On the structure of 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 (Ts), and the other is the mean number of nucleotide differences between two genes in the sample (ds). In the case of diminishing epistasis, in which the deleterious effect of a new mutation is attenuated, we find that the scale of ds with the population size depends on the mutation rate, leading then to the onset of a sharp threshold phenomenon as N becomes large.