "https://biology.stackexchange.com/users/8952/bandybabboon", "user_type": "registered"}, "created_at": "2024-02-05T01:11:46+00:00", "raw_file": "raw/codex_api_v1/4aa156cabb1f3edbc4e0a74ff84deb30f9cd06be13c7d021adab58e209db850d_1790824057164545000_0.json", "raw_sha256": "42ee08c1af6f231bf4bd10a51fd8384910e076e5d887f51c6dd79384012b46ec", "revision_guid": "BF5E74D2-CE4C-49B7-A3C5-B8628C3B8552", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/BF5E74D2-CE4C-49B7-A3C5-B8628C3B8552/view-source"}], "score": 2, "updated_at": "2024-02-05T01:11:46+00:00"}], "domain": "biology", "external_links": ["https://www.google.com/search?q=how+to+dissuade+%22ground+hornets%22"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:08.576606+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/1051d4f3e38449f1419d1973ac812b2286659e454a76f89a23fdaa941dfadddb_0.json", "raw_sha256": "583dcd577e20d33b29e9f8818a7ab6a1fab039c19ab79927e16096cff23fa61d", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=7&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Rachel Baskerville", "question_author_url": "https://biology.stackexchange.com/users/78790/rachel-baskerville", "question_author_user_type": "registered", "question_created_at": "2024-02-04T22:27:04+00:00", "question_html": "

We recently moved into a new house and when we mowed the yard we were being stung by these huge hornets. We couldn’t find anyone to remove them and I am terrified they are going to come back this year. They are in the ground and are about 1-2 inches long and chunky. They also come out at night when we are trying to sit on the patio. I need some advice. If they will be there this year, what can I do to rid of them.

\n", "question_id": 114031, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "We recently moved into a new house and when we mowed the yard we were being stung by these huge hornets. We couldn’t find anyone to remove them and I am terrified they are going to come back this year. They are in the ground and are about 1-2 inches long and chunky. They also come out at night when we are trying to sit on the patio. I need some advice. If they will be there this year, what can I do to rid of them.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Rachel Baskerville", "profile_url": "https://biology.stackexchange.com/users/78790/rachel-baskerville", "user_type": "registered"}, "created_at": "2024-02-04T22:27:04+00:00", "raw_file": "raw/codex_api_v1/7731e95f5b86805dcc210d6fef6f1ae90aedbea29d6d8084621d880fcd44e459_1790824059333573800_0.json", "raw_sha256": "75346ea86ff90b8db1427552949ecffb611214a9308b4f99afbdda87d5df239e", "revision_guid": "5B3F4B38-70A1-4F10-9011-F05897992946", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/5B3F4B38-70A1-4F10-9011-F05897992946/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/114031/will-ground-hornets-come-back-to-the-same-place-after-winter", "split": "test", "split_group": "83f5a6af84cfe7491c45ab88a3380691688ce87fb2cd21767deeba081ed26eba", "tags": ["entomology"], "thread_id": "biology:114031", "title": "Will “ground hornets” come back to the same place after winter?"}} {"citation_context": "\nVasopressin binding can result in both calcium release and cAMP increases.\n\n\n\n\nSame with glucagon: https://en.m.wikipedia.org/wiki/Glucagon_receptor (https://en.m.wikipedia.org/wiki/Glucagon_receptor)\n\n\n\n\nSpecificity comes from expression, co-expre", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.m.wikipedia.org/wiki/Glucagon_receptor", "kind": "external_url", "post_id": 114766, "post_url": "https://biology.stackexchange.com/a/114766", "product": "citations", "record_id": "Scientific-Citation-Graph:8095b277707e8a01a02e9a44", "split": "test", "thread": {"accepted_answer_id": 114766, "answers": [{"answer_html": "

There are typically multiple different second messenger systems used by a given hormone, and multiple hormones use the same second messenger system.

\n

Second messengers aren't really a property of the hormone/ligand, they are a property of the receptor, so you'll want to look for information about different receptors for a ligand to know what second messengers are involved.

\n

Take ADH/vasopressin for example: https://en.m.wikipedia.org/wiki/Vasopressin

\n

Vasopressin binding can result in both calcium release and cAMP increases.

\n

Same with glucagon: https://en.m.wikipedia.org/wiki/Glucagon_receptor

\n

Specificity comes from expression, co-expression, and localization. Only cells that express a receptor will be affected by a hormone. Only receptors for a second messenger that are expressed in that cell type will be affected by second messenger changes. And finally, second messenger signalling is often local, so it's not as if calcium for example increases in equal amounts throughout an entire cell, it increases and has effects locally and is sequestered by calcium binding proteins as it diffuses away.

\n", "answer_id": 114766, "answer_text": "There are typically multiple different second messenger systems used by a given hormone, and multiple hormones use the same second messenger system.\n\n\n\n\nSecond messengers aren't really a property of the hormone/ligand, they are a property of the receptor, so you'll want to look for information about different receptors for a ligand to know what second messengers are involved.\n\n\n\n\nTake ADH/vasopressin for example: https://en.m.wikipedia.org/wiki/Vasopressin (https://en.m.wikipedia.org/wiki/Vasopressin)\n\n\n\n\nVasopressin binding can result in both calcium release and cAMP increases.\n\n\n\n\nSame with glucagon: https://en.m.wikipedia.org/wiki/Glucagon_receptor (https://en.m.wikipedia.org/wiki/Glucagon_receptor)\n\n\n\n\nSpecificity comes from expression, co-expression, and localization. Only cells that express a receptor will be affected by a hormone. Only receptors for a second messenger that are expressed in that cell type will be affected by second messenger changes. And finally, second messenger signalling is often local, so it's not as if calcium for example increases in equal amounts throughout an entire cell, it increases and has effects locally and is sequestered by calcium binding proteins as it diffuses away.", "answer_url": "https://biology.stackexchange.com/a/114766", "author": "Bryan Krause", "author_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2024-05-27T12:54:27+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:27.977583+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/1cbf95322a17dce0fd00a109179063ffe60bcd4bddc6e720f0ca398ee7aa9da8_0.json", "raw_sha256": "a096c86028a279b01346143890b4827bd8ed05afc0a76bd7c8bcb840211dc20e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/114983;114969;114966;114963;114939;114936;114918;114909;114904;114899;114888;114885;114881;114875;114874;114873;114872;114864;114857;114850;114846;114841;114834;114827;114821;114819;114813;114804;114791;114784;114768;114765;114762;114760;114758;114755;114745;114741;114739;114738;114732;114730;114726;114714;114706;114695;114691;114690;114686;114683;114677;114675;114666;114660;114656;114653;114642;114641;114632;114628;114620;114618;114613;114601;114599;114597;114581;114577;114573;114567;114558;114555;114553;114552;114547;114545;114543;114542;114541;114539;114529;114524;114516;114502;114501;114498;114495;114492;114481;114476;114474;114470;114453;114451;114449;114448;114446;114440;114438;114435/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 114758, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Bryan Krause", "profile_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "user_type": "moderator"}, "created_at": "2024-05-27T12:54:27+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "9A3F5DF7-0B9A-4E0A-8F1E-AE380292D475", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/9A3F5DF7-0B9A-4E0A-8F1E-AE380292D475/view-source"}], "score": 3, "updated_at": "2024-05-27T12:54:27+00:00"}], "domain": "biology", "external_links": ["https://en.m.wikipedia.org/wiki/Glucagon_receptor", "https://en.m.wikipedia.org/wiki/Vasopressin"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:07.165481+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/b97a755f39b54a1e8a057fa5e484426784aa17a1971c6ef0ca759105de983078_0.json", "raw_sha256": "4c9dcc077d306d60a8b8a237ad3f9b3144c0d5885fa62ef1bfdd55d2fbbdaf6a", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=6&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Jojo", "question_author_url": "https://biology.stackexchange.com/users/75521/jojo", "question_author_user_type": "registered", "question_created_at": "2024-05-25T15:20:49+00:00", "question_html": "

I have learnt about a number of different types of second messenger molecules including cAMP, IP$_3$, Ca$^{2+}$ and DAGs. Hormones interact with signal proteins in the cell membrane which transduces a signal into second messenger molecules inside the cell. I haven't been able to find out how the hormones map onto these second messengers. For example, there could one second messenger for each hormone and so eg. maybe ADH and only ADH triggers cAMP. Then glucagon would have a different second messenger molecule etc.

\n

I got the impression that this is not the case however and things are more complex. Maybe each second messenger molecule has its own function in the cell and different hormones trigger different amounts of second messengers? So like, maybe ADH triggers cAMP a little bit, and glucagon triggers it a lot, but LH never triggers cAMP. And then ADH triggers IP$_3$ a lot and glucagon leaves it unchanged, etc.

\n

Anyway that's just two possible explanations that I came up with. So, how do hormones map onto second messenger molecules?

\n", "question_id": 114758, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "I have learnt about a number of different types of second messenger molecules including cAMP, IP$_3$, Ca$^{2+}$ and DAGs. Hormones interact with signal proteins in the cell membrane which transduces a signal into second messenger molecules inside the cell. I haven't been able to find out how the hormones map onto these second messengers. For example, there could one second messenger for each hormone and so eg. maybe ADH and only ADH triggers cAMP. Then glucagon would have a different second messenger molecule etc.\n\n\n\n\nI got the impression that this is not the case however and things are more complex. Maybe each second messenger molecule has its own function in the cell and different hormones trigger different amounts of second messengers? So like, maybe ADH triggers cAMP a little bit, and glucagon triggers it a lot, but LH never triggers cAMP. And then ADH triggers IP$_3$ a lot and glucagon leaves it unchanged, etc.\n\n\n\n\nAnyway that's just two possible explanations that I came up with. So, how do hormones map onto second messenger molecules?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Jojo", "profile_url": "https://biology.stackexchange.com/users/75521/jojo", "user_type": "registered"}, "created_at": "2024-05-25T15:20:49+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "7FAF651E-922E-4CA4-B0FC-EE5571DCA54C", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/7FAF651E-922E-4CA4-B0FC-EE5571DCA54C/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Jojo", "profile_url": "https://biology.stackexchange.com/users/75521/jojo", "user_type": "registered"}, "created_at": "2024-05-25T17:32:32+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "BE8D287F-2A9D-4B6F-9962-0036D69B6506", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/BE8D287F-2A9D-4B6F-9962-0036D69B6506/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Jojo", "profile_url": "https://biology.stackexchange.com/users/75521/jojo", "user_type": "registered"}, "created_at": "2024-05-26T10:19:22+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "A9418082-DCAD-4B7B-A535-724ABDDA28DF", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/A9418082-DCAD-4B7B-A535-724ABDDA28DF/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Jojo", "profile_url": "https://biology.stackexchange.com/users/75521/jojo", "user_type": "registered"}, "created_at": "2024-05-27T08:54:25+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "0784D223-5FA7-4786-8C0D-F882A16AABAC", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/0784D223-5FA7-4786-8C0D-F882A16AABAC/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/114758/is-there-one-second-messenger-molecule-for-each-hormone", "split": "test", "split_group": "241801be54db9451df4c8c51875a1534d0cd1d39c8fce2553edd67dcbccf4df3", "tags": ["cell-biology", "endocrinology", "cell-signaling", "signal-processing"], "thread_id": "biology:114758", "title": "Is there one second messenger molecule for each hormone?"}} {"citation_context": "ors for a ligand to know what second messengers are involved.\n\n\n\n\nTake ADH/vasopressin for example: https://en.m.wikipedia.org/wiki/Vasopressin (https://en.m.wikipedia.org/wiki/Vasopressin)\n\n\n\n\nVasopressin binding can result in both calcium re", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.m.wikipedia.org/wiki/Vasopressin", "kind": "external_url", "post_id": 114766, "post_url": "https://biology.stackexchange.com/a/114766", "product": "citations", "record_id": "Scientific-Citation-Graph:5779ca1fb0ff488ba50348b9", "split": "test", "thread": {"accepted_answer_id": 114766, "answers": [{"answer_html": "

There are typically multiple different second messenger systems used by a given hormone, and multiple hormones use the same second messenger system.

\n

Second messengers aren't really a property of the hormone/ligand, they are a property of the receptor, so you'll want to look for information about different receptors for a ligand to know what second messengers are involved.

\n

Take ADH/vasopressin for example: https://en.m.wikipedia.org/wiki/Vasopressin

\n

Vasopressin binding can result in both calcium release and cAMP increases.

\n

Same with glucagon: https://en.m.wikipedia.org/wiki/Glucagon_receptor

\n

Specificity comes from expression, co-expression, and localization. Only cells that express a receptor will be affected by a hormone. Only receptors for a second messenger that are expressed in that cell type will be affected by second messenger changes. And finally, second messenger signalling is often local, so it's not as if calcium for example increases in equal amounts throughout an entire cell, it increases and has effects locally and is sequestered by calcium binding proteins as it diffuses away.

\n", "answer_id": 114766, "answer_text": "There are typically multiple different second messenger systems used by a given hormone, and multiple hormones use the same second messenger system.\n\n\n\n\nSecond messengers aren't really a property of the hormone/ligand, they are a property of the receptor, so you'll want to look for information about different receptors for a ligand to know what second messengers are involved.\n\n\n\n\nTake ADH/vasopressin for example: https://en.m.wikipedia.org/wiki/Vasopressin (https://en.m.wikipedia.org/wiki/Vasopressin)\n\n\n\n\nVasopressin binding can result in both calcium release and cAMP increases.\n\n\n\n\nSame with glucagon: https://en.m.wikipedia.org/wiki/Glucagon_receptor (https://en.m.wikipedia.org/wiki/Glucagon_receptor)\n\n\n\n\nSpecificity comes from expression, co-expression, and localization. Only cells that express a receptor will be affected by a hormone. Only receptors for a second messenger that are expressed in that cell type will be affected by second messenger changes. And finally, second messenger signalling is often local, so it's not as if calcium for example increases in equal amounts throughout an entire cell, it increases and has effects locally and is sequestered by calcium binding proteins as it diffuses away.", "answer_url": "https://biology.stackexchange.com/a/114766", "author": "Bryan Krause", "author_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2024-05-27T12:54:27+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:27.977583+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/1cbf95322a17dce0fd00a109179063ffe60bcd4bddc6e720f0ca398ee7aa9da8_0.json", "raw_sha256": "a096c86028a279b01346143890b4827bd8ed05afc0a76bd7c8bcb840211dc20e", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/114983;114969;114966;114963;114939;114936;114918;114909;114904;114899;114888;114885;114881;114875;114874;114873;114872;114864;114857;114850;114846;114841;114834;114827;114821;114819;114813;114804;114791;114784;114768;114765;114762;114760;114758;114755;114745;114741;114739;114738;114732;114730;114726;114714;114706;114695;114691;114690;114686;114683;114677;114675;114666;114660;114656;114653;114642;114641;114632;114628;114620;114618;114613;114601;114599;114597;114581;114577;114573;114567;114558;114555;114553;114552;114547;114545;114543;114542;114541;114539;114529;114524;114516;114502;114501;114498;114495;114492;114481;114476;114474;114470;114453;114451;114449;114448;114446;114440;114438;114435/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 114758, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Bryan Krause", "profile_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "user_type": "moderator"}, "created_at": "2024-05-27T12:54:27+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "9A3F5DF7-0B9A-4E0A-8F1E-AE380292D475", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/9A3F5DF7-0B9A-4E0A-8F1E-AE380292D475/view-source"}], "score": 3, "updated_at": "2024-05-27T12:54:27+00:00"}], "domain": "biology", "external_links": ["https://en.m.wikipedia.org/wiki/Glucagon_receptor", "https://en.m.wikipedia.org/wiki/Vasopressin"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:07.165481+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/b97a755f39b54a1e8a057fa5e484426784aa17a1971c6ef0ca759105de983078_0.json", "raw_sha256": "4c9dcc077d306d60a8b8a237ad3f9b3144c0d5885fa62ef1bfdd55d2fbbdaf6a", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=6&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "Jojo", "question_author_url": "https://biology.stackexchange.com/users/75521/jojo", "question_author_user_type": "registered", "question_created_at": "2024-05-25T15:20:49+00:00", "question_html": "

I have learnt about a number of different types of second messenger molecules including cAMP, IP$_3$, Ca$^{2+}$ and DAGs. Hormones interact with signal proteins in the cell membrane which transduces a signal into second messenger molecules inside the cell. I haven't been able to find out how the hormones map onto these second messengers. For example, there could one second messenger for each hormone and so eg. maybe ADH and only ADH triggers cAMP. Then glucagon would have a different second messenger molecule etc.

