Nath H B, Griffiths R C
School of Applied Science, Monash University Gippsland Campus, Churchill, Vic., Australia.
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.
金曼合并过程被扩展到具有对称迁移的两个群体。得到了从两个群体中抽取的一组基因合并到一个共同祖先之前的平均等待时间。观察到该过程在被吸收到1之前等待时间的最后一步具有一种有趣的行为。随着迁移率趋于零，这个最终等待时间的分布收敛到单一种群情况下相应等待时间的已知分布。然而，均值并不收敛。直到一组样本有两个共同祖先的等待时间被建模为迁移率的函数。最后，推导出了两个群体具有j>l个祖先时预期等待时间的界限。
