On the genealogy of nested subsamples from a haploid population

For the haploid genetic model of Moran, the joint distribution of the numbers of distinct ancestors of a collection of nested subsamples is derived. These results are shown to apply to the diffusion approximations of a wide variety of other genetic models, including the Wright–Fisher process. The results allow us to relate the ancestries of populations sampled at different times. Analogous results for a line-of-descent process that incorporates the effect of mutation are given. Some results about the ages of alleles in an infinite-alleles model are described.