An inclusive fitness analysis of synergistic interactions in structured populations

Publication Date

9-12-2012

Document Type

Article

Publication Title

Proceedings of the Royal Society B

Volume

279

Issue

1747

DOI

10.1098/rspb.2012.1408

First Page

4596

Last Page

4603

Abstract

We study the evolution of a pair of competing behavioural alleles in a structured population when there are non-additive or ‘synergistic’ fitness effects. Under a form of weak selection and with a simple symmetry condition between a pair of competing alleles, Tarnita et al. provide a surprisingly simple condition for one allele to dominate the other. Their condition can be obtained from an analysis of a corresponding simpler model in which fitness effects are additive. Their result uses an average measure of selective advantage where the average is taken over the long-term—that is, over all possible allele frequencies—and this precludes consideration of any frequency dependence the allelic fitness might exhibit. However, in a considerable body of work with non-additive fitness effects—for example, hawk–dove and prisoner's dilemma games—frequency dependence plays an essential role in the establishment of conditions for a stable allele-frequency equilibrium. Here, we present a frequency-dependent generalization of their result that provides an expression for allelic fitness at any given allele frequency p. We use an inclusive fitness approach and provide two examples for an infinite structured population. We illustrate our results with an analysis of the hawk–dove game.

Keywords

allele frequency, frequency dependence, non-additive games, relatedness, evolutionary game theory, Price equation

Comments

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Department

Mathematics and Statistics

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