\n

I got the impression that this is not the case however and things are more complex. Maybe each second messenger molecule has its own function in the cell and different hormones trigger different amounts of second messengers? So like, maybe ADH triggers cAMP a little bit, and glucagon triggers it a lot, but LH never triggers cAMP. And then ADH triggers IP$_3$ a lot and glucagon leaves it unchanged, etc.

\n

Anyway that's just two possible explanations that I came up with. So, how do hormones map onto second messenger molecules?

\n", "question_id": 114758, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "I have learnt about a number of different types of second messenger molecules including cAMP, IP$_3$, Ca$^{2+}$ and DAGs. Hormones interact with signal proteins in the cell membrane which transduces a signal into second messenger molecules inside the cell. I haven't been able to find out how the hormones map onto these second messengers. For example, there could one second messenger for each hormone and so eg. maybe ADH and only ADH triggers cAMP. Then glucagon would have a different second messenger molecule etc.\n\n\n\n\nI got the impression that this is not the case however and things are more complex. Maybe each second messenger molecule has its own function in the cell and different hormones trigger different amounts of second messengers? So like, maybe ADH triggers cAMP a little bit, and glucagon triggers it a lot, but LH never triggers cAMP. And then ADH triggers IP$_3$ a lot and glucagon leaves it unchanged, etc.\n\n\n\n\nAnyway that's just two possible explanations that I came up with. So, how do hormones map onto second messenger molecules?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Jojo", "profile_url": "https://biology.stackexchange.com/users/75521/jojo", "user_type": "registered"}, "created_at": "2024-05-25T15:20:49+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "7FAF651E-922E-4CA4-B0FC-EE5571DCA54C", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/7FAF651E-922E-4CA4-B0FC-EE5571DCA54C/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Jojo", "profile_url": "https://biology.stackexchange.com/users/75521/jojo", "user_type": "registered"}, "created_at": "2024-05-25T17:32:32+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "BE8D287F-2A9D-4B6F-9962-0036D69B6506", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/BE8D287F-2A9D-4B6F-9962-0036D69B6506/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Jojo", "profile_url": "https://biology.stackexchange.com/users/75521/jojo", "user_type": "registered"}, "created_at": "2024-05-26T10:19:22+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "A9418082-DCAD-4B7B-A535-724ABDDA28DF", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/A9418082-DCAD-4B7B-A535-724ABDDA28DF/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Jojo", "profile_url": "https://biology.stackexchange.com/users/75521/jojo", "user_type": "registered"}, "created_at": "2024-05-27T08:54:25+00:00", "raw_file": "raw/codex_api_v1/41500cf35bca9ae31b7ea454bad8679af7e3276d71713db5d1815d84a971bb0e_1790824088925435600_0.json", "raw_sha256": "a764902131a161e2a7978a1f607c4912689efa157d70c2752a5b31e3a042aacb", "revision_guid": "0784D223-5FA7-4786-8C0D-F882A16AABAC", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/0784D223-5FA7-4786-8C0D-F882A16AABAC/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/114758/is-there-one-second-messenger-molecule-for-each-hormone", "split": "test", "split_group": "241801be54db9451df4c8c51875a1534d0cd1d39c8fce2553edd67dcbccf4df3", "tags": ["cell-biology", "endocrinology", "cell-signaling", "signal-processing"], "thread_id": "biology:114758", "title": "Is there one second messenger molecule for each hormone?"}} {"citation_context": "nge in their combined reaction.\n\n\n\n\n[image: Energy profile of an enzyme-catalysed reaction; source: https://i.sstatic.net/TaxmZAJj.png] (https://i.sstatic.net/TaxmZAJj.png)\n\n\n\n\n[Example of the energy changes during a simple unimolecul", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://i.sstatic.net/TaxmZAJj.png", "kind": "external_url", "post_id": 115781, "post_url": "https://biology.stackexchange.com/a/115781", "product": "citations", "record_id": "Scientific-Citation-Graph:b0a5b945a22ba44dd6147f6e", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

Definition of Terms: Energy and Work in metabolic interconversions
\nThe title of this question uses the terms “cellular work” and “energy release” in a very general sense, so I think it is important to start be establishing what ‘energy’ and ‘work’ mean in relation to biochemical reactions, in order to relate them more rigorously to the role of ATP in metabolism.
\nEnergy. Biochemists — and biolochemical texts — consider metabolism energy in thermodynamic terms, specifically in relation to what is known as the Gibbs Free Energy (G). This is not as it applies to individual compounds (which is difficult or impossible to measure) but in relation to the overall change in this Gibbs Free Energy (ΔG) that occurs during a particular chemical reaction, considering both the reactants and products. The basic precept is that if ΔG is negative, the reaction proceeds ‘spontaneously’. I would emphasize that this is a ‘black box approach’: we do not need to know, and do not consider how the change is accomplished in molecular terms — that is the realm of reaction mechanism and kinetics, not thermodynamic energy.
\nWork. A general definition of energy I remember from school physics is “the ability to do work”, and searching the internet I find this is still used (with ‘capacity’ replacing ‘ability’). Elsewhere I find it defined as “… the energy transferred from one thermodynamic system into another thermodynamic system”. This is most easily envisaged in terms of mechanical work, but, although ATP is involved in this in biological systems, the question is about the ‘work’ done in facilitating a non-spontaneous reaction — one with a positive ΔG. (The difference of this from mechanical or electrical work means that the term ‘work’ is quite infrequently used in biochemical texts in relation to metabolic reactions.)

\n

Restating the question
\nThe phrases “drive cellular work” and “energy release” in the title do not fit well with the definitions above. I suggest it would be best to rephrase the question as:

\n
\n

“Does ATP perform cellular work solely from the free energy change\nduring its hydrolysis, or is additional energy obtained by repulsion\nbetween ADP and inorganic phosphate?”

\n
\n

Thermodynamics of ATP hydrolysis in coupled biochemical reactions
\nTwo things are required for ATP hydrolysis to facilitate a non-spontaneous chemical reaction:

\n
    \n
  1. The unsigned value of the negative ΔG for the reaction of ATP hydrolysis must be greater than that of the positive ΔG for the reaction that is being enabled. i.e. The overall ΔG for the two reactions considered together must be negative.
    2. \n
  2. There must be a mechanism to couple the reactions, i.e. to ensure that the energy of the phosphoanhydride bond is used to form bonds in other reactants and not lost as heat.
    3. \n
\n

An enzymic reaction mechanism will involve a pathway that differs from an uncatalyzed reaction and will have intermediates with different energy states (e.g. below), but the details of this have no relevance to the thermodynamics of the overall change involved. This depends solely on the overall free energies of the reactants and the products, and the change in their combined reaction.

\n

\"Energy

\n

[Example of the energy changes during a simple unimolecular enzymic reaction]

\n

Answer to the question
\nFrom this it can be seen that the answer to the question of whether additional energy is obtained by repulsion between ADP and inorganic phosphate is

\n
\n

“No, The energy driving the reaction arises solely from the free\nenergy change during hydrolysis”.

\n
\n

Any repulsion of ADP and Pi on the enzyme has no bearing on the energetics. If such repulsion does, in fact, occur, its influence would be on the release of the reaction intermediates at some point along the reaction pathway of the type illustrated. The energy changes along the pathway have no effect on the overall free energy change.

\n

Coda: Does direct hydrolysis of ATP to inorganic phosphate actually occur in metabolism?
\nThe assumption in the question is that in coupled metabolic reactions involving ATP, inorganic phosphate is released directly by hydrolysis of the phosphoanhydride bond. This is generally not the case, as multi-step reactions normally occur in which the phosphoryl group is transferred to another participant, ‘activating it’ for the energetically unfavourable reaction. (Or the ADP (or AMP) moiety is transferred to another compound and phosphate released.) I have addressed this point in more detail in an answer to a related question from the poster.

\n

Bibliography
\nA good place to read about biochemical thermodynamics is in Biochemistry, by Berg et al. It should be possible to pick up an older edition cheaply on eBay etc. Although not as good in my opinion, there is a freely accessible chapter in a book on NCBI Bookshelf in which the section on Metabolic Energy explains this generally accepted approach to biochemical thermodynamics.

\n", "answer_id": 115781, "answer_text": "Definition of Terms: Energy and Work in metabolic interconversions\n\nThe title of this question uses the terms “cellular work” and “energy release” in a very general sense, so I think it is important to start be establishing what ‘energy’ and ‘work’ mean in relation to biochemical reactions, in order to relate them more rigorously to the role of ATP in metabolism.\n\nEnergy. Biochemists — and biolochemical texts — consider metabolism energy in thermodynamic terms, specifically in relation to what is known as the Gibbs Free Energy (G). This is not as it applies to individual compounds (which is difficult or impossible to measure) but in relation to the overall change in this Gibbs Free Energy (ΔG) that occurs during a particular chemical reaction, considering both the reactants and products. The basic precept is that if ΔG is negative, the reaction proceeds ‘spontaneously’. I would emphasize that this is a ‘black box approach’: we do not need to know, and do not consider how the change is accomplished in molecular terms — that is the realm of reaction mechanism and kinetics, not thermodynamic energy.\n\nWork. A general definition of energy I remember from school physics is “the ability to do work”, and searching the internet I find this is still used (with ‘capacity’ replacing ‘ability’). Elsewhere I find it defined as “… the energy transferred from one thermodynamic system into another thermodynamic system”. This is most easily envisaged in terms of mechanical work, but, although ATP is involved in this in biological systems, the question is about the ‘work’ done in facilitating a non-spontaneous reaction — one with a positive ΔG. (The difference of this from mechanical or electrical work means that the term ‘work’ is quite infrequently used in biochemical texts in relation to metabolic reactions.)\n\n\n\n\nRestating the question\n\nThe phrases “drive cellular work” and “energy release” in the title do not fit well with the definitions above. I suggest it would be best to rephrase the question as:\n\n\n\n\n\n\n\n\n“Does ATP perform cellular work solely from the free energy change\nduring its hydrolysis, or is additional energy obtained by repulsion\nbetween ADP and inorganic phosphate?”\n\n\n\n\n\n\n\nThermodynamics of ATP hydrolysis in coupled biochemical reactions\n\nTwo things are required for ATP hydrolysis to facilitate a non-spontaneous chemical reaction:\n\n\n\n\n\nThe unsigned value of the negative ΔG for the reaction of ATP hydrolysis must be greater than that of the positive ΔG for the reaction that is being enabled. i.e. The overall ΔG for the two reactions considered together must be negative.\n\n\n\n\nThere must be a mechanism to couple the reactions, i.e. to ensure that the energy of the phosphoanhydride bond is used to form bonds in other reactants and not lost as heat.\n\n\n\n\n\nAn enzymic reaction mechanism will involve a pathway that differs from an uncatalyzed reaction and will have intermediates with different energy states (e.g. below), but the details of this have no relevance to the thermodynamics of the overall change involved. This depends solely on the overall free energies of the reactants and the products, and the change in their combined reaction.\n\n\n\n\n[image: Energy profile of an enzyme-catalysed reaction; source: https://i.sstatic.net/TaxmZAJj.png] (https://i.sstatic.net/TaxmZAJj.png)\n\n\n\n\n[Example of the energy changes during a simple unimolecular enzymic reaction]\n\n\n\n\nAnswer to the question\n\nFrom this it can be seen that the answer to the question of whether additional energy is obtained by repulsion between ADP and inorganic phosphate is\n\n\n\n\n\n\n\n“No, The energy driving the reaction arises solely from the free\nenergy change during hydrolysis”.\n\n\n\n\n\n\n\nAny repulsion of ADP and Pi on the enzyme has no bearing on the energetics. If such repulsion does, in fact, occur, its influence would be on the release of the reaction intermediates at some point along the reaction pathway of the type illustrated. The energy changes along the pathway have no effect on the overall free energy change.\n\n\n\n\nCoda: Does direct hydrolysis of ATP to inorganic phosphate actually occur in metabolism?\n\nThe assumption in the question is that in coupled metabolic reactions involving ATP, inorganic phosphate is released directly by hydrolysis of the phosphoanhydride bond. This is generally not the case, as multi-step reactions normally occur in which the phosphoryl group is transferred to another participant, ‘activating it’ for the energetically unfavourable reaction. (Or the ADP (or AMP) moiety is transferred to another compound and phosphate released.) I have addressed this point in more detail in an answer to a related question from the poster (https://biology.stackexchange.com/questions/115773/why-is-the-transfer-of-a-phosphate-group-instead-of-atp-hydrolysis-or-some-othe/115858#115858).\n\n\n\n\nBibliography\n\nA good place to read about biochemical thermodynamics is in Biochemistry, by Berg et al. It should be possible to pick up an older edition cheaply on eBay etc. Although not as good in my opinion, there is a freely accessible chapter in a book on NCBI Bookshelf in which the section on Metabolic Energy (https://www.ncbi.nlm.nih.gov/books/NBK9903/) explains this generally accepted approach to biochemical thermodynamics.", "answer_url": "https://biology.stackexchange.com/a/115781", "author": "David", "author_url": "https://biology.stackexchange.com/users/22057/david", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-12-12T23:53:37+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:22.614155+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/2c8799380b8f5d7bf0fd42e594fd78a1835b27e1da9f481cc00f096bab9c01ca_0.json", "raw_sha256": "348375a094fdfd6d9ca55d0bddc65d8dc7a7f0757e1e5a44c25e22a66b1a4892", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/116119;116113;116097;116096;116091;116087;116076;116067;116063;116059;116055;116037;116034;116028;116022;116012;116005;115997;115989;115988;115987;115979;115978;115976;115974;115973;115970;115966;115965;115957;115952;115939;115933;115932;115927;115921;115915;115903;115897;115894;115886;115885;115884;115881;115880;115868;115867;115857;115852;115840;115830;115825;115819;115815;115791;115780;115773;115764;115759;115756;115743;115736;115726;115723;115713;115699;115691;115689;115685;115678;115668;115664;115657;115650;115642;115639;115632;115627;115626;115609;115602;115598;115592;115588;115587;115580;115578;115570;115566;115562;115549;115537;115536;115531;115530;115528;115525;115521;115513;115510/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115780, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2024-12-12T23:53:37+00:00", "raw_file": "raw/codex_api_v1/5ced1a9f1ef6cec4e5ea414f5920558abe1f2afe671db804d768d0c0886f0b02_1790824127343029500_0.json", "raw_sha256": "9b7f4987291adc582d9a7ae47056606e7a91fc10c512e504e60da3797727c346", "revision_guid": "9772CCE1-6A29-4B1E-A4DE-75843A878738", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/9772CCE1-6A29-4B1E-A4DE-75843A878738/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2024-12-16T09:32:04+00:00", "raw_file": "raw/codex_api_v1/5ced1a9f1ef6cec4e5ea414f5920558abe1f2afe671db804d768d0c0886f0b02_1790824127343029500_0.json", "raw_sha256": "9b7f4987291adc582d9a7ae47056606e7a91fc10c512e504e60da3797727c346", "revision_guid": "0ADDDDE2-225F-4C30-A06B-ECCE57028384", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/0ADDDDE2-225F-4C30-A06B-ECCE57028384/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2024-12-20T16:43:32+00:00", "raw_file": "raw/codex_api_v1/5ced1a9f1ef6cec4e5ea414f5920558abe1f2afe671db804d768d0c0886f0b02_1790824127343029500_0.json", "raw_sha256": "9b7f4987291adc582d9a7ae47056606e7a91fc10c512e504e60da3797727c346", "revision_guid": "C9F64F8F-3FBB-45F8-9575-568F31AC993C", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/C9F64F8F-3FBB-45F8-9575-568F31AC993C/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2024-12-24T15:13:24+00:00", "raw_file": "raw/codex_api_v1/6498de963750b51efbda1119ed6af944d93448730fd638915c3f01fbcab0c1ec_1790824125196761600_0.json", "raw_sha256": "6bc4a347798a1508410269e30549f130720c68f4c848e3ea1eb2f60991f67851", "revision_guid": "BE09F7C0-1127-4534-A6D9-63F1E7809819", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/BE09F7C0-1127-4534-A6D9-63F1E7809819/view-source"}], "score": 3, "updated_at": "2024-12-24T15:13:24+00:00"}], "domain": "biology", "external_links": ["https://i.sstatic.net/TaxmZAJj.png", "https://www.ncbi.nlm.nih.gov/books/NBK9903/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:04.377249+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/54ece81cba3a5a552bb15d6d3feedc4324a2ba2706d33480080ece9537efd4b1_0.json", "raw_sha256": "f1eb8f7eda9336b81701b663029f9411e040c0bcf262148b7ede9a103ae73e69", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=4&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "elijah whipple", "question_author_url": "https://biology.stackexchange.com/users/95505/elijah-whipple", "question_author_user_type": "registered", "question_created_at": "2024-12-12T19:39:16+00:00", "question_html": "

After ADP and Pi are no longer bound to each other but still bound to an enzyme, do they repel each other? If so, does that contribute to the work that ATP hydrolysis can do?

