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Evolution and Selection of Quantitative Traits$
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Bruce Walsh and Michael Lynch

Print publication date: 2018

Print ISBN-13: 9780198830870

Published to Oxford Scholarship Online: September 2018

DOI: 10.1093/oso/9780198830870.001.0001

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Theorems of Natural Selection: Results of Price, Fisher, and Robertson

Theorems of Natural Selection: Results of Price, Fisher, and Robertson

(p.145) 6 Theorems of Natural Selection: Results of Price, Fisher, and Robertson
Evolution and Selection of Quantitative Traits

Bruce Walsh

Michael Lynch

Oxford University Press

This chapter reviews a number of “theorems” of natural selection. These include exact results (true mathematical theorems): the Robertson-Price identity, Price's general expression for any form of selection response, and the Fisher-Price-Ewens version of Fisher's fundamental theorem. Their generality comes as the cost of usually being very difficult to apply. An important exception is the Robertson-Price identity, which expresses the within-generation change in the mean of a trait as its covariance with relative fitness. This chapter also examines three classic approximations: Fisher's fundamental theorem for the behavior of mean population fitness, and Robertson's secondary theorem and the breeder's equation for the expected response in a trait under selection, showing both how these results are connected and the error given by the various approximations. Finally, the chapter examines the connection between the additive variance of a trait and its correlation with fitness.

Keywords:   asymptotic fundamental theorem, breeder's equation, evolvability, Fisher's fundamental theorem, Fisher-Price-Ewens theorem, Price's theorem, Robertson-Price identity, Robertson's secondary theorem

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