Natural selection with varying selection coefficients – a haploid model

Abstract

In this paper an exact treatment is given for the stochastic behaviour of the frequency of haploid genotypes in an infinite population when the absolute fitnesses of the two genotypes vary at random over generations. The main qualitative result from this treatment is that natural selection will favour that allele with the largest geometric mean fitness. A diffusion equation is derived whose solution is identical to the exact solution. The drift coefficient for this equation is of the form − μp(1 −p) + σ²(½ −p)p(l −p). This differs from the drift coefficient used in previous treatments of this problem and reduces the rate of quasi-fixation. Various waiting time problems are solved using this diffusion equation.