\n", "question_id": 115780, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "After ADP and Pi are no longer bound to each other but still bound to an enzyme, do they repel each other? If so, does that contribute to the work that ATP hydrolysis can do?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "elijah whipple", "profile_url": "https://biology.stackexchange.com/users/95505/elijah-whipple", "user_type": "registered"}, "created_at": "2024-12-12T19:39:16+00:00", "raw_file": "raw/codex_api_v1/5ced1a9f1ef6cec4e5ea414f5920558abe1f2afe671db804d768d0c0886f0b02_1790824127343029500_0.json", "raw_sha256": "9b7f4987291adc582d9a7ae47056606e7a91fc10c512e504e60da3797727c346", "revision_guid": "CB91403E-2BC4-4E8B-A581-D7CE1E8E5768", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/CB91403E-2BC4-4E8B-A581-D7CE1E8E5768/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2024-12-13T09:24:18+00:00", "raw_file": "raw/codex_api_v1/5ced1a9f1ef6cec4e5ea414f5920558abe1f2afe671db804d768d0c0886f0b02_1790824127343029500_0.json", "raw_sha256": "9b7f4987291adc582d9a7ae47056606e7a91fc10c512e504e60da3797727c346", "revision_guid": "0182791D-B3F3-490A-842E-E3DC3B0C7B1F", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/0182791D-B3F3-490A-842E-E3DC3B0C7B1F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "elijah whipple", "profile_url": "https://biology.stackexchange.com/users/95505/elijah-whipple", "user_type": "registered"}, "created_at": "2025-01-20T03:11:38+00:00", "raw_file": "raw/codex_api_v1/9208faf10edface85b193538ceee277a2c29dd57b691eaef3dbbd7fcb70c256f_1790824112025498400_0.json", "raw_sha256": "cacf2fdbe629fb39b1a0932a5485abc61f5635b5e51482d0d3b8ab40f1450c36", "revision_guid": "9B9F769A-32BE-4E5E-B8BF-B608137D79A2", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/9B9F769A-32BE-4E5E-B8BF-B608137D79A2/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/115780/does-atp-drive-unfavorable-reactions-with-the-free-energy-change-of-a-reaction", "split": "test", "split_group": "d7257f630e46f436b2bf631bc7be4b95a12e26afe14c7c25c2b52947f531434a", "tags": ["biochemistry", "bioenergetics"], "thread_id": "biology:115780", "title": "Does ATP drive unfavorable reactions with the free energy change of a reaction, or is additional energy obtained by repulsion between ADP and Pi?"}} {"citation_context": "s a freely accessible chapter in a book on NCBI Bookshelf in which the section on Metabolic Energy (https://www.ncbi.nlm.nih.gov/books/NBK9903/) explains this generally accepted approach to biochemical thermodynamics.", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.ncbi.nlm.nih.gov/books/NBK9903/", "kind": "external_url", "post_id": 115781, "post_url": "https://biology.stackexchange.com/a/115781", "product": "citations", "record_id": "Scientific-Citation-Graph:2387c89441464cdf37795b0a", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

Definition of Terms: Energy and Work in metabolic interconversions
\nThe title of this question uses the terms “cellular work” and “energy release” in a very general sense, so I think it is important to start be establishing what ‘energy’ and ‘work’ mean in relation to biochemical reactions, in order to relate them more rigorously to the role of ATP in metabolism.
\nEnergy. Biochemists — and biolochemical texts — consider metabolism energy in thermodynamic terms, specifically in relation to what is known as the Gibbs Free Energy (G). This is not as it applies to individual compounds (which is difficult or impossible to measure) but in relation to the overall change in this Gibbs Free Energy (ΔG) that occurs during a particular chemical reaction, considering both the reactants and products. The basic precept is that if ΔG is negative, the reaction proceeds ‘spontaneously’. I would emphasize that this is a ‘black box approach’: we do not need to know, and do not consider how the change is accomplished in molecular terms — that is the realm of reaction mechanism and kinetics, not thermodynamic energy.
\nWork. A general definition of energy I remember from school physics is “the ability to do work”, and searching the internet I find this is still used (with ‘capacity’ replacing ‘ability’). Elsewhere I find it defined as “… the energy transferred from one thermodynamic system into another thermodynamic system”. This is most easily envisaged in terms of mechanical work, but, although ATP is involved in this in biological systems, the question is about the ‘work’ done in facilitating a non-spontaneous reaction — one with a positive ΔG. (The difference of this from mechanical or electrical work means that the term ‘work’ is quite infrequently used in biochemical texts in relation to metabolic reactions.)

\n

Restating the question
\nThe phrases “drive cellular work” and “energy release” in the title do not fit well with the definitions above. I suggest it would be best to rephrase the question as:

\n
\n

“Does ATP perform cellular work solely from the free energy change\nduring its hydrolysis, or is additional energy obtained by repulsion\nbetween ADP and inorganic phosphate?”

\n
\n

Thermodynamics of ATP hydrolysis in coupled biochemical reactions
\nTwo things are required for ATP hydrolysis to facilitate a non-spontaneous chemical reaction:

\n
    \n
  1. The unsigned value of the negative ΔG for the reaction of ATP hydrolysis must be greater than that of the positive ΔG for the reaction that is being enabled. i.e. The overall ΔG for the two reactions considered together must be negative.
    2. \n
  2. There must be a mechanism to couple the reactions, i.e. to ensure that the energy of the phosphoanhydride bond is used to form bonds in other reactants and not lost as heat.
    3. \n
\n

An enzymic reaction mechanism will involve a pathway that differs from an uncatalyzed reaction and will have intermediates with different energy states (e.g. below), but the details of this have no relevance to the thermodynamics of the overall change involved. This depends solely on the overall free energies of the reactants and the products, and the change in their combined reaction.

\n

\"Energy

\n

[Example of the energy changes during a simple unimolecular enzymic reaction]

\n

Answer to the question
\nFrom this it can be seen that the answer to the question of whether additional energy is obtained by repulsion between ADP and inorganic phosphate is

\n
\n

“No, The energy driving the reaction arises solely from the free\nenergy change during hydrolysis”.

\n
\n

Any repulsion of ADP and Pi on the enzyme has no bearing on the energetics. If such repulsion does, in fact, occur, its influence would be on the release of the reaction intermediates at some point along the reaction pathway of the type illustrated. The energy changes along the pathway have no effect on the overall free energy change.

\n

Coda: Does direct hydrolysis of ATP to inorganic phosphate actually occur in metabolism?
\nThe assumption in the question is that in coupled metabolic reactions involving ATP, inorganic phosphate is released directly by hydrolysis of the phosphoanhydride bond. This is generally not the case, as multi-step reactions normally occur in which the phosphoryl group is transferred to another participant, ‘activating it’ for the energetically unfavourable reaction. (Or the ADP (or AMP) moiety is transferred to another compound and phosphate released.) I have addressed this point in more detail in an answer to a related question from the poster.

\n

Bibliography
\nA good place to read about biochemical thermodynamics is in Biochemistry, by Berg et al. It should be possible to pick up an older edition cheaply on eBay etc. Although not as good in my opinion, there is a freely accessible chapter in a book on NCBI Bookshelf in which the section on Metabolic Energy explains this generally accepted approach to biochemical thermodynamics.

\n", "answer_id": 115781, "answer_text": "Definition of Terms: Energy and Work in metabolic interconversions\n\nThe title of this question uses the terms “cellular work” and “energy release” in a very general sense, so I think it is important to start be establishing what ‘energy’ and ‘work’ mean in relation to biochemical reactions, in order to relate them more rigorously to the role of ATP in metabolism.\n\nEnergy. Biochemists — and biolochemical texts — consider metabolism energy in thermodynamic terms, specifically in relation to what is known as the Gibbs Free Energy (G). This is not as it applies to individual compounds (which is difficult or impossible to measure) but in relation to the overall change in this Gibbs Free Energy (ΔG) that occurs during a particular chemical reaction, considering both the reactants and products. The basic precept is that if ΔG is negative, the reaction proceeds ‘spontaneously’. I would emphasize that this is a ‘black box approach’: we do not need to know, and do not consider how the change is accomplished in molecular terms — that is the realm of reaction mechanism and kinetics, not thermodynamic energy.\n\nWork. A general definition of energy I remember from school physics is “the ability to do work”, and searching the internet I find this is still used (with ‘capacity’ replacing ‘ability’). Elsewhere I find it defined as “… the energy transferred from one thermodynamic system into another thermodynamic system”. This is most easily envisaged in terms of mechanical work, but, although ATP is involved in this in biological systems, the question is about the ‘work’ done in facilitating a non-spontaneous reaction — one with a positive ΔG. (The difference of this from mechanical or electrical work means that the term ‘work’ is quite infrequently used in biochemical texts in relation to metabolic reactions.)\n\n\n\n\nRestating the question\n\nThe phrases “drive cellular work” and “energy release” in the title do not fit well with the definitions above. I suggest it would be best to rephrase the question as:\n\n\n\n\n\n\n\n\n“Does ATP perform cellular work solely from the free energy change\nduring its hydrolysis, or is additional energy obtained by repulsion\nbetween ADP and inorganic phosphate?”\n\n\n\n\n\n\n\nThermodynamics of ATP hydrolysis in coupled biochemical reactions\n\nTwo things are required for ATP hydrolysis to facilitate a non-spontaneous chemical reaction:\n\n\n\n\n\nThe unsigned value of the negative ΔG for the reaction of ATP hydrolysis must be greater than that of the positive ΔG for the reaction that is being enabled. i.e. The overall ΔG for the two reactions considered together must be negative.\n\n\n\n\nThere must be a mechanism to couple the reactions, i.e. to ensure that the energy of the phosphoanhydride bond is used to form bonds in other reactants and not lost as heat.\n\n\n\n\n\nAn enzymic reaction mechanism will involve a pathway that differs from an uncatalyzed reaction and will have intermediates with different energy states (e.g. below), but the details of this have no relevance to the thermodynamics of the overall change involved. This depends solely on the overall free energies of the reactants and the products, and the change in their combined reaction.\n\n\n\n\n[image: Energy profile of an enzyme-catalysed reaction; source: https://i.sstatic.net/TaxmZAJj.png] (https://i.sstatic.net/TaxmZAJj.png)\n\n\n\n\n[Example of the energy changes during a simple unimolecular enzymic reaction]\n\n\n\n\nAnswer to the question\n\nFrom this it can be seen that the answer to the question of whether additional energy is obtained by repulsion between ADP and inorganic phosphate is\n\n\n\n\n\n\n\n“No, The energy driving the reaction arises solely from the free\nenergy change during hydrolysis”.\n\n\n\n\n\n\n\nAny repulsion of ADP and Pi on the enzyme has no bearing on the energetics. If such repulsion does, in fact, occur, its influence would be on the release of the reaction intermediates at some point along the reaction pathway of the type illustrated. The energy changes along the pathway have no effect on the overall free energy change.\n\n\n\n\nCoda: Does direct hydrolysis of ATP to inorganic phosphate actually occur in metabolism?\n\nThe assumption in the question is that in coupled metabolic reactions involving ATP, inorganic phosphate is released directly by hydrolysis of the phosphoanhydride bond. This is generally not the case, as multi-step reactions normally occur in which the phosphoryl group is transferred to another participant, ‘activating it’ for the energetically unfavourable reaction. (Or the ADP (or AMP) moiety is transferred to another compound and phosphate released.) I have addressed this point in more detail in an answer to a related question from the poster (https://biology.stackexchange.com/questions/115773/why-is-the-transfer-of-a-phosphate-group-instead-of-atp-hydrolysis-or-some-othe/115858#115858).\n\n\n\n\nBibliography\n\nA good place to read about biochemical thermodynamics is in Biochemistry, by Berg et al. It should be possible to pick up an older edition cheaply on eBay etc. Although not as good in my opinion, there is a freely accessible chapter in a book on NCBI Bookshelf in which the section on Metabolic Energy (https://www.ncbi.nlm.nih.gov/books/NBK9903/) explains this generally accepted approach to biochemical thermodynamics.", "answer_url": "https://biology.stackexchange.com/a/115781", "author": "David", "author_url": "https://biology.stackexchange.com/users/22057/david", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2024-12-12T23:53:37+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:22.614155+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/2c8799380b8f5d7bf0fd42e594fd78a1835b27e1da9f481cc00f096bab9c01ca_0.json", "raw_sha256": "348375a094fdfd6d9ca55d0bddc65d8dc7a7f0757e1e5a44c25e22a66b1a4892", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/116119;116113;116097;116096;116091;116087;116076;116067;116063;116059;116055;116037;116034;116028;116022;116012;116005;115997;115989;115988;115987;115979;115978;115976;115974;115973;115970;115966;115965;115957;115952;115939;115933;115932;115927;115921;115915;115903;115897;115894;115886;115885;115884;115881;115880;115868;115867;115857;115852;115840;115830;115825;115819;115815;115791;115780;115773;115764;115759;115756;115743;115736;115726;115723;115713;115699;115691;115689;115685;115678;115668;115664;115657;115650;115642;115639;115632;115627;115626;115609;115602;115598;115592;115588;115587;115580;115578;115570;115566;115562;115549;115537;115536;115531;115530;115528;115525;115521;115513;115510/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 115780, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2024-12-12T23:53:37+00:00", "raw_file": "raw/codex_api_v1/5ced1a9f1ef6cec4e5ea414f5920558abe1f2afe671db804d768d0c0886f0b02_1790824127343029500_0.json", "raw_sha256": "9b7f4987291adc582d9a7ae47056606e7a91fc10c512e504e60da3797727c346", "revision_guid": "9772CCE1-6A29-4B1E-A4DE-75843A878738", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/9772CCE1-6A29-4B1E-A4DE-75843A878738/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2024-12-16T09:32:04+00:00", "raw_file": "raw/codex_api_v1/5ced1a9f1ef6cec4e5ea414f5920558abe1f2afe671db804d768d0c0886f0b02_1790824127343029500_0.json", "raw_sha256": "9b7f4987291adc582d9a7ae47056606e7a91fc10c512e504e60da3797727c346", "revision_guid": "0ADDDDE2-225F-4C30-A06B-ECCE57028384", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/0ADDDDE2-225F-4C30-A06B-ECCE57028384/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2024-12-20T16:43:32+00:00", "raw_file": "raw/codex_api_v1/5ced1a9f1ef6cec4e5ea414f5920558abe1f2afe671db804d768d0c0886f0b02_1790824127343029500_0.json", "raw_sha256": "9b7f4987291adc582d9a7ae47056606e7a91fc10c512e504e60da3797727c346", "revision_guid": "C9F64F8F-3FBB-45F8-9575-568F31AC993C", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/C9F64F8F-3FBB-45F8-9575-568F31AC993C/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2024-12-24T15:13:24+00:00", "raw_file": "raw/codex_api_v1/6498de963750b51efbda1119ed6af944d93448730fd638915c3f01fbcab0c1ec_1790824125196761600_0.json", "raw_sha256": "6bc4a347798a1508410269e30549f130720c68f4c848e3ea1eb2f60991f67851", "revision_guid": "BE09F7C0-1127-4534-A6D9-63F1E7809819", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/BE09F7C0-1127-4534-A6D9-63F1E7809819/view-source"}], "score": 3, "updated_at": "2024-12-24T15:13:24+00:00"}], "domain": "biology", "external_links": ["https://i.sstatic.net/TaxmZAJj.png", "https://www.ncbi.nlm.nih.gov/books/NBK9903/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:04.377249+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/54ece81cba3a5a552bb15d6d3feedc4324a2ba2706d33480080ece9537efd4b1_0.json", "raw_sha256": "f1eb8f7eda9336b81701b663029f9411e040c0bcf262148b7ede9a103ae73e69", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=4&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "elijah whipple", "question_author_url": "https://biology.stackexchange.com/users/95505/elijah-whipple", "question_author_user_type": "registered", "question_created_at": "2024-12-12T19:39:16+00:00", "question_html": "

After ADP and Pi are no longer bound to each other but still bound to an enzyme, do they repel each other? If so, does that contribute to the work that ATP hydrolysis can do?

