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The stationary distribution of the infinitely-many neutral alleles diffusion model

Published online by Cambridge University Press:  14 July 2016

G. A. Watterson
G. A. Watterson*
Affiliation:
Monash University, Clayton, Victoria
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Abstract

An expression is found for the stationary density of the allele frequencies, in the infinitely-many alleles model. It is assumed that all alleles are neutral, that there is a constant mutation rate, and that the population is sufficiently large for the diffusion model to apply. Bounds on some moments are calculated from the density, and some applications are made to the problem of which allele is oldest in a population. A postulate made by Ewens (1972), concerning the distribution of allele numbers in a finite random sample from the neutral diffusion population, is shown to be correct.

Keywords

ALLELE FREQUENCIESSELECTIVE NEUTRALITYDIRICHLET DISTRIBUTIONORDER STATISTICSSAMPLE DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 4 , December 1976 , pp. 639 - 651
Copyright
Copyright © Applied Probability Trust 1976 

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References

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