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September, 1962 Some Theoretical Aspects of Diffusion Theory in Population Genetics
G. A. Watterson
Ann. Math. Statist. 33(3): 939-957 (September, 1962). DOI: 10.1214/aoms/1177704463


This paper considers the problem of approximating a discrete time, discrete states, non-Markov process by a continuous diffusion process. The problem is set in the context of population genetics but may have more general application. In the genetic situation, most authors have treated the stochastic behavior of a gene frequency subject to evolutionary factors by assuming its probability distribution may be approximated by the solution of the Fokker-Planck diffusion equation. It is here shown that under certain sufficient conditions such an approximation is valid, even for genetic models in which the gene frequency does not necessarily form a Markov process. A summary of some old and new results concerning the asymptotic behavior of gene frequency is given, with special emphasis on the case when mutation is absent so that an absorbing state will ultimately be reached.


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G. A. Watterson. "Some Theoretical Aspects of Diffusion Theory in Population Genetics." Ann. Math. Statist. 33 (3) 939 - 957, September, 1962.


Published: September, 1962
First available in Project Euclid: 27 April 2007

zbMATH: 0113.35502
MathSciNet: MR141164
Digital Object Identifier: 10.1214/aoms/1177704463

Rights: Copyright © 1962 Institute of Mathematical Statistics

Vol.33 • No. 3 • September, 1962
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