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Convergence to a diffusion of a multi-allelic model in population genetics

Published online by Cambridge University Press:  01 July 2016

Ken-Iti Sato
Ken-Iti Sato*
Affiliation:
Kanazawa University
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Abstract

We consider a Markov chain on the d-dimensional (d-allelî) non-negative lattice points with the sum of components being N, for which one-step transition consists of two stages—independent reproduction and random sampling. Convergence to a degenerate diffusion process when N → ∞ is proved. We show how difference among alleles in means and variances of offspring numbers affects the limit diffusion, giving a rigorous multi-allelic version of a result of Gillespie.

Keywords

MARKOV CHAINPOPULATION GENETICSOFFSPRING DISTRIBUTIONDEGENERATE DIFFUSIONSTOCHASTIC DIFFERENTIAL EQUATION
Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 3 , September 1978 , pp. 538 - 562
Copyright
Copyright © Applied Probability Trust 1978 

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