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

Published online by Cambridge University Press:  14 July 2016

Edward Pollak*
Affiliation:
Iowa State University
*
Postal address: Department of Statistics, Iowa State University, Ames, IA 50011-1210, USA. Email address: [email protected]
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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 KN. It is assumed that all matings except for selfing are possible and equally probable. At time 0 a random sample of nN 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.

Type
Research Article
Copyright
Copyright © Applied Probability Trust 2010 

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