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TU Berlin

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Preprint 37-2012

Genealogy of a Wright-Fisher model with strong seed bank component

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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.

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