Random selective advantages of genes and their probabilities of fixation

Abstract

SUMMARYThe question of what is meant by random fluctuations in selection intensities in a finite population is re-examined. The model presented describes the change in the frequency of a gene in a haploid population of sizeM. It is assumed that in any generation the adaptive values ofAandaare equally likely to be 1 +s: 1 or 1: 1 +s. Ifsis the selective advantage andxthe frequency of geneA, then the first two moments of the change in frequency are found to bem(Δx) =x(1 −x)(1 − 2x) θ/2MandwhereE(s2) = θ/M. The ultimate probability of fixation is computed, showing that variability in selection increases the chance of fixation of a rare gene. A more general form form(Δx) also is obtained. This form is compared with the equation currently used in describing random fluctuations in selection intensities.