Diffusion approximation of the Wright-Fisher model of population genetics: Single-locus two alleles

We investigate an autoregressive diffusion approximation method applied to the Wright-Fisher model in population genetics by considering a Markov chain with Bernoulli distributed independent variables. The use of an autoregressive diffusion method and an averaged allelic frequency process lead to an...

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Bibliographic Details
Date:2000
Main Author: Coad, R.W.
Format: Article
Language:English
Published: Інститут математики НАН України 2000
Series:Український математичний журнал
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Online Access:http://dspace.nbuv.gov.ua/handle/123456789/156152
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Diffusion approximation of the Wright-Fisher model of population genetics: Single-locus two alleles / R.W. Coad // Український математичний журнал. — 2000. — Т. 52, № 3. — С. 336–345. — Бібліогр.: 25 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary:We investigate an autoregressive diffusion approximation method applied to the Wright-Fisher model in population genetics by considering a Markov chain with Bernoulli distributed independent variables. The use of an autoregressive diffusion method and an averaged allelic frequency process lead to an Orn-stein-Uhlenbeck diffusion process with discrete time. The normalized averaged frequency process possesses independent allele frequency indicators with constant conditional variance at equilibrium. In a monoecious diploid population of size N with r generations, we consider the time to equilibrium of averaged allele frequency in a single-locus two allele pure sampling model.