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

For a class of Cannings models we prove Haldane's formula, pi(s(N)) similar to 2s(N)/rho(2), 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 s(N) similar to N-b and 0 < b < 1/2. Here, s(N) is the selective advantage of an individual carrying the beneficial type, and rho(2) 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.