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The neutral two-locus model as a measure-valued diffusion

Published online by Cambridge University Press:  01 July 2016

S. N. Ethier  and
R. C. Griffiths
S. N. Ethier*
Affiliation:
University of Utah
R. C. Griffiths*
Affiliation:
Monash University
*
∗Postal address: Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA. Supported in part by NSF grant DMS-8704369.
∗∗Postal address: Department of Mathematics, Monash University, Clayton, VIC 3168, Australia.
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Abstract

The neutral two-locus model in population genetics is reformulated as a measure-valued diffusion process and is shown under certain conditions to have a unique stationary distribution and be weakly ergodic. The limits of the process and its stationary distribution as the recombination parameter tends to infinity are found. Genealogies are incorporated into the model, and it is shown that a random sample of size n from the population at stationarity has a common ancestor.

Keywords

POPULATION GENETICSRECOMBINATIONMARTINGALE PROBLEMWEAK ERGODICITY
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 4 , December 1990 , pp. 773 - 786
Copyright
Copyright © Applied Probability Trust 1990 

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References

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