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A limit theorem for two-locus diffusion models in population genetics

Published online by Cambridge University Press:  14 July 2016

S. N. Ethier
S. N. Ethier*
Affiliation:
Michigan State University
*
∗Postal address: Department of Statistics and Probability, Wells Hall, Michigan State University, East Lansing, Michigan 48824, U.S.A.
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Abstract

A limit theorem of Kurtz for perturbed operator semigroups is applied to show that the two-locus diffusion model in population genetics (allowing for selection, mutation, and migration) converges to a linkage-equilibrium diffusion model as Nc →∞, where N is the population size and c is the recombination fraction; in fact, with an appropriate change of variables, the limiting diffusion is what has been called the independent-loci diffusion model. This generalizes a result of Littler.

Keywords

POPULATION GENETICSRANDOM GENETIC DRIFTLINKAGEDIFFUSION PROCESSESOPERATOR SEMIGROUPS
Type
Short Communications
Information
Journal of Applied Probability , Volume 16 , Issue 2 , June 1979 , pp. 402 - 408
Copyright
Copyright © Applied Probability Trust 1979 

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References

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