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Decompositions of Price’s formula in an inhomogeneous population structure
Author(s) -
TAYLOR P.
Publication year - 2009
Publication title -
journal of evolutionary biology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 128
eISSN - 1420-9101
pISSN - 1010-061X
DOI - 10.1111/j.1420-9101.2008.01640.x
Subject(s) - simple (philosophy) , population , allele frequency , biology , value (mathematics) , selection (genetic algorithm) , reproductive value , allele , econometrics , evolutionary biology , mathematical economics , statistical physics , statistics , mathematics , genetics , computer science , artificial intelligence , demography , physics , pregnancy , philosophy , epistemology , sociology , offspring , gene
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.