\n", "question_id": 115780, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "After ADP and Pi are no longer bound to each other but still bound to an enzyme, do they repel each other? If so, does that contribute to the work that ATP hydrolysis can do?", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "elijah whipple", "profile_url": "https://biology.stackexchange.com/users/95505/elijah-whipple", "user_type": "registered"}, "created_at": "2024-12-12T19:39:16+00:00", "raw_file": "raw/codex_api_v1/5ced1a9f1ef6cec4e5ea414f5920558abe1f2afe671db804d768d0c0886f0b02_1790824127343029500_0.json", "raw_sha256": "9b7f4987291adc582d9a7ae47056606e7a91fc10c512e504e60da3797727c346", "revision_guid": "CB91403E-2BC4-4E8B-A581-D7CE1E8E5768", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/CB91403E-2BC4-4E8B-A581-D7CE1E8E5768/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "David", "profile_url": "https://biology.stackexchange.com/users/22057/david", "user_type": "registered"}, "created_at": "2024-12-13T09:24:18+00:00", "raw_file": "raw/codex_api_v1/5ced1a9f1ef6cec4e5ea414f5920558abe1f2afe671db804d768d0c0886f0b02_1790824127343029500_0.json", "raw_sha256": "9b7f4987291adc582d9a7ae47056606e7a91fc10c512e504e60da3797727c346", "revision_guid": "0182791D-B3F3-490A-842E-E3DC3B0C7B1F", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/0182791D-B3F3-490A-842E-E3DC3B0C7B1F/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "elijah whipple", "profile_url": "https://biology.stackexchange.com/users/95505/elijah-whipple", "user_type": "registered"}, "created_at": "2025-01-20T03:11:38+00:00", "raw_file": "raw/codex_api_v1/9208faf10edface85b193538ceee277a2c29dd57b691eaef3dbbd7fcb70c256f_1790824112025498400_0.json", "raw_sha256": "cacf2fdbe629fb39b1a0932a5485abc61f5635b5e51482d0d3b8ab40f1450c36", "revision_guid": "9B9F769A-32BE-4E5E-B8BF-B608137D79A2", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/9B9F769A-32BE-4E5E-B8BF-B608137D79A2/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/115780/does-atp-drive-unfavorable-reactions-with-the-free-energy-change-of-a-reaction", "split": "test", "split_group": "d7257f630e46f436b2bf631bc7be4b95a12e26afe14c7c25c2b52947f531434a", "tags": ["biochemistry", "bioenergetics"], "thread_id": "biology:115780", "title": "Does ATP drive unfavorable reactions with the free energy change of a reaction, or is additional energy obtained by repulsion between ADP and Pi?"}} {"citation_context": "ponse to this injected current are then measured.\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/xFHwbNzi.png] (https://i.sstatic.net/xFHwbNzi.png)\n\n\n\n\nI wanted to ask what the values -50 mV, -53 mV and -46 mV", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://i.sstatic.net/xFHwbNzi.png", "kind": "external_url", "post_id": 119180, "post_url": "https://biology.stackexchange.com/questions/119180/neurophysiology-understanding-a-figure-from-a-whole-cell-patch-clamp-experiment", "product": "citations", "record_id": "Scientific-Citation-Graph:fd91b68f968443e3bd993f4a", "split": "test", "thread": {"accepted_answer_id": 119181, "answers": [{"answer_html": "
\n

I have read that in current-clamp mode, a constant, known current is injected into the cell through the patch micropipette

\n
\n

Yes, that's correct, though also it's common that this constant known current is zero which seems to be the case at least for figure 6D. For current clamp experiments, the Y axis is voltage and X axis is time.

\n

Another common thing to do in current clamp is steps of current, positive and negative, to look at the voltage response. They do this in figure 6A. There, the voltage on the left is basically an axis label" for the resting membrane potential (the voltage when current = 0).

\n

I think that's what they're plotting in 6D, too, with the voltage listed being an axis label. It's not clear how exactly they chose that voltage since there isn't a well-defined "rest" if a cell is spontaneously active. They might have used a median or they might have just eyeballed a value.

\n

The inset tells you scale of the x and y axes: 20 mV and 2 seconds are the lengths of those bars.

\n", "answer_id": 119181, "answer_text": "I have read that in current-clamp mode, a constant, known current is injected into the cell through the patch micropipette\n\n\n\n\n\n\n\nYes, that's correct, though also it's common that this constant known current is zero which seems to be the case at least for figure 6D. For current clamp experiments, the Y axis is voltage and X axis is time.\n\n\n\n\nAnother common thing to do in current clamp is steps of current, positive and negative, to look at the voltage response. They do this in figure 6A. There, the voltage on the left is basically an axis label\" for the resting membrane potential (the voltage when current = 0).\n\n\n\n\nI think that's what they're plotting in 6D, too, with the voltage listed being an axis label. It's not clear how exactly they chose that voltage since there isn't a well-defined \"rest\" if a cell is spontaneously active. They might have used a median or they might have just eyeballed a value.\n\n\n\n\nThe inset tells you scale of the x and y axes: 20 mV and 2 seconds are the lengths of those bars.", "answer_url": "https://biology.stackexchange.com/a/119181", "author": "Bryan Krause", "author_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2025-12-14T15:15:09+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:14.203473+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/bc31fe4e1e84f43ae95f846a38e90acc9e22beb08e25c5d964f94cb8f2d4bfcb_0.json", "raw_sha256": "d7cf716376a9764909548809f10c8760f535f0ca4093eb29d910aae44edf1878", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/119725;119721;119720;119695;119675;119670;119661;119648;119640;119639;119635;119631;119628;119607;119605;119601;119598;119586;119582;119579;119577;119565;119561;119560;119542;119539;119529;119527;119522;119518;119506;119501;119497;119489;119487;119479;119465;119455;119453;119450;119444;119439;119434;119430;119421;119416;119404;119399;119398;119377;119376;119369;119362;119361;119355;119353;119350;119342;119340;119328;119326;119321;119317;119313;119312;119311;119306;119304;119287;119275;119273;119270;119268;119267;119260;119256;119251;119248;119238;119237;119235;119231;119227;119221;119212;119211;119209;119207;119201;119195;119193;119190;119185;119180;118180;118175;118172;118168;118158;118155/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 119180, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Bryan Krause", "profile_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "user_type": "moderator"}, "created_at": "2025-12-14T15:15:09+00:00", "raw_file": "raw/codex_api_v1/758108496d7e56a3cf6614dffa5104a8870c129dcf518abbe860f55a089c6a12_1790824171594894000_0.json", "raw_sha256": "5e5d792a6c484fda48193064d730da32774df13fc12222582feb4605d4472664", "revision_guid": "5BBCD74F-E5FC-4243-A303-E146581E6726", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/5BBCD74F-E5FC-4243-A303-E146581E6726/view-source"}], "score": 1, "updated_at": "2025-12-14T15:15:09+00:00"}], "domain": "biology", "external_links": ["https://i.sstatic.net/xFHwbNzi.png", "https://pmc.ncbi.nlm.nih.gov/articles/PMC6397563/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:02:59.816967+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/55bbc2350ddd64077cfc2cba10ad5323a3aabdbe06356ba63f9b4f2161e7b47f_0.json", "raw_sha256": "816eaaa302266f8cc647e663e24b4d7ecdb9f8cc125751c689d3329286131873", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "ceno980", "question_author_url": "https://biology.stackexchange.com/users/62032/ceno980", "question_author_user_type": "registered", "question_created_at": "2025-12-14T05:12:52+00:00", "question_html": "

I am reading a journal paper investigating the effect of insulin-like growth factor 1 (IGF1) on the firing activity of midbrain dopamine neurons. In this study, they investigated the effect of the conditional knockout of IGF1 on the spontaneous firing of dopamine neurons. To do this, they used whole-cell patch clamp recording (in current-clamp mode) in the presence of synaptic blockers. I have read that in current-clamp mode, a constant, known current is injected into the cell through the patch micropipette. Changes in the neuron's membrane potential that occur in response to this injected current are then measured.

\n

\"enter

\n

I wanted to ask what the values -50 mV, -53 mV and -46 mV in the above figure represent. Any advice is appreciated.

\n", "question_id": 119180, "question_license": "CC BY-SA 4.0", "question_score": 0, "question_text": "I am reading a journal paper (https://pmc.ncbi.nlm.nih.gov/articles/PMC6397563/) investigating the effect of insulin-like growth factor 1 (IGF1) on the firing activity of midbrain dopamine neurons. In this study, they investigated the effect of the conditional knockout of IGF1 on the spontaneous firing of dopamine neurons. To do this, they used whole-cell patch clamp recording (in current-clamp mode) in the presence of synaptic blockers. I have read that in current-clamp mode, a constant, known current is injected into the cell through the patch micropipette. Changes in the neuron's membrane potential that occur in response to this injected current are then measured.\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/xFHwbNzi.png] (https://i.sstatic.net/xFHwbNzi.png)\n\n\n\n\nI wanted to ask what the values -50 mV, -53 mV and -46 mV in the above figure represent. Any advice is appreciated.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "ceno980", "profile_url": "https://biology.stackexchange.com/users/62032/ceno980", "user_type": "registered"}, "created_at": "2025-12-14T05:12:52+00:00", "raw_file": "raw/codex_api_v1/758108496d7e56a3cf6614dffa5104a8870c129dcf518abbe860f55a089c6a12_1790824171594894000_0.json", "raw_sha256": "5e5d792a6c484fda48193064d730da32774df13fc12222582feb4605d4472664", "revision_guid": "9D022864-2106-4DAA-9123-DB81B2C4A283", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/9D022864-2106-4DAA-9123-DB81B2C4A283/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/119180/neurophysiology-understanding-a-figure-from-a-whole-cell-patch-clamp-experiment", "split": "test", "split_group": "dcf101e4f8ae56b1319c8f4d0945d12ee0268870a1b6a01e6edbd55d9e0ed714", "tags": ["neuroscience", "neurophysiology"], "thread_id": "biology:119180", "title": "Neurophysiology: Understanding a figure from a whole-cell patch clamp experiment (current-clamp mode) measuring the firing of dopamine neurons"}} {"citation_context": "I am reading a journal paper (https://pmc.ncbi.nlm.nih.gov/articles/PMC6397563/) investigating the effect of insulin-like growth factor 1 (IGF1) on the firing activity of midbrain", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC6397563/", "kind": "external_url", "post_id": 119180, "post_url": "https://biology.stackexchange.com/questions/119180/neurophysiology-understanding-a-figure-from-a-whole-cell-patch-clamp-experiment", "product": "citations", "record_id": "Scientific-Citation-Graph:55f65b0c1d3a916f72221ae4", "split": "test", "thread": {"accepted_answer_id": 119181, "answers": [{"answer_html": "
\n

I have read that in current-clamp mode, a constant, known current is injected into the cell through the patch micropipette

\n
\n

Yes, that's correct, though also it's common that this constant known current is zero which seems to be the case at least for figure 6D. For current clamp experiments, the Y axis is voltage and X axis is time.

\n

Another common thing to do in current clamp is steps of current, positive and negative, to look at the voltage response. They do this in figure 6A. There, the voltage on the left is basically an axis label" for the resting membrane potential (the voltage when current = 0).

\n

I think that's what they're plotting in 6D, too, with the voltage listed being an axis label. It's not clear how exactly they chose that voltage since there isn't a well-defined "rest" if a cell is spontaneously active. They might have used a median or they might have just eyeballed a value.

\n

The inset tells you scale of the x and y axes: 20 mV and 2 seconds are the lengths of those bars.

\n", "answer_id": 119181, "answer_text": "I have read that in current-clamp mode, a constant, known current is injected into the cell through the patch micropipette\n\n\n\n\n\n\n\nYes, that's correct, though also it's common that this constant known current is zero which seems to be the case at least for figure 6D. For current clamp experiments, the Y axis is voltage and X axis is time.\n\n\n\n\nAnother common thing to do in current clamp is steps of current, positive and negative, to look at the voltage response. They do this in figure 6A. There, the voltage on the left is basically an axis label\" for the resting membrane potential (the voltage when current = 0).\n\n\n\n\nI think that's what they're plotting in 6D, too, with the voltage listed being an axis label. It's not clear how exactly they chose that voltage since there isn't a well-defined \"rest\" if a cell is spontaneously active. They might have used a median or they might have just eyeballed a value.\n\n\n\n\nThe inset tells you scale of the x and y axes: 20 mV and 2 seconds are the lengths of those bars.", "answer_url": "https://biology.stackexchange.com/a/119181", "author": "Bryan Krause", "author_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "author_user_type": "moderator", "content_license": "CC BY-SA 4.0", "created_at": "2025-12-14T15:15:09+00:00", "is_accepted": true, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:14.203473+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/bc31fe4e1e84f43ae95f846a38e90acc9e22beb08e25c5d964f94cb8f2d4bfcb_0.json", "raw_sha256": "d7cf716376a9764909548809f10c8760f535f0ca4093eb29d910aae44edf1878", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/119725;119721;119720;119695;119675;119670;119661;119648;119640;119639;119635;119631;119628;119607;119605;119601;119598;119586;119582;119579;119577;119565;119561;119560;119542;119539;119529;119527;119522;119518;119506;119501;119497;119489;119487;119479;119465;119455;119453;119450;119444;119439;119434;119430;119421;119416;119404;119399;119398;119377;119376;119369;119362;119361;119355;119353;119350;119342;119340;119328;119326;119321;119317;119313;119312;119311;119306;119304;119287;119275;119273;119270;119268;119267;119260;119256;119251;119248;119238;119237;119235;119231;119227;119221;119212;119211;119209;119207;119201;119195;119193;119190;119185;119180;118180;118175;118172;118168;118158;118155/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 119180, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Bryan Krause", "profile_url": "https://biology.stackexchange.com/users/27148/bryan-krause", "user_type": "moderator"}, "created_at": "2025-12-14T15:15:09+00:00", "raw_file": "raw/codex_api_v1/758108496d7e56a3cf6614dffa5104a8870c129dcf518abbe860f55a089c6a12_1790824171594894000_0.json", "raw_sha256": "5e5d792a6c484fda48193064d730da32774df13fc12222582feb4605d4472664", "revision_guid": "5BBCD74F-E5FC-4243-A303-E146581E6726", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/5BBCD74F-E5FC-4243-A303-E146581E6726/view-source"}], "score": 1, "updated_at": "2025-12-14T15:15:09+00:00"}], "domain": "biology", "external_links": ["https://i.sstatic.net/xFHwbNzi.png", "https://pmc.ncbi.nlm.nih.gov/articles/PMC6397563/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:02:59.816967+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/55bbc2350ddd64077cfc2cba10ad5323a3aabdbe06356ba63f9b4f2161e7b47f_0.json", "raw_sha256": "816eaaa302266f8cc647e663e24b4d7ecdb9f8cc125751c689d3329286131873", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "ceno980", "question_author_url": "https://biology.stackexchange.com/users/62032/ceno980", "question_author_user_type": "registered", "question_created_at": "2025-12-14T05:12:52+00:00", "question_html": "

I am reading a journal paper investigating the effect of insulin-like growth factor 1 (IGF1) on the firing activity of midbrain dopamine neurons. In this study, they investigated the effect of the conditional knockout of IGF1 on the spontaneous firing of dopamine neurons. To do this, they used whole-cell patch clamp recording (in current-clamp mode) in the presence of synaptic blockers. I have read that in current-clamp mode, a constant, known current is injected into the cell through the patch micropipette. Changes in the neuron's membrane potential that occur in response to this injected current are then measured.

\n

\"enter

\n

I wanted to ask what the values -50 mV, -53 mV and -46 mV in the above figure represent. Any advice is appreciated.

