For our coalescent simulations, we assumed a phylogenetic tree on the populations, and at each simulated marker, ran the coalescent back in time to the root of the tree. At this point we have a set of ancestors A of the sampled chromosomes. We now assume that the marker is biallelic and that the population frequency f of the variant allele in the ancestral population is distributed uniformly on the unit interval. Sample the frequency f and then choose an allele for each ancestor of A, picking the allele for each ancestor with probability f. Now retain the marker if it is polymorphic in our samples. This process is mathematically equivalent to having a very large outgroup population diverging from the sampled populations at the phylogenetic root, with the population panmictic before any population divergence, and ascertaining by finding heterozygotes in the outgroup. If our simulated samples have n individuals, our procedure yields a sample frequency that is approximately uniform on (1,2,…,2n − 1).
