Diffusion approximations for onelocus multiallel

Authors: Sabin Lessard

Publish Date: 2009/01/21

Volume: 59, Issue: 5, Pages: 659-696

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Abstract

Diffusion approximations are ascertained from a twotimescale argument in the case of a groupstructured diploid population with scaled viability parameters depending on the individual genotype and the group type at a single multiallelic locus under recurrent mutation and applied to the case of random pairwise interactions within groups The main step consists in proving global and uniform convergence of the distribution of the group types in an infinite population in the absence of selection and mutation using a coalescent approach An inclusive fitness formulation with coefficient of relatedness between a focal individual J affecting the reproductive success of an individual I defined as the expected fraction of genes in I that are identical by descent to one or more genes in J in a neutral infinite population given that J is allozygous or autozygous yields the correct selection drift functions These are analogous to the selection drift functions obtained with pure viability selection in a population with inbreeding They give the changes of the allele frequencies in an infinite population without mutation that correspond to the replicator equation with fitness matrix expressed as a linear combination of a symmetric matrix for allozygous individuals and a rankone matrix for autozygous individuals In the case of no inbreeding the mean inclusive fitness is a strict Lyapunov function with respect to this deterministic dynamics Connections are made between dispersal with exact replacement proportional dispersal uniform dispersal and local extinction and recolonization The timing of dispersal before or after selection before or after mating is shown to have an effect on group competition and the effective population size

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