\n", "question_id": 119180, "question_license": "CC BY-SA 4.0", "question_score": 0, "question_text": "I am reading a journal paper (https://pmc.ncbi.nlm.nih.gov/articles/PMC6397563/) investigating the effect of insulin-like growth factor 1 (IGF1) on the firing activity of midbrain dopamine neurons. In this study, they investigated the effect of the conditional knockout of IGF1 on the spontaneous firing of dopamine neurons. To do this, they used whole-cell patch clamp recording (in current-clamp mode) in the presence of synaptic blockers. I have read that in current-clamp mode, a constant, known current is injected into the cell through the patch micropipette. Changes in the neuron's membrane potential that occur in response to this injected current are then measured.\n\n\n\n\n[image: enter image description here; source: https://i.sstatic.net/xFHwbNzi.png] (https://i.sstatic.net/xFHwbNzi.png)\n\n\n\n\nI wanted to ask what the values -50 mV, -53 mV and -46 mV in the above figure represent. Any advice is appreciated.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "ceno980", "profile_url": "https://biology.stackexchange.com/users/62032/ceno980", "user_type": "registered"}, "created_at": "2025-12-14T05:12:52+00:00", "raw_file": "raw/codex_api_v1/758108496d7e56a3cf6614dffa5104a8870c129dcf518abbe860f55a089c6a12_1790824171594894000_0.json", "raw_sha256": "5e5d792a6c484fda48193064d730da32774df13fc12222582feb4605d4472664", "revision_guid": "9D022864-2106-4DAA-9123-DB81B2C4A283", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/9D022864-2106-4DAA-9123-DB81B2C4A283/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/119180/neurophysiology-understanding-a-figure-from-a-whole-cell-patch-clamp-experiment", "split": "test", "split_group": "dcf101e4f8ae56b1319c8f4d0945d12ee0268870a1b6a01e6edbd55d9e0ed714", "tags": ["neuroscience", "neurophysiology"], "thread_id": "biology:119180", "title": "Neurophysiology: Understanding a figure from a whole-cell patch clamp experiment (current-clamp mode) measuring the firing of dopamine neurons"}} {"citation_context": "h I checked stem cells, I just googled sex change by stem cells and find some articles\nClick first (https://www.cell.com/stem-cell-reports/fulltext/S2213-6711(22)00513-6?_returnURL=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS2213671122005136%3Fshowall%3Dtrue#secsectitle0010)! \"They produce male and female stem cells from same person that have mosaicism\"\n\n\n\n\nAnd also seco", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.cell.com/stem-cell-reports/fulltext/S2213-6711(22)00513-6?_returnURL=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS2213671122005136%3Fshowall%3Dtrue#secsectitle0010", "kind": "external_url", "post_id": 112903, "post_url": "https://biology.stackexchange.com/a/112903", "product": "citations", "record_id": "Scientific-Citation-Graph:b5dbac07006082ec9ce05a41", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I don't have in depth knowledge about how amphibians are regenerate their limbs but in embryonic development all tissue's cells differentiate and come from stem cells according to tissue they inhibit or enhance the transcription of which genes that defines the attributes of tissue. Connective tissue such as fibroblasts differentiated from mesenchymal stem cells. So, in theory if you want to regnerate or in this case replace the "Feminine" muscle and bone alignment with "masculine" we need Embryonic STEM cells to generate it but also we need to broke down former ones. So just we need to utilize apoptosis and use gene therapy to do that. There is risks involved currently with recent gene theraphy techniques and also concentrations and conditions in vitro are affecting the differentiation process when using ste cells. In short every tissues fate decided by STEM cells. Ah I checked stem cells, I just googled sex change by stem cells and find some articles\nClick first! "They produce male and female stem cells from same person that have mosaicism"

\n

And also second!"Tissue Engineering Neovagina for Vaginoplasty in Mayer–Rokitansky–Küster–Hauser Syndrome and Gender Dysphoria Patients: A Systematic Review"

\n

And lastly!"Biotechnologies that empower transgender persons to self-actualize as individuals, partners, spouses, and parents are defining new ways to conceive a child: psychological considerations and ethical issues"

\n", "answer_id": 112903, "answer_text": "I don't have in depth knowledge about how amphibians are regenerate their limbs but in embryonic development all tissue's cells differentiate and come from stem cells according to tissue they inhibit or enhance the transcription of which genes that defines the attributes of tissue. Connective tissue such as fibroblasts differentiated from mesenchymal stem cells. So, in theory if you want to regnerate or in this case replace the \"Feminine\" muscle and bone alignment with \"masculine\" we need Embryonic STEM cells to generate it but also we need to broke down former ones. So just we need to utilize apoptosis and use gene therapy to do that. There is risks involved currently with recent gene theraphy techniques and also concentrations and conditions in vitro are affecting the differentiation process when using ste cells. In short every tissues fate decided by STEM cells. Ah I checked stem cells, I just googled sex change by stem cells and find some articles\nClick first (https://www.cell.com/stem-cell-reports/fulltext/S2213-6711(22)00513-6?_returnURL=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS2213671122005136%3Fshowall%3Dtrue#secsectitle0010)! \"They produce male and female stem cells from same person that have mosaicism\"\n\n\n\n\nAnd also second (https://www.liebertpub.com/doi/10.1089/ten.teb.2022.0067)!\"Tissue Engineering Neovagina for Vaginoplasty in Mayer–Rokitansky–Küster–Hauser Syndrome and Gender Dysphoria Patients: A Systematic Review\"\n\n\n\n\nAnd lastly (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5772725/)!\"Biotechnologies that empower transgender persons to self-actualize as individuals, partners, spouses, and parents are defining new ways to conceive a child: psychological considerations and ethical issues\"", "answer_url": "https://biology.stackexchange.com/a/112903", "author": "Nehir Altun", "author_url": "https://biology.stackexchange.com/users/76747/nehir-altun", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2023-08-30T00:10:08+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:38.885561+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/a145de97eabc007745b45919875489a41261075cbdf33d916d9640ba4ad0bd35_0.json", "raw_sha256": "e7d8d4315eef8e039a452d2811869cbe305575c6ff8a6bef8f80d6dfb58c5bfd", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/112982;112980;112979;112977;112972;112967;112962;112956;112952;112948;112941;112938;112937;112936;112927;112925;112923;112919;112909;112905;112904;112898;112895;112893;112884;112881;112880;112879;112873;112872;112870;112869;112867;112850;112849;112848;112841;112835;112831;112824;112818;112811;112808;112807;112790;112789;112785;112777;112773;112770;112762;112759;112757;112756;112746;112739;112738;112737;112731;112705;112703;112700;112699;112698;112693;112691;112687;112685;112677;112671;112667;112663;112659;112653;112647;112646;112645;112636;112625;112621;112615;112614;112613;112610;112598;112593;112592;112586;112580;112575;112574;112564;112558;112552;112550;112549;112544;112539;112535;112531/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 112893, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Nehir Altun", "profile_url": "https://biology.stackexchange.com/users/76747/nehir-altun", "user_type": "registered"}, "created_at": "2023-08-30T00:10:08+00:00", "raw_file": "raw/codex_api_v1/9b8fea4e5df4051aa25c1aa90b42eca7481ee703f92ba25aeabed3d0b53e7a04_1790824026598483100_0.json", "raw_sha256": "f252fc1b154815b8794116efb3b685202eda8dddb2cd870ae32ee5e82716c300", "revision_guid": "2DBBABFC-9A78-4CFC-9C57-D7726A3FD158", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/2DBBABFC-9A78-4CFC-9C57-D7726A3FD158/view-source"}], "score": 0, "updated_at": "2023-08-30T00:10:08+00:00"}], "domain": "biology", "external_links": ["https://www.cell.com/stem-cell-reports/fulltext/S2213-6711(22)00513-6?_returnURL=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS2213671122005136%3Fshowall%3Dtrue#secsectitle0010", "https://www.liebertpub.com/doi/10.1089/ten.teb.2022.0067", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5772725/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:12.794960+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/01e5186067e30dc1b8d7a145670ab7edd6b017797b271a481af8b7b7f55f13c2_0.json", "raw_sha256": "6c3960de7e1d3d7920bb88d02e2184614c219b391f39d9bddc2a582fdc9a71e7", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=10&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "user105463", "question_author_url": "https://biology.stackexchange.com/users/76635/user105463", "question_author_user_type": "registered", "question_created_at": "2023-08-29T03:21:50+00:00", "question_html": "

I have a question regarding how positional memory in fibroblasts work, specifically, where the memory comes from/how its made.

\n

For example, the Salamander & other amphibians are able to regenerate almost perfect copies of decapitated limbs, but lets say we have a female Salamander who is effectively given hormone therapy to “masculinise” them, if a limb was severed, would it grow back according to the hormone profile? So essentially a bit smaller since males are typically smaller?

\n

I’m very interested in the possibility of sex change through genetics, especially after bones have fused, effectively a reversal. It seems as though this may be a way forward though I am unsure.

\n

Thank you for reading!

\n", "question_id": 112893, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "I have a question regarding how positional memory in fibroblasts work, specifically, where the memory comes from/how its made.\n\n\n\n\nFor example, the Salamander & other amphibians are able to regenerate almost perfect copies of decapitated limbs, but lets say we have a female Salamander who is effectively given hormone therapy to “masculinise” them, if a limb was severed, would it grow back according to the hormone profile? So essentially a bit smaller since males are typically smaller?\n\n\n\n\nI’m very interested in the possibility of sex change through genetics, especially after bones have fused, effectively a reversal. It seems as though this may be a way forward though I am unsure.\n\n\n\n\nThank you for reading!", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "user105463", "profile_url": "https://biology.stackexchange.com/users/76635/user105463", "user_type": "registered"}, "created_at": "2023-08-29T03:21:50+00:00", "raw_file": "raw/codex_api_v1/9b8fea4e5df4051aa25c1aa90b42eca7481ee703f92ba25aeabed3d0b53e7a04_1790824026598483100_0.json", "raw_sha256": "f252fc1b154815b8794116efb3b685202eda8dddb2cd870ae32ee5e82716c300", "revision_guid": "CECAFD10-43F7-49EE-B35A-9FB16B8023F4", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/CECAFD10-43F7-49EE-B35A-9FB16B8023F4/view-source"}, {"content_license": null, "contributor": {"display_name": "Community", "profile_url": "https://biology.stackexchange.com/users/-1/community", "user_type": "moderator"}, "created_at": "2023-09-29T02:04:25+00:00", 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(https://www.liebertpub.com/doi/10.1089/ten.teb.2022.0067)!\"Tissue Engineering Neovagina for Vaginoplasty in Mayer–Rokitansky–Küster–Hauser Syndrome and Gend", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": "10.1089/ten.teb.2022.0067", "external_url": "https://www.liebertpub.com/doi/10.1089/ten.teb.2022.0067", "kind": "doi_url", "post_id": 112903, "post_url": "https://biology.stackexchange.com/a/112903", "product": "citations", "record_id": "Scientific-Citation-Graph:d1293681416dd4a3c1092ab8", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I don't have in depth knowledge about how amphibians are regenerate their limbs but in embryonic development all tissue's cells differentiate and come from stem cells according to tissue they inhibit or enhance the transcription of which genes that defines the attributes of tissue. Connective tissue such as fibroblasts differentiated from mesenchymal stem cells. So, in theory if you want to regnerate or in this case replace the "Feminine" muscle and bone alignment with "masculine" we need Embryonic STEM cells to generate it but also we need to broke down former ones. So just we need to utilize apoptosis and use gene therapy to do that. There is risks involved currently with recent gene theraphy techniques and also concentrations and conditions in vitro are affecting the differentiation process when using ste cells. In short every tissues fate decided by STEM cells. Ah I checked stem cells, I just googled sex change by stem cells and find some articles\nClick first! "They produce male and female stem cells from same person that have mosaicism"

\n

And also second!"Tissue Engineering Neovagina for Vaginoplasty in Mayer–Rokitansky–Küster–Hauser Syndrome and Gender Dysphoria Patients: A Systematic Review"

\n

And lastly!"Biotechnologies that empower transgender persons to self-actualize as individuals, partners, spouses, and parents are defining new ways to conceive a child: psychological considerations and ethical issues"

\n", "answer_id": 112903, "answer_text": "I don't have in depth knowledge about how amphibians are regenerate their limbs but in embryonic development all tissue's cells differentiate and come from stem cells according to tissue they inhibit or enhance the transcription of which genes that defines the attributes of tissue. Connective tissue such as fibroblasts differentiated from mesenchymal stem cells. So, in theory if you want to regnerate or in this case replace the \"Feminine\" muscle and bone alignment with \"masculine\" we need Embryonic STEM cells to generate it but also we need to broke down former ones. So just we need to utilize apoptosis and use gene therapy to do that. There is risks involved currently with recent gene theraphy techniques and also concentrations and conditions in vitro are affecting the differentiation process when using ste cells. In short every tissues fate decided by STEM cells. Ah I checked stem cells, I just googled sex change by stem cells and find some articles\nClick first (https://www.cell.com/stem-cell-reports/fulltext/S2213-6711(22)00513-6?_returnURL=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS2213671122005136%3Fshowall%3Dtrue#secsectitle0010)! \"They produce male and female stem cells from same person that have mosaicism\"\n\n\n\n\nAnd also second (https://www.liebertpub.com/doi/10.1089/ten.teb.2022.0067)!\"Tissue Engineering Neovagina for Vaginoplasty in Mayer–Rokitansky–Küster–Hauser Syndrome and Gender Dysphoria Patients: A Systematic Review\"\n\n\n\n\nAnd lastly (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5772725/)!\"Biotechnologies that empower transgender persons to self-actualize as individuals, partners, spouses, and parents are defining new ways to conceive a child: psychological considerations and ethical issues\"", "answer_url": "https://biology.stackexchange.com/a/112903", "author": "Nehir Altun", "author_url": "https://biology.stackexchange.com/users/76747/nehir-altun", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2023-08-30T00:10:08+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:38.885561+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/a145de97eabc007745b45919875489a41261075cbdf33d916d9640ba4ad0bd35_0.json", "raw_sha256": "e7d8d4315eef8e039a452d2811869cbe305575c6ff8a6bef8f80d6dfb58c5bfd", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/112982;112980;112979;112977;112972;112967;112962;112956;112952;112948;112941;112938;112937;112936;112927;112925;112923;112919;112909;112905;112904;112898;112895;112893;112884;112881;112880;112879;112873;112872;112870;112869;112867;112850;112849;112848;112841;112835;112831;112824;112818;112811;112808;112807;112790;112789;112785;112777;112773;112770;112762;112759;112757;112756;112746;112739;112738;112737;112731;112705;112703;112700;112699;112698;112693;112691;112687;112685;112677;112671;112667;112663;112659;112653;112647;112646;112645;112636;112625;112621;112615;112614;112613;112610;112598;112593;112592;112586;112580;112575;112574;112564;112558;112552;112550;112549;112544;112539;112535;112531/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 112893, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Nehir Altun", "profile_url": "https://biology.stackexchange.com/users/76747/nehir-altun", "user_type": "registered"}, "created_at": "2023-08-30T00:10:08+00:00", "raw_file": "raw/codex_api_v1/9b8fea4e5df4051aa25c1aa90b42eca7481ee703f92ba25aeabed3d0b53e7a04_1790824026598483100_0.json", "raw_sha256": "f252fc1b154815b8794116efb3b685202eda8dddb2cd870ae32ee5e82716c300", "revision_guid": "2DBBABFC-9A78-4CFC-9C57-D7726A3FD158", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/2DBBABFC-9A78-4CFC-9C57-D7726A3FD158/view-source"}], "score": 0, "updated_at": "2023-08-30T00:10:08+00:00"}], "domain": "biology", "external_links": ["https://www.cell.com/stem-cell-reports/fulltext/S2213-6711(22)00513-6?_returnURL=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS2213671122005136%3Fshowall%3Dtrue#secsectitle0010", "https://www.liebertpub.com/doi/10.1089/ten.teb.2022.0067", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5772725/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:12.794960+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/01e5186067e30dc1b8d7a145670ab7edd6b017797b271a481af8b7b7f55f13c2_0.json", "raw_sha256": "6c3960de7e1d3d7920bb88d02e2184614c219b391f39d9bddc2a582fdc9a71e7", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=10&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "user105463", "question_author_url": "https://biology.stackexchange.com/users/76635/user105463", "question_author_user_type": "registered", "question_created_at": "2023-08-29T03:21:50+00:00", "question_html": "

I have a question regarding how positional memory in fibroblasts work, specifically, where the memory comes from/how its made.

\n

For example, the Salamander & other amphibians are able to regenerate almost perfect copies of decapitated limbs, but lets say we have a female Salamander who is effectively given hormone therapy to “masculinise” them, if a limb was severed, would it grow back according to the hormone profile? So essentially a bit smaller since males are typically smaller?

\n

I’m very interested in the possibility of sex change through genetics, especially after bones have fused, effectively a reversal. It seems as though this may be a way forward though I am unsure.

\n

Thank you for reading!

