Genealogy of a Wright Fisher model with strong seed bank component

Jochen Blath, Bjarki Eldon, Adrián González Casanova, Noemi Kurt
(Submitted on 12 Mar 2014)

We investigate the behaviour of the genealogy of a Wright-Fisher population model under the influence of a strong seed-bank effect. More precisely, we consider a simple seed-bank age distribution with two atoms, leading to either classical or long genealogical jumps (the latter modeling the effect of seed-dormancy). We assume that the length of these long jumps scales like a power Nβ of the original population size N, thus giving rise to a `strong’ seed-bank effect. For a certain range of β, we prove that the ancestral process of a sample of n individuals converges under a non-classical time-scaling to Kingman’s n−coalescent. Further, for a wider range of parameters, we analyze the time to the most recent common ancestor of two individuals analytically and by simulation.