Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-11T23:14:04.653Z Has data issue: false hasContentIssue false
  • English
  • Français

Weak limit for the stationary distribution of the infinite-alleles model

Published online by Cambridge University Press:  14 July 2016

Haim Avni
Haim Avni*
Affiliation:
The Weizmann Institute of Science
*
∗ Currently at the Israel Institute for Biological Research, P.O.B. 19, Nes-Ziona, Israel.
Get access Rights & Permissions [Opens in a new window]

Abstract

The limit behavior of the stationary distribution of the infinite-alleles model is reduced to a single Laplace transform formula. Some known results, such as Ewens' sampling formula, the distribution of the order-statistics and the frequency spectrum density are shown to follow from this relation. All the results are obtained within the framework of the configuration process, without recourse to finite alleles models.

In view of some recent results by Kingman (1977), the results apply wherever the Ewens' sampling formula is valid.

Keywords

ALLELE FREQUENCESGENERALIZED LAPLACE TRANSFORMORDER STATISTICSSAMPLE DISTRIBUTION
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 3 , September 1979 , pp. 459 - 472
Copyright
Copyright © Applied Probability Trust 1979 

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

Ewens, W. J. (1972) The sampling theory of selectively neutral alleles. Theoret. Popn Biol. 3, 87–112.Google Scholar
Karlin, S. and Mcgregor, J. L. (1965) The number of mutant forms maintained in a population. Proc. 5th Berkeley Symp. Math. Statist. Prob. 4, 415–438.Google Scholar
Karlin, S. and Mcgregor, J. L. (1972) An addendum to a paper by W. J. Ewens. Theoret. Popn Biol. 3, 113–117.Google Scholar
Kingman, J. F. C. (1975) Random discrete distributions. J. R. Statist. Soc. B 37, 1–15.Google Scholar
Kingman, J. F. C. (1977) The population structure associated with the Ewens sampling formula. Theoret. Popn Biol. 11, 274–283.Google Scholar
Trajstman, A. C. (1974) On a conjecture of G. A. Watterson. Adv. Appl. Prob. 6, 489–493.Google Scholar
Watterson, G. A. (1974) The sampling theory of selectively neutral alleles. Adv. Appl. Prob. 6, 463–488.Google Scholar
Watterson, G. A. (1976) The stationary distribution of the infinitely many neutral alleles diffusion model. J. Appl. Prob. 13, 639–651.Google Scholar
Watterson, G. A. and Guess, H. A. (1977) Is the most frequent allele the oldest? Theoret. Popn Biol. 11, 141–160.Google Scholar