Haldane's formula in Cannings models: the case of moderately strong selection

Abstract

For a class of Cannings models we prove Haldane's formula, [Formula: see text], for the fixation probability of a single beneficial mutant in the limit of large population size N and in the regime of moderately strong selection, i.e. for [Formula: see text] and [Formula: see text]. Here, [Formula: see text] is the selective advantage of an individual carrying the beneficial type, and [Formula: see text] is the (asymptotic) offspring variance. Our assumptions on the reproduction mechanism allow for a coupling of the beneficial allele's frequency process with slightly supercritical Galton-Watson processes in the early phase of fixation.

Keywords: Branching process approximation; Cannings model; Directional selection; Probability of fixation.