\n", "question_id": 112893, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "I have a question regarding how positional memory in fibroblasts work, specifically, where the memory comes from/how its made.\n\n\n\n\nFor example, the Salamander & other amphibians are able to regenerate almost perfect copies of decapitated limbs, but lets say we have a female Salamander who is effectively given hormone therapy to “masculinise” them, if a limb was severed, would it grow back according to the hormone profile? So essentially a bit smaller since males are typically smaller?\n\n\n\n\nI’m very interested in the possibility of sex change through genetics, especially after bones have fused, effectively a reversal. It seems as though this may be a way forward though I am unsure.\n\n\n\n\nThank you for reading!", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "user105463", "profile_url": "https://biology.stackexchange.com/users/76635/user105463", "user_type": "registered"}, "created_at": "2023-08-29T03:21:50+00:00", "raw_file": "raw/codex_api_v1/9b8fea4e5df4051aa25c1aa90b42eca7481ee703f92ba25aeabed3d0b53e7a04_1790824026598483100_0.json", "raw_sha256": "f252fc1b154815b8794116efb3b685202eda8dddb2cd870ae32ee5e82716c300", "revision_guid": "CECAFD10-43F7-49EE-B35A-9FB16B8023F4", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/CECAFD10-43F7-49EE-B35A-9FB16B8023F4/view-source"}, {"content_license": null, "contributor": {"display_name": "Community", "profile_url": "https://biology.stackexchange.com/users/-1/community", "user_type": "moderator"}, "created_at": "2023-09-29T02:04:25+00:00", 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(https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5772725/)!\"Biotechnologies that empower transgender persons to self-actualize as individuals, partners, spou", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5772725/", "kind": "external_url", "post_id": 112903, "post_url": "https://biology.stackexchange.com/a/112903", "product": "citations", "record_id": "Scientific-Citation-Graph:7a43503f7ffb527472698009", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I don't have in depth knowledge about how amphibians are regenerate their limbs but in embryonic development all tissue's cells differentiate and come from stem cells according to tissue they inhibit or enhance the transcription of which genes that defines the attributes of tissue. Connective tissue such as fibroblasts differentiated from mesenchymal stem cells. So, in theory if you want to regnerate or in this case replace the "Feminine" muscle and bone alignment with "masculine" we need Embryonic STEM cells to generate it but also we need to broke down former ones. So just we need to utilize apoptosis and use gene therapy to do that. There is risks involved currently with recent gene theraphy techniques and also concentrations and conditions in vitro are affecting the differentiation process when using ste cells. In short every tissues fate decided by STEM cells. Ah I checked stem cells, I just googled sex change by stem cells and find some articles\nClick first! "They produce male and female stem cells from same person that have mosaicism"

\n

And also second!"Tissue Engineering Neovagina for Vaginoplasty in Mayer–Rokitansky–Küster–Hauser Syndrome and Gender Dysphoria Patients: A Systematic Review"

\n

And lastly!"Biotechnologies that empower transgender persons to self-actualize as individuals, partners, spouses, and parents are defining new ways to conceive a child: psychological considerations and ethical issues"

\n", "answer_id": 112903, "answer_text": "I don't have in depth knowledge about how amphibians are regenerate their limbs but in embryonic development all tissue's cells differentiate and come from stem cells according to tissue they inhibit or enhance the transcription of which genes that defines the attributes of tissue. Connective tissue such as fibroblasts differentiated from mesenchymal stem cells. So, in theory if you want to regnerate or in this case replace the \"Feminine\" muscle and bone alignment with \"masculine\" we need Embryonic STEM cells to generate it but also we need to broke down former ones. So just we need to utilize apoptosis and use gene therapy to do that. There is risks involved currently with recent gene theraphy techniques and also concentrations and conditions in vitro are affecting the differentiation process when using ste cells. In short every tissues fate decided by STEM cells. Ah I checked stem cells, I just googled sex change by stem cells and find some articles\nClick first (https://www.cell.com/stem-cell-reports/fulltext/S2213-6711(22)00513-6?_returnURL=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS2213671122005136%3Fshowall%3Dtrue#secsectitle0010)! \"They produce male and female stem cells from same person that have mosaicism\"\n\n\n\n\nAnd also second (https://www.liebertpub.com/doi/10.1089/ten.teb.2022.0067)!\"Tissue Engineering Neovagina for Vaginoplasty in Mayer–Rokitansky–Küster–Hauser Syndrome and Gender Dysphoria Patients: A Systematic Review\"\n\n\n\n\nAnd lastly (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5772725/)!\"Biotechnologies that empower transgender persons to self-actualize as individuals, partners, spouses, and parents are defining new ways to conceive a child: psychological considerations and ethical issues\"", "answer_url": "https://biology.stackexchange.com/a/112903", "author": "Nehir Altun", "author_url": "https://biology.stackexchange.com/users/76747/nehir-altun", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2023-08-30T00:10:08+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:38.885561+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/a145de97eabc007745b45919875489a41261075cbdf33d916d9640ba4ad0bd35_0.json", "raw_sha256": "e7d8d4315eef8e039a452d2811869cbe305575c6ff8a6bef8f80d6dfb58c5bfd", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/112982;112980;112979;112977;112972;112967;112962;112956;112952;112948;112941;112938;112937;112936;112927;112925;112923;112919;112909;112905;112904;112898;112895;112893;112884;112881;112880;112879;112873;112872;112870;112869;112867;112850;112849;112848;112841;112835;112831;112824;112818;112811;112808;112807;112790;112789;112785;112777;112773;112770;112762;112759;112757;112756;112746;112739;112738;112737;112731;112705;112703;112700;112699;112698;112693;112691;112687;112685;112677;112671;112667;112663;112659;112653;112647;112646;112645;112636;112625;112621;112615;112614;112613;112610;112598;112593;112592;112586;112580;112575;112574;112564;112558;112552;112550;112549;112544;112539;112535;112531/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 112893, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Nehir Altun", "profile_url": "https://biology.stackexchange.com/users/76747/nehir-altun", "user_type": "registered"}, "created_at": "2023-08-30T00:10:08+00:00", "raw_file": "raw/codex_api_v1/9b8fea4e5df4051aa25c1aa90b42eca7481ee703f92ba25aeabed3d0b53e7a04_1790824026598483100_0.json", "raw_sha256": "f252fc1b154815b8794116efb3b685202eda8dddb2cd870ae32ee5e82716c300", "revision_guid": "2DBBABFC-9A78-4CFC-9C57-D7726A3FD158", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/2DBBABFC-9A78-4CFC-9C57-D7726A3FD158/view-source"}], "score": 0, "updated_at": "2023-08-30T00:10:08+00:00"}], "domain": "biology", "external_links": ["https://www.cell.com/stem-cell-reports/fulltext/S2213-6711(22)00513-6?_returnURL=https%3A%2F%2Flinkinghub.elsevier.com%2Fretrieve%2Fpii%2FS2213671122005136%3Fshowall%3Dtrue#secsectitle0010", "https://www.liebertpub.com/doi/10.1089/ten.teb.2022.0067", "https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5772725/"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:12.794960+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/01e5186067e30dc1b8d7a145670ab7edd6b017797b271a481af8b7b7f55f13c2_0.json", "raw_sha256": "6c3960de7e1d3d7920bb88d02e2184614c219b391f39d9bddc2a582fdc9a71e7", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=10&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "user105463", "question_author_url": "https://biology.stackexchange.com/users/76635/user105463", "question_author_user_type": "registered", "question_created_at": "2023-08-29T03:21:50+00:00", "question_html": "

I have a question regarding how positional memory in fibroblasts work, specifically, where the memory comes from/how its made.

\n

For example, the Salamander & other amphibians are able to regenerate almost perfect copies of decapitated limbs, but lets say we have a female Salamander who is effectively given hormone therapy to “masculinise” them, if a limb was severed, would it grow back according to the hormone profile? So essentially a bit smaller since males are typically smaller?

\n

I’m very interested in the possibility of sex change through genetics, especially after bones have fused, effectively a reversal. It seems as though this may be a way forward though I am unsure.

\n

Thank you for reading!

\n", "question_id": 112893, "question_license": "CC BY-SA 4.0", "question_score": 2, "question_text": "I have a question regarding how positional memory in fibroblasts work, specifically, where the memory comes from/how its made.\n\n\n\n\nFor example, the Salamander & other amphibians are able to regenerate almost perfect copies of decapitated limbs, but lets say we have a female Salamander who is effectively given hormone therapy to “masculinise” them, if a limb was severed, would it grow back according to the hormone profile? So essentially a bit smaller since males are typically smaller?\n\n\n\n\nI’m very interested in the possibility of sex change through genetics, especially after bones have fused, effectively a reversal. It seems as though this may be a way forward though I am unsure.\n\n\n\n\nThank you for reading!", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "user105463", "profile_url": "https://biology.stackexchange.com/users/76635/user105463", "user_type": "registered"}, "created_at": "2023-08-29T03:21:50+00:00", "raw_file": "raw/codex_api_v1/9b8fea4e5df4051aa25c1aa90b42eca7481ee703f92ba25aeabed3d0b53e7a04_1790824026598483100_0.json", "raw_sha256": "f252fc1b154815b8794116efb3b685202eda8dddb2cd870ae32ee5e82716c300", "revision_guid": "CECAFD10-43F7-49EE-B35A-9FB16B8023F4", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/CECAFD10-43F7-49EE-B35A-9FB16B8023F4/view-source"}, {"content_license": null, "contributor": {"display_name": "Community", "profile_url": "https://biology.stackexchange.com/users/-1/community", "user_type": "moderator"}, "created_at": "2023-09-29T02:04:25+00:00", 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The bloom is white with purple tips.\n[image: Unidentified plant; source: https://i.sstatic.net/TpM20EvJ.png] (https://i.sstatic.net/TpM20EvJ.png)", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://i.sstatic.net/TpM20EvJ.png", "kind": "external_url", "post_id": 119489, "post_url": "https://biology.stackexchange.com/questions/119489/where-is-this-plant-from-and-its-name", "product": "citations", "record_id": "Scientific-Citation-Graph:e151d838e7b835e53cabd3d9", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

Answer just to boost this website as its such a cool site

\n

https://www.inaturalist.org/observations?place_id=21&subview=map&taxon_id=141327&view=species

\n

Put in location and scroll through every species of plant, animal or what else...

\n

The plant is Bromelia pinguin native to Central America, Mexico, the West Indies and northern South America.

\n", "answer_id": 119491, "answer_text": "Answer just to boost this website as its such a cool site\n\n\n\n\nhttps://www.inaturalist.org/observations?place_id=21&subview=map&taxon_id=141327&view=species (https://www.inaturalist.org/observations?place_id=21&subview=map&taxon_id=141327&view=species)\n\n\n\n\nPut in location and scroll through every species of plant, animal or what else...\n\n\n\n\nThe plant is Bromelia pinguin (https://en.wikipedia.org/wiki/Bromelia_pinguin) native to Central America, Mexico, the West Indies and northern South America.", "answer_url": "https://biology.stackexchange.com/a/119491", "author": "Lukas4235", "author_url": "https://biology.stackexchange.com/users/83315/lukas4235", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-05-23T20:10:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:14.203473+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/bc31fe4e1e84f43ae95f846a38e90acc9e22beb08e25c5d964f94cb8f2d4bfcb_0.json", "raw_sha256": "d7cf716376a9764909548809f10c8760f535f0ca4093eb29d910aae44edf1878", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/119725;119721;119720;119695;119675;119670;119661;119648;119640;119639;119635;119631;119628;119607;119605;119601;119598;119586;119582;119579;119577;119565;119561;119560;119542;119539;119529;119527;119522;119518;119506;119501;119497;119489;119487;119479;119465;119455;119453;119450;119444;119439;119434;119430;119421;119416;119404;119399;119398;119377;119376;119369;119362;119361;119355;119353;119350;119342;119340;119328;119326;119321;119317;119313;119312;119311;119306;119304;119287;119275;119273;119270;119268;119267;119260;119256;119251;119248;119238;119237;119235;119231;119227;119221;119212;119211;119209;119207;119201;119195;119193;119190;119185;119180;118180;118175;118172;118168;118158;118155/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 119489, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Lukas4235", "profile_url": "https://biology.stackexchange.com/users/83315/lukas4235", "user_type": "registered"}, "created_at": "2026-05-23T20:10:14+00:00", "raw_file": "raw/codex_api_v1/579a4d2562ba9524cfbccb0521aa128aef0c357c985479e84dfae99b419043f3_1790824187996707100_0.json", "raw_sha256": "498851e9e2788dd78c09b5bc32fc2c43c0983eaa43d2c56d9c618718c8202873", "revision_guid": "9F63CDA7-5332-4BD8-97C4-F15FCD14F677", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/9F63CDA7-5332-4BD8-97C4-F15FCD14F677/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "bob1", "profile_url": "https://biology.stackexchange.com/users/65284/bob1", "user_type": "registered"}, "created_at": "2026-05-24T20:58:39+00:00", "raw_file": "raw/codex_api_v1/579a4d2562ba9524cfbccb0521aa128aef0c357c985479e84dfae99b419043f3_1790824187996707100_0.json", "raw_sha256": "498851e9e2788dd78c09b5bc32fc2c43c0983eaa43d2c56d9c618718c8202873", "revision_guid": "3058C636-EEDA-4348-81E4-62FE10BF0620", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/3058C636-EEDA-4348-81E4-62FE10BF0620/view-source"}], "score": 5, "updated_at": "2026-05-24T20:58:39+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/Bromelia_pinguin", "https://i.sstatic.net/TpM20EvJ.png", "https://www.inaturalist.org/observations?place_id=21&subview=map&taxon_id=141327&view=species"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:02:59.816967+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/55bbc2350ddd64077cfc2cba10ad5323a3aabdbe06356ba63f9b4f2161e7b47f_0.json", "raw_sha256": "816eaaa302266f8cc647e663e24b4d7ecdb9f8cc125751c689d3329286131873", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "VICKI RELYEA", "question_author_url": "https://biology.stackexchange.com/users/128256/vicki-relyea", "question_author_user_type": "registered", "question_created_at": "2026-05-23T12:58:24+00:00", "question_html": "

I live in Central Florida. This plant started growing wild in my backyard. It is very invasive. The leaves have thorns on the edge. Possibly a succulent? Can you help me identify the species of this plant?\nWhen it blooms, the top leaves turn deep red orange. The bloom is white with purple tips.\n\"Unidentified

\n", "question_id": 119489, "question_license": "CC BY-SA 4.0", "question_score": 3, "question_text": "I live in Central Florida. This plant started growing wild in my backyard. It is very invasive. The leaves have thorns on the edge. Possibly a succulent? Can you help me identify the species of this plant?\nWhen it blooms, the top leaves turn deep red orange. The bloom is white with purple tips.\n[image: Unidentified plant; source: https://i.sstatic.net/TpM20EvJ.png] (https://i.sstatic.net/TpM20EvJ.png)", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "VICKI RELYEA", "profile_url": "https://biology.stackexchange.com/users/128256/vicki-relyea", "user_type": "registered"}, "created_at": "2026-05-23T12:58:24+00:00", "raw_file": "raw/codex_api_v1/579a4d2562ba9524cfbccb0521aa128aef0c357c985479e84dfae99b419043f3_1790824187996707100_0.json", "raw_sha256": "498851e9e2788dd78c09b5bc32fc2c43c0983eaa43d2c56d9c618718c8202873", "revision_guid": "E99241A3-BDA1-453E-A1BE-514505182305", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E99241A3-BDA1-453E-A1BE-514505182305/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "VICKI RELYEA", "profile_url": "https://biology.stackexchange.com/users/128256/vicki-relyea", "user_type": "registered"}, "created_at": "2026-05-23T13:05:36+00:00", "raw_file": "raw/codex_api_v1/579a4d2562ba9524cfbccb0521aa128aef0c357c985479e84dfae99b419043f3_1790824187996707100_0.json", "raw_sha256": "498851e9e2788dd78c09b5bc32fc2c43c0983eaa43d2c56d9c618718c8202873", "revision_guid": "917F2807-FDB4-4F33-BEA0-DA843AB52AC4", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/917F2807-FDB4-4F33-BEA0-DA843AB52AC4/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "VICKI RELYEA", "profile_url": "https://biology.stackexchange.com/users/128256/vicki-relyea", "user_type": "registered"}, "created_at": "2026-05-23T13:06:27+00:00", "raw_file": "raw/codex_api_v1/579a4d2562ba9524cfbccb0521aa128aef0c357c985479e84dfae99b419043f3_1790824187996707100_0.json", "raw_sha256": "498851e9e2788dd78c09b5bc32fc2c43c0983eaa43d2c56d9c618718c8202873", "revision_guid": "644CA2FD-3146-40A8-AC45-F7C73D3C99A5", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/644CA2FD-3146-40A8-AC45-F7C73D3C99A5/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-05-25T07:04:47+00:00", "raw_file": "raw/codex_api_v1/579a4d2562ba9524cfbccb0521aa128aef0c357c985479e84dfae99b419043f3_1790824187996707100_0.json", "raw_sha256": "498851e9e2788dd78c09b5bc32fc2c43c0983eaa43d2c56d9c618718c8202873", "revision_guid": "7B18FFC0-3095-463B-A88C-E3D8069CFB1D", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/7B18FFC0-3095-463B-A88C-E3D8069CFB1D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2026-06-19T00:39:27+00:00", "raw_file": "raw/codex_api_v1/30edb57b578064458be0726e8f438b6e87f6be83f37b063b5f6097379fca514d_1790824174828155600_0.json", "raw_sha256": "88f86163c238074f8177d1ef634208b9e49a1f4e659b8032dd7e5061bf358244", "revision_guid": "067E80D8-5551-4D92-8595-8E71110B8BCB", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/067E80D8-5551-4D92-8595-8E71110B8BCB/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/119489/where-is-this-plant-from-and-its-name", "split": "test", "split_group": "1b75aad9c21617ceeb1f9497416666f00d3b32d62991efa95288fa5ef978d32c", "tags": ["botany"], "thread_id": "biology:119489", "title": "Where is this plant from and its name?"}} {"citation_context": "nd scroll through every species of plant, animal or what else...\n\n\n\n\nThe plant is Bromelia pinguin (https://en.wikipedia.org/wiki/Bromelia_pinguin) native to Central America, Mexico, the West Indies and northern South America.", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://en.wikipedia.org/wiki/Bromelia_pinguin", "kind": "external_url", "post_id": 119491, "post_url": "https://biology.stackexchange.com/a/119491", "product": "citations", "record_id": "Scientific-Citation-Graph:f79f42e5157c8d243a2045a3", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

Answer just to boost this website as its such a cool site

\n

https://www.inaturalist.org/observations?place_id=21&subview=map&taxon_id=141327&view=species

\n

Put in location and scroll through every species of plant, animal or what else...

