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Equivalence of two descriptions of the ages of alleles

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

S. N. Ethier
S. N. Ethier*
Affiliation:
University of Utah
*
∗ Postal address: Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA.
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Abstract

It is shown that the two descriptions of the ages of alleles corresponding to the two formulations of the stationary infinitely-many-neutral-alleles diffusion model discussed by Ethier (1990a) are equivalent.

Keywords

POPULATION GENETICSINFINITELY-MANY-NEUTRAL-ALLELES MODELFLEMING–VIOT PROCESSMEASURE-VALUED DIFFUSIONPOISSON–DIRICHLET DISTRIBUTIONGEM DISTRIBUTION

MSC classification

Primary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Secondary: 92D15: Problems related to evolution 60G57: Random measures
Type
Short Communications
Information
Journal of Applied Probability , Volume 29 , Issue 1 , March 1992 , pp. 185 - 189
Copyright
Copyright © Applied Probability Trust 1992 

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Footnotes

Research supported in part by NSF grant DMS-8902991.

References

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Ethier, S. N. (1990a) The infinitely-many-neutral-alleles diffusion model with ages. Adv. Appl. Prob. 22, 1–24.Google Scholar
Ethier, S. N. (1990b) The distribution of the frequencies of age-ordered alleles in a diffusion model. Adv. Appl. Prob. 22, 519–532.Google Scholar
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Hoppe, F. M. (1987) The sampling theory of neutral alleles and an urn model in population genetics. J. Math. Biol. 25, 123–159.Google Scholar
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