Genealogical properties of subsamples in highly fecund populations

Abstract

We consider some genealogical properties of nested samples. The complete sample is assumed to have been drawn from a natural population characterised by high fecundity and sweepstakes reproduction (abbreviated HFSR). The random gene genealogies of the samples are -- due to our assumption of HFSR -- modelled by coalescent processes which admit multiple mergers of ancestral lineages looking back in time. Among the genealogical properties we consider are the probability that the most recent common ancestor is shared between the complete sample and the subsample nested within the complete sample; we also compare the lengths of internal branches of nested genealogies between different coalescent processes. The results indicate how informative a subsample is about the properties of the larger complete sample, how much information is gained by increasing the sample size, and how the informativeness of the subsample varies between different coalescent processes.