\n

The plant is Bromelia pinguin native to Central America, Mexico, the West Indies and northern South America.

\n", "answer_id": 119491, "answer_text": "Answer just to boost this website as its such a cool site\n\n\n\n\nhttps://www.inaturalist.org/observations?place_id=21&subview=map&taxon_id=141327&view=species (https://www.inaturalist.org/observations?place_id=21&subview=map&taxon_id=141327&view=species)\n\n\n\n\nPut in location and scroll through every species of plant, animal or what else...\n\n\n\n\nThe plant is Bromelia pinguin (https://en.wikipedia.org/wiki/Bromelia_pinguin) native to Central America, Mexico, the West Indies and northern South America.", "answer_url": "https://biology.stackexchange.com/a/119491", "author": "Lukas4235", "author_url": "https://biology.stackexchange.com/users/83315/lukas4235", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-05-23T20:10:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:14.203473+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/bc31fe4e1e84f43ae95f846a38e90acc9e22beb08e25c5d964f94cb8f2d4bfcb_0.json", "raw_sha256": "d7cf716376a9764909548809f10c8760f535f0ca4093eb29d910aae44edf1878", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/119725;119721;119720;119695;119675;119670;119661;119648;119640;119639;119635;119631;119628;119607;119605;119601;119598;119586;119582;119579;119577;119565;119561;119560;119542;119539;119529;119527;119522;119518;119506;119501;119497;119489;119487;119479;119465;119455;119453;119450;119444;119439;119434;119430;119421;119416;119404;119399;119398;119377;119376;119369;119362;119361;119355;119353;119350;119342;119340;119328;119326;119321;119317;119313;119312;119311;119306;119304;119287;119275;119273;119270;119268;119267;119260;119256;119251;119248;119238;119237;119235;119231;119227;119221;119212;119211;119209;119207;119201;119195;119193;119190;119185;119180;118180;118175;118172;118168;118158;118155/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 119489, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Lukas4235", "profile_url": "https://biology.stackexchange.com/users/83315/lukas4235", "user_type": "registered"}, "created_at": "2026-05-23T20:10:14+00:00", "raw_file": "raw/codex_api_v1/579a4d2562ba9524cfbccb0521aa128aef0c357c985479e84dfae99b419043f3_1790824187996707100_0.json", "raw_sha256": "498851e9e2788dd78c09b5bc32fc2c43c0983eaa43d2c56d9c618718c8202873", "revision_guid": "9F63CDA7-5332-4BD8-97C4-F15FCD14F677", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/9F63CDA7-5332-4BD8-97C4-F15FCD14F677/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "bob1", "profile_url": "https://biology.stackexchange.com/users/65284/bob1", "user_type": "registered"}, "created_at": "2026-05-24T20:58:39+00:00", "raw_file": "raw/codex_api_v1/579a4d2562ba9524cfbccb0521aa128aef0c357c985479e84dfae99b419043f3_1790824187996707100_0.json", "raw_sha256": "498851e9e2788dd78c09b5bc32fc2c43c0983eaa43d2c56d9c618718c8202873", "revision_guid": "3058C636-EEDA-4348-81E4-62FE10BF0620", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/3058C636-EEDA-4348-81E4-62FE10BF0620/view-source"}], "score": 5, "updated_at": "2026-05-24T20:58:39+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/Bromelia_pinguin", "https://i.sstatic.net/TpM20EvJ.png", "https://www.inaturalist.org/observations?place_id=21&subview=map&taxon_id=141327&view=species"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:02:59.816967+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/55bbc2350ddd64077cfc2cba10ad5323a3aabdbe06356ba63f9b4f2161e7b47f_0.json", "raw_sha256": "816eaaa302266f8cc647e663e24b4d7ecdb9f8cc125751c689d3329286131873", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "VICKI RELYEA", "question_author_url": "https://biology.stackexchange.com/users/128256/vicki-relyea", "question_author_user_type": "registered", "question_created_at": "2026-05-23T12:58:24+00:00", "question_html": "

I live in Central Florida. This plant started growing wild in my backyard. It is very invasive. The leaves have thorns on the edge. Possibly a succulent? Can you help me identify the species of this plant?\nWhen it blooms, the top leaves turn deep red orange. The bloom is white with purple tips.\n\"Unidentified

\n", "question_id": 119489, "question_license": "CC BY-SA 4.0", "question_score": 3, "question_text": "I live in Central Florida. This plant started growing wild in my backyard. It is very invasive. The leaves have thorns on the edge. Possibly a succulent? Can you help me identify the species of this plant?\nWhen it blooms, the top leaves turn deep red orange. The bloom is white with purple tips.\n[image: Unidentified plant; source: https://i.sstatic.net/TpM20EvJ.png] (https://i.sstatic.net/TpM20EvJ.png)", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "VICKI RELYEA", "profile_url": "https://biology.stackexchange.com/users/128256/vicki-relyea", "user_type": "registered"}, "created_at": "2026-05-23T12:58:24+00:00", "raw_file": "raw/codex_api_v1/579a4d2562ba9524cfbccb0521aa128aef0c357c985479e84dfae99b419043f3_1790824187996707100_0.json", "raw_sha256": "498851e9e2788dd78c09b5bc32fc2c43c0983eaa43d2c56d9c618718c8202873", "revision_guid": "E99241A3-BDA1-453E-A1BE-514505182305", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E99241A3-BDA1-453E-A1BE-514505182305/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "VICKI RELYEA", "profile_url": "https://biology.stackexchange.com/users/128256/vicki-relyea", "user_type": "registered"}, "created_at": "2026-05-23T13:05:36+00:00", "raw_file": "raw/codex_api_v1/579a4d2562ba9524cfbccb0521aa128aef0c357c985479e84dfae99b419043f3_1790824187996707100_0.json", "raw_sha256": "498851e9e2788dd78c09b5bc32fc2c43c0983eaa43d2c56d9c618718c8202873", "revision_guid": "917F2807-FDB4-4F33-BEA0-DA843AB52AC4", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/917F2807-FDB4-4F33-BEA0-DA843AB52AC4/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "VICKI RELYEA", "profile_url": "https://biology.stackexchange.com/users/128256/vicki-relyea", "user_type": "registered"}, "created_at": "2026-05-23T13:06:27+00:00", "raw_file": "raw/codex_api_v1/579a4d2562ba9524cfbccb0521aa128aef0c357c985479e84dfae99b419043f3_1790824187996707100_0.json", "raw_sha256": "498851e9e2788dd78c09b5bc32fc2c43c0983eaa43d2c56d9c618718c8202873", "revision_guid": "644CA2FD-3146-40A8-AC45-F7C73D3C99A5", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/644CA2FD-3146-40A8-AC45-F7C73D3C99A5/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-05-25T07:04:47+00:00", "raw_file": "raw/codex_api_v1/579a4d2562ba9524cfbccb0521aa128aef0c357c985479e84dfae99b419043f3_1790824187996707100_0.json", "raw_sha256": "498851e9e2788dd78c09b5bc32fc2c43c0983eaa43d2c56d9c618718c8202873", "revision_guid": "7B18FFC0-3095-463B-A88C-E3D8069CFB1D", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/7B18FFC0-3095-463B-A88C-E3D8069CFB1D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2026-06-19T00:39:27+00:00", "raw_file": "raw/codex_api_v1/30edb57b578064458be0726e8f438b6e87f6be83f37b063b5f6097379fca514d_1790824174828155600_0.json", "raw_sha256": "88f86163c238074f8177d1ef634208b9e49a1f4e659b8032dd7e5061bf358244", "revision_guid": "067E80D8-5551-4D92-8595-8E71110B8BCB", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/067E80D8-5551-4D92-8595-8E71110B8BCB/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/119489/where-is-this-plant-from-and-its-name", "split": "test", "split_group": "1b75aad9c21617ceeb1f9497416666f00d3b32d62991efa95288fa5ef978d32c", "tags": ["botany"], "thread_id": "biology:119489", "title": "Where is this plant from and its name?"}} {"citation_context": "Answer just to boost this website as its such a cool site\n\n\n\n\nhttps://www.inaturalist.org/observations?place_id=21&subview=map&taxon_id=141327&view=species (https://www.inaturalist.org/observations?place_id=21&subview=map&taxon_id=141327&view=species)\n\n\n\n", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": null, "external_url": "https://www.inaturalist.org/observations?place_id=21&subview=map&taxon_id=141327&view=species", "kind": "external_url", "post_id": 119491, "post_url": "https://biology.stackexchange.com/a/119491", "product": "citations", "record_id": "Scientific-Citation-Graph:7053ec09f23f311abfa41af8", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

Answer just to boost this website as its such a cool site

\n

https://www.inaturalist.org/observations?place_id=21&subview=map&taxon_id=141327&view=species

\n

Put in location and scroll through every species of plant, animal or what else...

\n

The plant is Bromelia pinguin native to Central America, Mexico, the West Indies and northern South America.

\n", "answer_id": 119491, "answer_text": "Answer just to boost this website as its such a cool site\n\n\n\n\nhttps://www.inaturalist.org/observations?place_id=21&subview=map&taxon_id=141327&view=species (https://www.inaturalist.org/observations?place_id=21&subview=map&taxon_id=141327&view=species)\n\n\n\n\nPut in location and scroll through every species of plant, animal or what else...\n\n\n\n\nThe plant is Bromelia pinguin (https://en.wikipedia.org/wiki/Bromelia_pinguin) native to Central America, Mexico, the West Indies and northern South America.", "answer_url": "https://biology.stackexchange.com/a/119491", "author": "Lukas4235", "author_url": "https://biology.stackexchange.com/users/83315/lukas4235", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2026-05-23T20:10:14+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:14.203473+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/bc31fe4e1e84f43ae95f846a38e90acc9e22beb08e25c5d964f94cb8f2d4bfcb_0.json", "raw_sha256": "d7cf716376a9764909548809f10c8760f535f0ca4093eb29d910aae44edf1878", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/119725;119721;119720;119695;119675;119670;119661;119648;119640;119639;119635;119631;119628;119607;119605;119601;119598;119586;119582;119579;119577;119565;119561;119560;119542;119539;119529;119527;119522;119518;119506;119501;119497;119489;119487;119479;119465;119455;119453;119450;119444;119439;119434;119430;119421;119416;119404;119399;119398;119377;119376;119369;119362;119361;119355;119353;119350;119342;119340;119328;119326;119321;119317;119313;119312;119311;119306;119304;119287;119275;119273;119270;119268;119267;119260;119256;119251;119248;119238;119237;119235;119231;119227;119221;119212;119211;119209;119207;119201;119195;119193;119190;119185;119180;118180;118175;118172;118168;118158;118155/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 119489, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Lukas4235", "profile_url": "https://biology.stackexchange.com/users/83315/lukas4235", "user_type": "registered"}, "created_at": "2026-05-23T20:10:14+00:00", "raw_file": "raw/codex_api_v1/579a4d2562ba9524cfbccb0521aa128aef0c357c985479e84dfae99b419043f3_1790824187996707100_0.json", "raw_sha256": "498851e9e2788dd78c09b5bc32fc2c43c0983eaa43d2c56d9c618718c8202873", "revision_guid": "9F63CDA7-5332-4BD8-97C4-F15FCD14F677", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/9F63CDA7-5332-4BD8-97C4-F15FCD14F677/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "bob1", "profile_url": "https://biology.stackexchange.com/users/65284/bob1", "user_type": "registered"}, "created_at": "2026-05-24T20:58:39+00:00", "raw_file": "raw/codex_api_v1/579a4d2562ba9524cfbccb0521aa128aef0c357c985479e84dfae99b419043f3_1790824187996707100_0.json", "raw_sha256": "498851e9e2788dd78c09b5bc32fc2c43c0983eaa43d2c56d9c618718c8202873", "revision_guid": "3058C636-EEDA-4348-81E4-62FE10BF0620", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/3058C636-EEDA-4348-81E4-62FE10BF0620/view-source"}], "score": 5, "updated_at": "2026-05-24T20:58:39+00:00"}], "domain": "biology", "external_links": ["https://en.wikipedia.org/wiki/Bromelia_pinguin", "https://i.sstatic.net/TpM20EvJ.png", "https://www.inaturalist.org/observations?place_id=21&subview=map&taxon_id=141327&view=species"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:02:59.816967+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/55bbc2350ddd64077cfc2cba10ad5323a3aabdbe06356ba63f9b4f2161e7b47f_0.json", "raw_sha256": "816eaaa302266f8cc647e663e24b4d7ecdb9f8cc125751c689d3329286131873", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "VICKI RELYEA", "question_author_url": "https://biology.stackexchange.com/users/128256/vicki-relyea", "question_author_user_type": "registered", "question_created_at": "2026-05-23T12:58:24+00:00", "question_html": "

I live in Central Florida. This plant started growing wild in my backyard. It is very invasive. The leaves have thorns on the edge. Possibly a succulent? Can you help me identify the species of this plant?\nWhen it blooms, the top leaves turn deep red orange. The bloom is white with purple tips.\n\"Unidentified

