On the structure pf genealogical trees in the presence of selection

We investigate through numerical simulations the effect of selection on two summary statistics for nucleotide variation in a sample of two genes from a population of N asexually reproducing haploid individuals. One is the mean time since two individuals had their most recent common ancestor ($\overline{T_s}$), and the other is the mean number of nucleotide differences between two genes in the sample ($\overline{d_s}$). In the case of diminishing epistasis, in which the deleterious effect of a new mutation is attenuated, we find that the scale of $\overline{d_s}$ with the population size depends on the mutation rate, leading then to the onset of a sharp threshold phenomenon as N becomes large.