The coalescent in two colonies with symmetric migration

J Math Biol. 1993;31(8):841-51. doi: 10.1007/BF00168049.


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.

MeSH terms

  • Genetics, Population*
  • Mathematics
  • Models, Genetic*
  • Models, Statistical
  • Probability