The probability of fixation of a favoured allele in a subdivided population

Abstract

In a stably subdivided population with symmetric migration, the chance that a favoured allele will be fixed is independent of population structure. However, random extinction introduces an extra component of sampling drift, and reduces the probability of fixation. In this paper, the fixation probability is calculated using the diffusion approximation; comparison with exact solution of the discrete model shows this to be accurate. The key parameters are the rates of selection, migration and extinction, scaled relative to population size (S = 4Ns, M = 4Nm, Λ = 4Nλ); results apply to a haploid model, or to diploids with additive selection. If new colonies derive from many demes, the fixation probability cannot be reduced by more than half. However, if colonies are initially homogeneous, fixation probability can be much reduced. In the limit of low migration and extinction rates (M, Λ [formula omitted] 1), it is 2s/{1 + (Λ/MS)(1 −exp(−S))}, whilst in the opposite limit (S [formula omitted] 1), it is 4sM/{Λ(Λ + M)}. In the limit of weak selection (M, Λ [formula omitted] 1), it is 4sM/{Λ(Λ + M)}. These factors are not the same as the reduction in effective population size (Ne/N), showing that the effects of population structure on selected alleles cannot be understood from the behaviour of neutral markers. © 1993, Cambridge University Press. All rights reserved.