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 > l ancestors are derived.
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School of Applied Science, Monash University Gippsland Campus, Churchill, Vic., Australia.
Griffiths
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D005828:Genetics, Population; D008433:Mathematics; D008957:Models, Genetic; D015233:Models, Statistical; D011336:Probability