\n", "question_id": 119489, "question_license": "CC BY-SA 4.0", "question_score": 3, "question_text": "I live in Central Florida. This plant started growing wild in my backyard. It is very invasive. The leaves have thorns on the edge. Possibly a succulent? Can you help me identify the species of this plant?\nWhen it blooms, the top leaves turn deep red orange. The bloom is white with purple tips.\n[image: Unidentified plant; source: https://i.sstatic.net/TpM20EvJ.png] (https://i.sstatic.net/TpM20EvJ.png)", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "VICKI RELYEA", "profile_url": "https://biology.stackexchange.com/users/128256/vicki-relyea", "user_type": "registered"}, "created_at": "2026-05-23T12:58:24+00:00", "raw_file": "raw/codex_api_v1/579a4d2562ba9524cfbccb0521aa128aef0c357c985479e84dfae99b419043f3_1790824187996707100_0.json", "raw_sha256": "498851e9e2788dd78c09b5bc32fc2c43c0983eaa43d2c56d9c618718c8202873", "revision_guid": "E99241A3-BDA1-453E-A1BE-514505182305", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/E99241A3-BDA1-453E-A1BE-514505182305/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "VICKI RELYEA", "profile_url": "https://biology.stackexchange.com/users/128256/vicki-relyea", "user_type": "registered"}, "created_at": "2026-05-23T13:05:36+00:00", "raw_file": "raw/codex_api_v1/579a4d2562ba9524cfbccb0521aa128aef0c357c985479e84dfae99b419043f3_1790824187996707100_0.json", "raw_sha256": "498851e9e2788dd78c09b5bc32fc2c43c0983eaa43d2c56d9c618718c8202873", "revision_guid": "917F2807-FDB4-4F33-BEA0-DA843AB52AC4", "revision_number": 2, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/917F2807-FDB4-4F33-BEA0-DA843AB52AC4/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "VICKI RELYEA", "profile_url": "https://biology.stackexchange.com/users/128256/vicki-relyea", "user_type": "registered"}, "created_at": "2026-05-23T13:06:27+00:00", "raw_file": "raw/codex_api_v1/579a4d2562ba9524cfbccb0521aa128aef0c357c985479e84dfae99b419043f3_1790824187996707100_0.json", "raw_sha256": "498851e9e2788dd78c09b5bc32fc2c43c0983eaa43d2c56d9c618718c8202873", "revision_guid": "644CA2FD-3146-40A8-AC45-F7C73D3C99A5", "revision_number": 3, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/644CA2FD-3146-40A8-AC45-F7C73D3C99A5/view-source"}, {"content_license": null, "contributor": {"display_name": "[deleted/unavailable user]", "profile_url": null, "user_type": "does_not_exist"}, "created_at": "2026-05-25T07:04:47+00:00", "raw_file": "raw/codex_api_v1/579a4d2562ba9524cfbccb0521aa128aef0c357c985479e84dfae99b419043f3_1790824187996707100_0.json", "raw_sha256": "498851e9e2788dd78c09b5bc32fc2c43c0983eaa43d2c56d9c618718c8202873", "revision_guid": "7B18FFC0-3095-463B-A88C-E3D8069CFB1D", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/7B18FFC0-3095-463B-A88C-E3D8069CFB1D/view-source"}, {"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Shayan", "profile_url": "https://biology.stackexchange.com/users/114723/shayan", "user_type": "registered"}, "created_at": "2026-06-19T00:39:27+00:00", "raw_file": "raw/codex_api_v1/30edb57b578064458be0726e8f438b6e87f6be83f37b063b5f6097379fca514d_1790824174828155600_0.json", "raw_sha256": "88f86163c238074f8177d1ef634208b9e49a1f4e659b8032dd7e5061bf358244", "revision_guid": "067E80D8-5551-4D92-8595-8E71110B8BCB", "revision_number": 4, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/067E80D8-5551-4D92-8595-8E71110B8BCB/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/119489/where-is-this-plant-from-and-its-name", "split": "test", "split_group": "1b75aad9c21617ceeb1f9497416666f00d3b32d62991efa95288fa5ef978d32c", "tags": ["botany"], "thread_id": "biology:119489", "title": "Where is this plant from and its name?"}} {"citation_context": "y, here's the paper: Economic Transition, Male Competition, and Sex Differences in Mortality Rates (https://journals.sagepub.com/doi/full/10.1177/147470490700500213)\n\n\n\n\nI hope you enjoy reading it, and if you have any follow-up questions I'd be more than happy to", "content_license": "CC BY-SA 4.0", "context_method": "literal text window; null if identifier only in original HTML", "correctness_verified": false, "doi": "10.1177/147470490700500213", "external_url": "https://journals.sagepub.com/doi/full/10.1177/147470490700500213", "kind": "doi_url", "post_id": 113159, "post_url": "https://biology.stackexchange.com/a/113159", "product": "citations", "record_id": "Scientific-Citation-Graph:1b461e293f2be8e747584631", "split": "test", "thread": {"accepted_answer_id": null, "answers": [{"answer_html": "

I like your question, and it got me looking for some answers to similar questions I've been thinking about too.

\n

I don't have the full answer; the exact disparity between specific hormones and the differences between mood regulation, but I do have a pretty good research paper that looked into this.

\n

I'd highly recommend anyone and everyone to read it - it's free to access, and even if you only read the abstract you may hopefully take something from it.

\n

In summary though, to answer your question, there seems to be due to (as you said) riskier decision making, but just in young men, and increased stress levels in middle aged men.

\n

I guess the men who make it through to old age (due to socioeconomic, genetic/epigenetic reasons or just pure luck) managed to not be situated on the upper end of either of these spectrums of risk taking and physical stress response, as is most likely thanks to selection pressures. However, these high mortality-linked traits have not entirely been bred out of our populations around the world as many of these high-mortality-associated men do live long enough to pass on their genome, of which some, (roughly half, on average), will be inherited.

\n

These physical, inheritable traits are a bit like radioactive decay: They will decline in the population over many many generations if nothing else happens, but they will never truly disappear. And the problem is that the way that society works is it does in fact exert an external force on many people, pushing them towards making risky decisions (e.g. gambling, impulse buying expensive items on a pay £0 today finance deals et cetera) and to experience much higher daily levels of stress than people can cope with day-to-day. There may even possibly be epigenetic modifications occurring in individuals that would possibly be passed down to offspring if that is the case. This, I believe, alongside the increased media attention recently on mental health, is why we are seeing much more of it these days than ever before, unfortunately.

\n

Anyway, here's the paper: Economic Transition, Male Competition, and Sex Differences in Mortality Rates

\n

I hope you enjoy reading it, and if you have any follow-up questions I'd be more than happy to try to answer them.

\n", "answer_id": 113159, "answer_text": "I like your question, and it got me looking for some answers to similar questions I've been thinking about too.\n\n\n\n\nI don't have the full answer; the exact disparity between specific hormones and the differences between mood regulation, but I do have a pretty good research paper that looked into this.\n\n\n\n\nI'd highly recommend anyone and everyone to read it - it's free to access, and even if you only read the abstract you may hopefully take something from it.\n\n\n\n\nIn summary though, to answer your question, there seems to be due to (as you said) riskier decision making, but just in young men, and increased stress levels in middle aged men.\n\n\n\n\nI guess the men who make it through to old age (due to socioeconomic, genetic/epigenetic reasons or just pure luck) managed to not be situated on the upper end of either of these spectrums of risk taking and physical stress response, as is most likely thanks to selection pressures. However, these high mortality-linked traits have not entirely been bred out of our populations around the world as many of these high-mortality-associated men do live long enough to pass on their genome, of which some, (roughly half, on average), will be inherited.\n\n\n\n\nThese physical, inheritable traits are a bit like radioactive decay: They will decline in the population over many many generations if nothing else happens, but they will never truly disappear. And the problem is that the way that society works is it does in fact exert an external force on many people, pushing them towards making risky decisions (e.g. gambling, impulse buying expensive items on a pay £0 today finance deals et cetera) and to experience much higher daily levels of stress than people can cope with day-to-day. There may even possibly be epigenetic modifications occurring in individuals that would possibly be passed down to offspring if that is the case. This, I believe, alongside the increased media attention recently on mental health, is why we are seeing much more of it these days than ever before, unfortunately.\n\n\n\n\nAnyway, here's the paper: Economic Transition, Male Competition, and Sex Differences in Mortality Rates (https://journals.sagepub.com/doi/full/10.1177/147470490700500213)\n\n\n\n\nI hope you enjoy reading it, and if you have any follow-up questions I'd be more than happy to try to answer them.", "answer_url": "https://biology.stackexchange.com/a/113159", "author": "Louie", "author_url": "https://biology.stackexchange.com/users/77170/louie", "author_user_type": "registered", "content_license": "CC BY-SA 4.0", "created_at": "2023-10-03T21:07:26+00:00", "is_accepted": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:36.208962+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/ce9de3cf6525f1e283f75a76c7c279c0bd53024cf8e6597abc34f072e18cfbf7_0.json", "raw_sha256": "c65c49a81e92972be3758d3b220c036300d85c38ce4d9079a6203d2eeac0d96d", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/questions/113468;113465;113459;113453;113451;113449;113442;113437;113425;113421;113416;113415;113413;113406;113400;113398;113386;113378;113364;113363;113347;113340;113333;113324;113317;113315;113310;113303;113307;113299;113293;113291;113284;113282;113279;113277;113275;113274;113263;113253;113252;113243;113239;113235;113231;113229;113223;113221;113218;113216;113210;113198;113191;113183;113180;113175;113164;113158;113153;113146;113141;113118;113116;113115;113113;113110;113109;113106;113104;113101;113095;113089;113086;113081;113080;113077;113076;113075;113070;113067;113064;113053;113046;113043;113039;113031;113030;113028;113027;113024;113017;113016;113015;113014;113009;113008;113007;113005;112998;112984/answers?filter=withbody&order=asc&page=1&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_id": 113077, "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "Louie", "profile_url": "https://biology.stackexchange.com/users/77170/louie", "user_type": "registered"}, "created_at": "2023-10-03T21:07:26+00:00", "raw_file": "raw/codex_api_v1/94d9f1e30b5dd1767475c05e1b94ebc9b51251f35d208b9800a4aa1aae1f7188_1790824031839073700_0.json", "raw_sha256": "cce2a5f3b306f6a39571358a0439bc231c3ba14bee317be498ab1ef3965e7c77", "revision_guid": "541D1FBE-708E-4216-B12E-81550390EF88", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/541D1FBE-708E-4216-B12E-81550390EF88/view-source"}, {"content_license": null, "contributor": {"display_name": "Community", "profile_url": "https://biology.stackexchange.com/users/-1/community", "user_type": "moderator"}, "created_at": "2023-10-06T10:02:15+00:00", "raw_file": "raw/codex_api_v1/94d9f1e30b5dd1767475c05e1b94ebc9b51251f35d208b9800a4aa1aae1f7188_1790824031839073700_0.json", "raw_sha256": "cce2a5f3b306f6a39571358a0439bc231c3ba14bee317be498ab1ef3965e7c77", "revision_guid": "79FC8DB9-5700-4E59-89EA-87A2D9CCA09B", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/79FC8DB9-5700-4E59-89EA-87A2D9CCA09B/view-source"}], "score": 2, "updated_at": "2023-10-03T21:07:26+00:00"}], "domain": "biology", "external_links": ["https://journals.sagepub.com/doi/full/10.1177/147470490700500213"], "medical_sensitive": false, "patient_specific": false, "provenance": {"attribution_required": true, "collected_at": "2026-10-01T03:03:11.333206+00:00", "license": "CC BY-SA 4.0", "license_url": "https://creativecommons.org/licenses/by-sa/4.0/", "raw_file": "raw/codex_api_v1/3e71d6afdfe444c721dbb1321f43c14066813d2fd740fb255123cf87e737d071_0.json", "raw_sha256": "84992ad678a40907dca3af99f849ee653142b680281a54e02542dc7f47d30773", "source_api": "Stack Exchange API 2.3", "source_url": "https://api.stackexchange.com/2.3/search/advanced?answers=1&filter=withbody&order=desc&page=9&pagesize=100&site=biology&sort=creation", "transformation": "API HTML retained; mechanical HTML-to-text; no LLM rewriting"}, "question_author": "daniel.sedlacek", "question_author_url": "https://biology.stackexchange.com/users/4952/daniel-sedlacek", "question_author_user_type": "registered", "question_created_at": "2023-09-25T09:56:02+00:00", "question_html": "

I can't find any data/study bringing some light to the components of the life expectancy gender gap. But this should't be difficult:

\n
    \n

  • Men suffer many more accidents and suicides, these are clearly not biological factors, it should be easy to calculate life expectancy gap excluding these.

    \n
    • \n

  • Men abuse alcohol and tobacco more than women, it should be possible to compare life expectancy for non-smokers and non-drinkers only.

    \n
    • \n
\n

Please let me know if you know of any study.

\n", "question_id": 113077, "question_license": "CC BY-SA 4.0", "question_score": 1, "question_text": "I can't find any data/study bringing some light to the components of the life expectancy gender gap. But this should't be difficult:\n\n\n\n\n\n\n\nMen suffer many more accidents and suicides, these are clearly not biological factors, it should be easy to calculate life expectancy gap excluding these.\n\n\n\n\n\n\n\n\n\nMen abuse alcohol and tobacco more than women, it should be possible to compare life expectancy for non-smokers and non-drinkers only.\n\n\n\n\n\n\n\n\nPlease let me know if you know of any study.", "revision_attribution": [{"content_license": "CC BY-SA 4.0", "contributor": {"display_name": "daniel.sedlacek", "profile_url": "https://biology.stackexchange.com/users/4952/daniel-sedlacek", "user_type": "registered"}, "created_at": "2023-09-25T09:56:02+00:00", "raw_file": "raw/codex_api_v1/7990290f44c327838228c7b3c3814c3a2aa21e981eefca82d28f255bb804f6fa_1790824034012716800_0.json", "raw_sha256": "1938cd4833c1e706cad2a86a721cda79c53cf3432479a2d574c35bc2c5ebc71a", "revision_guid": "CCEE18E9-5825-4037-8A7E-D81E3A354FAC", "revision_number": 1, "revision_type": "single_user", "revision_url": "https://biology.stackexchange.com/revisions/CCEE18E9-5825-4037-8A7E-D81E3A354FAC/view-source"}, {"content_license": null, "contributor": {"display_name": "daniel.sedlacek", "profile_url": "https://biology.stackexchange.com/users/4952/daniel-sedlacek", "user_type": "registered"}, "created_at": "2023-09-28T08:25:13+00:00", "raw_file": "raw/codex_api_v1/7990290f44c327838228c7b3c3814c3a2aa21e981eefca82d28f255bb804f6fa_1790824034012716800_0.json", "raw_sha256": "1938cd4833c1e706cad2a86a721cda79c53cf3432479a2d574c35bc2c5ebc71a", "revision_guid": "7C2E7DB9-C397-4D6C-95CB-71CBA9A9ED52", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/7C2E7DB9-C397-4D6C-95CB-71CBA9A9ED52/view-source"}, {"content_license": null, "contributor": {"display_name": "daniel.sedlacek", "profile_url": "https://biology.stackexchange.com/users/4952/daniel-sedlacek", "user_type": "registered"}, "created_at": "2023-09-28T08:25:13+00:00", "raw_file": "raw/codex_api_v1/7990290f44c327838228c7b3c3814c3a2aa21e981eefca82d28f255bb804f6fa_1790824034012716800_0.json", "raw_sha256": "1938cd4833c1e706cad2a86a721cda79c53cf3432479a2d574c35bc2c5ebc71a", "revision_guid": "C3D67E96-D7D4-439A-B948-B7B6EAFD6377", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/C3D67E96-D7D4-439A-B948-B7B6EAFD6377/view-source"}, {"content_license": null, "contributor": {"display_name": "Community", "profile_url": "https://biology.stackexchange.com/users/-1/community", "user_type": "moderator"}, "created_at": "2023-10-06T10:02:15+00:00", "raw_file": "raw/codex_api_v1/94d9f1e30b5dd1767475c05e1b94ebc9b51251f35d208b9800a4aa1aae1f7188_1790824031839073700_0.json", "raw_sha256": "cce2a5f3b306f6a39571358a0439bc231c3ba14bee317be498ab1ef3965e7c77", "revision_guid": "3620FFE5-64F1-4DAB-A70A-60188314A407", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/3620FFE5-64F1-4DAB-A70A-60188314A407/view-source"}, {"content_license": null, "contributor": {"display_name": "Community", "profile_url": "https://biology.stackexchange.com/users/-1/community", "user_type": "moderator"}, "created_at": "2023-10-06T10:02:15+00:00", "raw_file": "raw/codex_api_v1/94d9f1e30b5dd1767475c05e1b94ebc9b51251f35d208b9800a4aa1aae1f7188_1790824031839073700_0.json", "raw_sha256": "cce2a5f3b306f6a39571358a0439bc231c3ba14bee317be498ab1ef3965e7c77", "revision_guid": "E593F81D-9799-4A3D-A26C-445105BEC271", "revision_number": null, "revision_type": "vote_based", "revision_url": "https://biology.stackexchange.com/revisions/E593F81D-9799-4A3D-A26C-445105BEC271/view-source"}], "source_site": "biology", "source_url": "https://biology.stackexchange.com/questions/113077/how-much-of-life-expectancy-gender-gap-is-caused-by-social-vs-biological-factors", "split": "test", "split_group": "7e03d393451483eba81786dd9334ff5ccefd26e383727789306e22ce79303292", "tags": ["statistics", "lifespan", "gender"], "thread_id": "biology:113077", "title": "How much of life expectancy gender gap is caused by social vs biological factors?"}}