title: Decompositions of Price's formula in an inhomogeneous population structure.
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.
authors.affiliation: Department of Mathematics & Statistics, Queen's University, Kingston, ON, Canada. peter.taylor@queensu.ca
authors.forename: P
authors.initials: P
authors.lastname: Taylor
mesh_terms: D000465:Algorithms; D000818:Animals; D005787:Gene Frequency; D005828:Genetics, Population / Q000379:methods*; D008957:Models, Genetic