The distribution of the coalescence time and the number of pairwise nucleotide differences in the “isolation with migration” model

This paper is concerned with the “isolation with migration” model, where a panmictic ancestral population gave rise to a symmetric nn-island model, time ττ ago. Explicit analytical expressions are derived for the probability density function of the coalescence time of a pair of genes sampled at random from the same subpopulation or from different subpopulations, and for the probability distribution of the number of pairwise nucleotide differences.