Author(s) :
Jochen Blath
,
Bjarki Eldon
,
Adrian Gonzalez Casanova
,
Noemi Kurt
Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 37-2012
MSC 2000
- 92D15 Problems related to evolution
-
60K05 Renewal theory
Abstract :
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 $N^\beta$ of the original population size $N$, thus giving rise to a `strong' seed-bank effect. For a certain range of $\beta$, 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.
Notes :
Completely revised version.