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Coalescent theory for seed bank models

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  14 July 2016

Ingemar Kaj ,
Stephen M. Krone  and
Martin Lascoux
Ingemar Kaj*
Affiliation:
Uppsala University
Stephen M. Krone*
Affiliation:
University of Idaho
Martin Lascoux*
Affiliation:
Uppsala University
*
∗ Postal address: Department of Mathematics, Uppsala University, S-751 06 Uppsala, Sweden.
∗∗ Postal address: Department of Mathematics, University of Idaho, Moscow, ID 83844-1103, USA. Email address: [email protected]
∗∗∗ Postal address: Department of Conservation Biology and Genetics, EBC, Uppsala University, S-752 36 Uppsala, Sweden.
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Abstract

We study the genealogical structure of samples from a population for which any given generation is made up of direct descendants from several previous generations. These occur in nature when there are seed banks or egg banks allowing an individual to leave offspring several generations in the future. We show how this temporal structure in the reproduction mechanism causes a decrease in the coalescence rate. We also investigate the effects of age-dependent neutral mutations. Our main result gives weak convergence of the scaled ancestral process, with the usual diffusion scaling, to a coalescent process which is equivalent to a time-changed version of Kingman's coalescent.

Keywords

coalescentseed bankage-dependent mutationurn modelweak convergence

MSC classification

Primary: 92D10: Genetics 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 60F05: Central limit and other weak theorems
Secondary: 92D25: Population dynamics (general)
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 2 , June 2001 , pp. 285 - 300
Copyright
Copyright © Applied Probability Trust 2001 

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