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Activity Number: 505
Type: Contributed
Date/Time: Thursday, August 2, 2007 : 8:30 AM to 10:20 AM
Sponsor: Biometrics Section
Abstract - #309055
Title: Coalescent Theory for a Monoecious Random Mating Population with a Varying Size
Author(s): Edward Pollak*+
Companies: Iowa State University
Address: Department of Statistics, Ames, IA, 50011-1210,
Keywords: Coalescent Theory ; Monoecious Population ; Varying Size
Abstract:

Consider a random mating monoecious population whose size varies according to an irreducible a periodic Markov chain having states 1N,...,xKN, where N is large. Its transition probabilities and stationary distribution are respectively pij=P[Ns-1=xjN|Ns=xiN],s=0,-1,-2,... and v1,v2,..,vK.. At time 0 a sample of n< < N genes is taken. Let Gij be the random number of successful gametes produced by any particular parent if Ns=xiN and Ns-1=xjN. Then coalescent theory holds, with the effective population size being the reciprocal of the sum of vipij{xj/[4N(xi squared)]}E[Gij(Gij-1)], provided that the Gijs are exchangeable, E[Gij(Gij-1)] is finite and E[Gij cubed]/N approaches 0 as N increases.

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Revised September, 2007