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The structured coalescent process with weak migration

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Morihiro Notohara
Morihiro Notohara*
Affiliation:
Kyushu University
*
∗ Postal address: Department of Biology, Faculty of Science, Kyushu University, Fukuoka 812-8581, Japan. Email address: [email protected]
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Abstract

The aim of this paper is to study genealogical processes in a geographically structured population with weak migration. The coalescence time for sampled genes from different colonies diverges to infinity as the migration rates among colonies are close to zero. We investigate the moment generating functions of the coalescence time, the number of segregating sites and the number of allele types in sampled genes when there is low migration. Employing a perturbation method, we obtain a system of recurrence relations for the approximate solutions of these moment generating functions and solve them in some cases.

Keywords

Structured coalescentweak migrationperturbation

MSC classification

Primary: 92D10: Genetics
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 38 , Issue 1 , March 2001 , pp. 1 - 17
Copyright
Copyright © by the Applied Probability Trust 2001 

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