Coalescence time for two genes from a subdivided population

In this paper a new form of the solution for the Laplace transform and moments of the distribution of the waiting time for two genes to coalescence is presented. The two genes are sampled from a subdivided population where migration rates between populations are constant in time. Equal subpopulation size is not assumed. For the special case of an island model with equal migration rates between islands, the Laplace transform of the coalescence time and the first and second moments are found explicitly. The new form of the solutions allows numerical calculation. The connection of how the results relate to a panmictic population when migration rates are large is illustrated using strong-migration-limit theory.