Markov Model of Haploid Random Mating with Given Distribution of Population Size

Author： Tyvand Peder Thorvaldsen Steinar

Publisher： Elsevier

ISSN： 0092-8240

Source： Bulletin of Mathematical Biology, Vol.68, Iss.4, 2006-05, pp. : 807-819

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Abstract

An exact Markov chain model is formulated and computed for random mating in a haploid gamete pool. There are two versions of the gamete, and there is a finite number of diploid monoecious organisms. The founder population is given, and the subsequent generations allow a prescribed statistical distribution over different population sizes. The non-homogeneous Markov chain works on the haploid gamete level provided the probability of self-fertilization is 1/n, where n is the number of diploid individuals. Standard deviations of gamete frequencies and fixation probabilities are calculated. Effective population sizes for different population size distributions are estimated, including periodic bottlenecks.