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Structured coalescent with nonconservative migration

Part of: Limit theorems Markov processes

Published online by Cambridge University Press:  14 July 2016

Koffi Y. Sampson
Koffi Y. Sampson*
Affiliation:
Florida State University
*
∗ Postal address: School of Computational Science, Florida State University, 150B Dirac Science Library, Tallahassee, FL 32306-4120, USA. Email address: sampson@csit.fsu.edu
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Abstract

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We study the ancestral process of a sample from a subdivided population with stochastically varying subpopulation sizes. The sizes of the subpopulations change very rapidly (almost every generation) with respect to the coalescent time scale. For haploid populations of size N, one coalescence time unit corresponds to N generations. Coalescence and migration events occur on the same time scale. We show that, when the total population size tends to infinity, the structured coalescent is obtained, thus confirming the robustness of the coalescent. Many population structure models have been shown to converge to the structured coalescent (see Herbots (1997), Hudson (1998), Nordborg (2001), Nordborg and Krone (2002), and Notohara (1990)).

Keywords

Structured coalescentstochastic population sizenonconservative migrationweak convergence

MSC classification

Primary: 92D10: Genetics 60F05: Central limit and other weak theorems 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Secondary: 92D25: Population dynamics (general)

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 2 , June 2006 , pp. 351 - 362
Copyright
© Applied Probability Trust 2006 

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