Random selective advantages of genes and their probabilities of fixation

Abstract

The 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 size M. It is assumed that in any generation the adaptive values of A and a are equally likely to be 1 + s: 1 or 1: 1 + s. If s is the selective advantage and x the frequency of gene A, then the first two moments of the change in frequency are found to be m(Δx) = x(1 − x)(1 − 2x) θ/2M and [formula omitted] where E(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 for m(Δx) also is obtained. This form is compared with the equation currently used in describing random fluctuations in selection intensities. © 1973, Cambridge University Press. All rights reserved.