{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T07:29:42Z","timestamp":1776756582868,"version":"3.51.2"},"update-to":[{"DOI":"10.1371\/journal.pcbi.1010407","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2022,8,15]],"date-time":"2022-08-15T00:00:00Z","timestamp":1660521600000}}],"reference-count":37,"publisher":"Public Library of Science (PLoS)","issue":"8","license":[{"start":{"date-parts":[[2022,8,3]],"date-time":"2022-08-03T00:00:00Z","timestamp":1659484800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["EXC 2064\/1 - 390727645"],"award-info":[{"award-number":["EXC 2064\/1 - 390727645"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["EXC 2124 - 390838134"],"award-info":[{"award-number":["EXC 2124 - 390838134"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Freiburg Center for Data Analysis and Modeling"},{"name":"Open Access Publishing Fund of University of T\u00fcbingen"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"abstract":"<jats:p>Estimating the mutation rate, or equivalently effective population size, is a common task in population genetics. If recombination is low or high, optimal linear estimation methods are known and well understood. For intermediate recombination rates, the calculation of optimal estimators is more challenging. As an alternative to model-based estimation, neural networks and other machine learning tools could help to develop good estimators in these involved scenarios. However, if no benchmark is available it is difficult to assess how well suited these tools are for different applications in population genetics.<\/jats:p>\n                  <jats:p>Here we investigate feedforward neural networks for the estimation of the mutation rate based on the site frequency spectrum and compare their performance with model-based estimators. For this we use the model-based estimators introduced by Fu, Futschik et al., and Watterson that minimize the variance or mean squared error for no and free recombination. We find that neural networks reproduce these estimators if provided with the appropriate features and training sets. Remarkably, using the model-based estimators to adjust the weights of the training data, only one hidden layer is necessary to obtain a single estimator that performs almost as well as model-based estimators for low and high recombination rates, and at the same time provides a superior estimation method for intermediate recombination rates. We apply the method to simulated data based on the human chromosome 2 recombination map, highlighting its robustness in a realistic setting where local recombination rates vary and\/or are unknown.<\/jats:p>","DOI":"10.1371\/journal.pcbi.1010407","type":"journal-article","created":{"date-parts":[[2022,8,3]],"date-time":"2022-08-03T13:40:35Z","timestamp":1659534035000},"page":"e1010407","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":16,"title":["Neural networks for self-adjusting mutation rate estimation when the recombination rate is unknown"],"prefix":"10.1371","volume":"18","author":[{"given":"Klara Elisabeth","family":"Burger","sequence":"first","affiliation":[]},{"given":"Peter","family":"Pfaffelhuber","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9106-7259","authenticated-orcid":true,"given":"Franz","family":"Baumdicker","sequence":"additional","affiliation":[]}],"member":"340","published-online":{"date-parts":[[2022,8,3]]},"reference":[{"issue":"4","key":"pcbi.1010407.ref001","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1016\/j.tig.2017.12.005","article-title":"Supervised Machine Learning for Population Genetics: A New Paradigm","volume":"34","author":"DR Schrider","year":"2018","journal-title":"Trends in Genetics"},{"issue":"3","key":"pcbi.1010407.ref002","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1038\/nrg2526","article-title":"Fundamental concepts in genetics: Effective population size and patterns of molecular evolution and variation","volume":"10","author":"B 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