Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-24T18:16:22.099Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M. and Stegun, I. A. (1965) Handbook of Mathematical Functions. Dover, New York.Google Scholar
Ewens, W. J. (1972) The sampling theory of selectively neutral alleles. Theor. Pop. Biol. 3, 87–112.Google Scholar
Karlin, S. and Mcgregor, J. (1972) Addendum to a paper of W. Ewens. Theor. Pop. Biol. 3, 113–116.CrossRefGoogle ScholarPubMed
Kingman, J. F. C. (1975) Random discrete distributions. J. R. Statist. Soc. B 37, 1–15.Google Scholar
Kirby, K. and Ewens, W. J. (1976) To appear.Google Scholar
Watterson, G. A. (1974) The sampling theory of selectively neutral alleles. Adv. Appl. Prob. 6, 463–488.CrossRefGoogle Scholar
Watterson, G. A. and Guess, H. A. (1976) Is the most frequent allele the oldest? Theor. Pop. Biol. To appear.Google Scholar
Wright, S. (1969) Evolution and the Genetics of Populations, Vol. 2. University of Chicago Press, Chicago.Google Scholar