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Equivalence of two descriptions of the ages of alleles

Part of: Markov processes Stochastic 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

Donnelly, P. and Joyce, P. (1989) Continuity and weak convergence of ranked and size-biased permutations on the infinite simplex. Stoch. Proc. Appl. 31, 89–103.Google Scholar
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
Fleming, W. H. and Viot, M. (1979) Some measure-valued Markov processes in population genetics theory. Indiana Univ. Math. J. 28, 817–843.Google Scholar
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
Patil, G. P. and Taillie, C. (1977) Diversity as a concept and its implications for random communities. Bull. Internat. Statist. Inst. 47, 497–515.Google Scholar