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Coalescent theory for a Monoecious Random Mating Population with a Varying Size

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Edward Pollak
Edward Pollak*
Affiliation:
Iowa State University
*
∗Postal address: Department of Statistics, Iowa State University, Ames, IA 50011-1210, USA. Email address: pllk@iastate.edu
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Abstract

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Consider a monoecious diploid population with nonoverlapping generations, whose size varies with time according to an irreducible, aperiodic Markov chain with states x1N,…,xKN, where K ≪ N. It is assumed that all matings except for selfing are possible and equally probable. At time 0 a random sample of n ≪ N genes is taken. Given two successive population sizes xjN and xiN, the numbers of gametes that individual parents contribute to offspring can be shown to be exchangeable random variables distributed as Gij. Under minimal conditions on the first three moments of Gij for all i and j, a suitable effective population size Ne is derived. Then if time is recorded in a backward direction in units of 2Ne generations, it can be shown that coalescent theory holds.

Keywords

Coalescentexchangeabilitypopulation genetics

MSC classification

Secondary: 92D10: Genetics 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 92D15: Problems related to evolution 60G09: Exchangeability
Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 1 , March 2010 , pp. 41 - 57
Copyright
Copyright © Applied Probability Trust 2010 

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