The coalescent in two colonies with symmetric migration

Kingman's coalescent process is extended to two colonies with symmetric migration. The mean waiting time until a sample of genes taken from two colonies coalesces to a common ancestor is obtained. The final step in the waiting time before the process is absorbed at 1 is observed to have an intriguing behaviour. The distribution of this final waiting time converges to the known distribution of the corresponding waiting time in the case of a single population as the migration rate tends to zero. The mean, however, does not converge. The waiting time until a sample has two common ancestors is modeled as a function of the migration rate. Finally bounds for the expected waiting time for the two colonies to have j > 1 ancestors are derived.