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arXiv · 1403.2925

Genealogy of a Wright Fisher model with strong seed bank component

Jochen Blath·Bjarki Eldon·Adrián González Casanova·Noemi Kurt
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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 $N^β$ 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.

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Jochen Blath, Bjarki Eldon, Adrián González Casanova, Noemi Kurt. 2014-03-12. Genealogy of a Wright Fisher model with strong seed bank component. https://arxiv.org/abs/1403.2925

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