A simple completion of Fisher’s fundamental theorem of natural selection

Abstract 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 e...

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Main Author:	Alan Grafen
Format:	Article
Language:	English
Published:	Wiley 2021-01-01
Series:	Ecology and Evolution
Subjects:	additive genetic component fitness definitions formal Darwinism fundamental theorem of natural selection partial change in mean fitness quantitative genetics
Online Access:	https://doi.org/10.1002/ece3.6918

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spelling	doaj-608f256d208846c6a9e0f07199c5cd7f2021-04-02T19:24:16ZengWileyEcology and Evolution2045-77582021-01-0111273574210.1002/ece3.6918A simple completion of Fisher’s fundamental theorem of natural selectionAlan Grafen0Zoology Department Oxford University Oxford UKAbstract 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.https://doi.org/10.1002/ece3.6918additive genetic componentfitness definitionsformal Darwinismfundamental theorem of natural selectionpartial change in mean fitnessquantitative genetics
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Alan Grafen
spellingShingle	Alan Grafen A simple completion of Fisher’s fundamental theorem of natural selection Ecology and Evolution additive genetic component fitness definitions formal Darwinism fundamental theorem of natural selection partial change in mean fitness quantitative genetics
author_facet	Alan Grafen
author_sort	Alan Grafen
title	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_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_sort	simple completion of fisher’s fundamental theorem of natural selection
publisher	Wiley
series	Ecology and Evolution
issn	2045-7758
publishDate	2021-01-01
description	Abstract 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.
topic	additive genetic component fitness definitions formal Darwinism fundamental theorem of natural selection partial change in mean fitness quantitative genetics
url	https://doi.org/10.1002/ece3.6918
work_keys_str_mv	AT alangrafen asimplecompletionoffishersfundamentaltheoremofnaturalselection AT alangrafen simplecompletionoffishersfundamentaltheoremofnaturalselection
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A simple completion of Fisher’s fundamental theorem of natural selection

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