On the genealogy of nested subsamples from a haploid population

This is the authors' abstract. We don't add key points for this paper.

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.