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Main Title: Genealogy of a Wright-Fisher model with strong seed bank component
Author(s): Blath, Jochen
Eldon, Bjarki
González Casanova, Adrin
Kurt, Noemi
Type: Research Paper
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.
Subject(s): rroblems related to evolution
renewal theory
Issue Date: 19-Dec-2012
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 92D15 Problems related to evolution
60K05 Renewal theory
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2012, 37
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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