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A simple completion of Fisher’s fundamental theorem of natural selection
Fisher's fundamental theorem of natural selection shows that the part of the rate of change of mean fitness that is due to natural selection equals the additive genetic variance in fitness. Fisher embedded this result in a model of total fitness, adding terms for deterioration of the environmen...
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Formato: | Online Artículo Texto |
Lenguaje: | English |
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John Wiley and Sons Inc.
2020
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Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7820154/ https://www.ncbi.nlm.nih.gov/pubmed/33520161 http://dx.doi.org/10.1002/ece3.6918 |
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author | Grafen, Alan |
author_facet | Grafen, Alan |
author_sort | Grafen, Alan |
collection | PubMed |
description | Fisher's fundamental theorem of natural selection shows that the part of the rate of change of mean fitness that is due to natural selection equals the additive genetic variance in fitness. Fisher embedded this result in a model of total fitness, adding terms for deterioration of the environment and density dependence. Here, a quantitative genetic version of this neglected model is derived that relaxes its assumptions that the additive genetic variance in fitness and the rate of deterioration of the environment do not change over time, allows population size to vary, and includes an input of mutational variance. The resulting formula for total rate of change in mean fitness contains two terms more than Fisher's original, representing the effects of stabilizing selection, on the one hand, and of mutational variance, on the other, making clear for the first time that the fundamental theorem deals only with natural selection that is directional (as opposed to stabilizing) on the underlying traits. In this model, the total (rather than just the additive) genetic variance increases mean fitness. The unstructured population allows an explanation of Fisher's concept of fitness as simply birth rate minus mortality rate, and building up to the definition in structured populations. |
format | Online Article Text |
id | pubmed-7820154 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | John Wiley and Sons Inc. |
record_format | MEDLINE/PubMed |
spelling | pubmed-78201542021-01-29 A simple completion of Fisher’s fundamental theorem of natural selection Grafen, Alan Ecol Evol Original Research Fisher's fundamental theorem of natural selection shows that the part of the rate of change of mean fitness that is due to natural selection equals the additive genetic variance in fitness. Fisher embedded this result in a model of total fitness, adding terms for deterioration of the environment and density dependence. Here, a quantitative genetic version of this neglected model is derived that relaxes its assumptions that the additive genetic variance in fitness and the rate of deterioration of the environment do not change over time, allows population size to vary, and includes an input of mutational variance. The resulting formula for total rate of change in mean fitness contains two terms more than Fisher's original, representing the effects of stabilizing selection, on the one hand, and of mutational variance, on the other, making clear for the first time that the fundamental theorem deals only with natural selection that is directional (as opposed to stabilizing) on the underlying traits. In this model, the total (rather than just the additive) genetic variance increases mean fitness. The unstructured population allows an explanation of Fisher's concept of fitness as simply birth rate minus mortality rate, and building up to the definition in structured populations. John Wiley and Sons Inc. 2020-12-27 /pmc/articles/PMC7820154/ /pubmed/33520161 http://dx.doi.org/10.1002/ece3.6918 Text en © 2020 The Authors. Ecology and Evolution published by John Wiley & Sons Ltd This is an open access article under the terms of the http://creativecommons.org/licenses/by/4.0/ License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. |
spellingShingle | Original Research Grafen, Alan A simple completion of Fisher’s fundamental theorem of natural selection |
title | A simple completion of Fisher’s fundamental theorem of natural selection |
title_full | A simple completion of Fisher’s fundamental theorem of natural selection |
title_fullStr | A simple completion of Fisher’s fundamental theorem of natural selection |
title_full_unstemmed | A simple completion of Fisher’s fundamental theorem of natural selection |
title_short | A simple completion of Fisher’s fundamental theorem of natural selection |
title_sort | simple completion of fisher’s fundamental theorem of natural selection |
topic | Original Research |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7820154/ https://www.ncbi.nlm.nih.gov/pubmed/33520161 http://dx.doi.org/10.1002/ece3.6918 |
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