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Coalescence theory for a general class of structured populations with fast migration

Part of: Markov processes Limit theorems

Published online by Cambridge University Press:  01 July 2016

O. Hössjer
O. Hössjer*
Affiliation:
Stockholm University
*
∗ Postal address: Department of Mathematics, Stockholm University, SE 106 91, Stockholm, Sweden. Email address: ola@math.su.se
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Abstract

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In this paper we study a general class of population genetic models where the total population is divided into a number of subpopulations or types. Migration between subpopulations is fast. Extending the results of Nordborg and Krone (2002) and Sagitov and Jagers (2005), we prove, as the total population size N tends to ∞, weak convergence of the joint ancestry of a given sample of haploid individuals in the Skorokhod topology towards Kingman's coalescent with a constant change of time scale c. Our framework includes age-structured models, geographically structured models, and combinations thereof. We also allow each individual to have offspring in several subpopulations, with general dependency structures between the number of offspring of various types. As a byproduct, explicit expressions for the coalescent effective population size N/c are obtained.

Keywords

Age-structured populationcoalescence theoryeffective population sizegeographical substructureweak convergence

MSC classification

Primary: 92D25: Population dynamics (general)
Secondary: 60J28: Applications of continuous-time Markov processes on discrete state spaces 60F17: Functional limit theorems; invariance principles
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 4 , December 2011 , pp. 1027 - 1047
Copyright
Copyright © Applied Probability Trust 2011 

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