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The mean number of alleles in multigene families

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

G. A. Watterson
G. A. Watterson*
Affiliation:
Monash University
*
∗Postal address: Department of Mathematics, Monash University, VIC 3168, Australia.
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Abstract

The paper considers a random sample of r chromosomes, each having n genes subject to intrachromosomal gene conversion, and mutation. The probability distribution and moments for the number of alleles present is investigated, when the number, k, of possible alleles at each locus, is either finite or infinite. Explicit formulas are given for the mean numbers of alleles on r = 1, 2, or 3 chromosomes, which simplify previously known results. For fixed r, in the infinitely-many-alleles case, the mean number increases asymptotically like r θ log (n) as n→∞, where θ is a mutation parameter. But results for large samples remain elusive.

Keywords

GENE CONVERSIONREVERSIBLE MARKOV PROCESS

MSC classification

Primary: 92D15: Problems related to evolution
Secondary: 60J85: Applications of branching processes
Type
Research Article
Information
Advances in Applied Probability , Volume 24 , Issue 1 , March 1992 , pp. 1 - 19
Copyright
Copyright © Applied Probability Trust 1992 

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