Decompositions of Price's formula in an inhomogeneous population structure

Journal of Evolutionary Biology
P Taylor

Abstract

The central tool for the study of allele frequency change due to selection is the remarkably simple but powerful formula of Price [Nature 227 (1970) 520]. Here, I provide what might be called a structural analysis of this formula. The formula essentially accumulates the average allele frequency change over many instances of a fitness-determining interaction, but there are different ways of organizing this average and these lead to quite different computational algorithms. I present three of these: an analysis by population state, an analysis by recipient and an analysis by actor. A comparison of these can lead to a heightened understanding of the different factors behind selective allele frequency change. In particular, I pay attention to the effects of structural inhomogeneity on reproductive value (RV) and emphasize that Price's formula measures RV-weighted allele frequency change. I examine in detail a simple example as a crucial way of cementing the different theoretical pathways. My aim was to produce a simple transparent presentation and therefore I work with a simple population structure and have omitted a number of technical details that are found elsewhere.

References

Jun 20, 1978·Journal of Theoretical Biology·F A Benford
Jun 7, 1977·Journal of Theoretical Biology·E L Charnov
Jan 23, 1976·Science·R L Trivers, H Hare
Oct 1, 1988·Theoretical Population Biology·P D Taylor
Jul 1, 1972·Annals of Human Genetics·G R Price, C A Smith
Aug 1, 1970·Nature·G R Price
Jul 1, 1964·Journal of Theoretical Biology·W D Hamilton
Jul 7, 1981·Journal of Theoretical Biology·J Seger
May 7, 1996·Journal of Theoretical Biology·P D Taylor, S A Frank
Nov 5, 2004·Journal of Evolutionary Biology·A Gardner, S A West
Jul 28, 2005·Journal of Theoretical Biology·Alan Grafen
Aug 12, 2006·Proceedings. Biological Sciences·Hisashi Ohtsuki, Martin A Nowak
May 25, 2007·Nature·Peter D TaylorGeoff Wild
Aug 31, 2007·Journal of Theoretical Biology·Peter D TaylorGeoff Wild
Mar 29, 2008·Journal of Theoretical Biology·Alan Grafen, Marco Archetti

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Citations

Jul 22, 2009·Genetics·Steinar EngenBernt-Erik Saether
Apr 2, 2014·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·Peter D Taylor, Wes Maciejewski
Mar 8, 2016·Journal of Theoretical Biology·Peter Taylor
May 25, 2015·Theoretical Population Biology·Jeremy Van Cleve
Dec 25, 2016·Evolution; International Journal of Organic Evolution·Peter Taylor
Oct 23, 2015·Journal of Evolutionary Biology·Bram Kuijper, Rufus A Johnstone
Feb 19, 2013·Journal of Theoretical Biology·Peter Taylor
Mar 1, 2011·Trends in Ecology & Evolution·Sébastien LionTroy Day

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