Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-28T01:17:17.940Z Has data issue: false hasContentIssue false
  • English
  • Français

The total number of heterozygotes before fixation

Published online by Cambridge University Press:  14 July 2016

P. Holgate
P. Holgate*
Affiliation:
Birkbeck College, London
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper is about the total number of individuals who are heterozygotic for a specified allele, before it is either lost or fixed. The exact distribution is found for small populations, and two limiting processes are investigated.

Keywords

STATISTICAL GENETICSHETEROZYGOSITYBOREL-TANNER DISTRIBUTIONDIFFUSION APPROXIMATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 13 , Issue 2 , June 1976 , pp. 201 - 207
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

[1] Borel, E. (1942) Sur l'emploi du théorème de Bernoulli pour faciliter le calcul d'une infinité de coefficients. Application au problème de l'attente à un guichet. Comptes Rendus Acad. Sci. Paris 214, 452–456. Oeuvres 2, 1187–1190.Google Scholar
[2] Daniels, H. E. (1961) Mixtures of geometric distributions. J. R. Statist. Soc. B 23, 409–413.Google Scholar
[3] Ewens, W. J. (1963) Numerical results and diffusion approximations in a genetic process. Biometrika 50, 241–249.Google Scholar
[4] Ewens, W. J. (1965) The adequacy of the diffusion approximation to certain distributions in genetics. Biometrics 21, 386–394.CrossRefGoogle ScholarPubMed
[5] Ewens, W. J. (1969) Population Genetics. Methuen, London.CrossRefGoogle Scholar
[6] Fisher, R. A. (1930) The Genetical Theory of Natural Selection. Clarendon Press, Oxford.CrossRefGoogle Scholar
[7] Khazanie, R. G. and Mckean, H. E. (1966) A Mendelian Markov process with binomial transition probabilities. Biometrika 53, 37–48.Google Scholar
[8] Kimura, M. and Crow, J. F. (1963) On the maximum avoidance of inbreeding. Genet. Res. 4, 399–415.CrossRefGoogle Scholar
[9] Maruyama, T. (1971) An invariant property of a geographically structured finite population. Genet. Res. 18, 81–84.CrossRefGoogle Scholar
[10] Maruyama, T. (1972) Some invariant properties of a geographically structured finite population: distribution of heterozygotes under irreversible mutation. Genet. Res. 20, 141–149.Google Scholar
[11] Nei, M. (1971) Total number of individuals affected by a single deleterious mutation in large populations. Theor. Pop. Biol. 2, 426–430.CrossRefGoogle ScholarPubMed
[12] Robertson, A. (1964) The effect of non-random mating within inbred lines on the rate of inbreeding. Genet. Res. 5, 164–167.CrossRefGoogle Scholar
[13] Tanner, J. C. (1953) A problem of interference between two queues. Biometrika 40, 58–69.CrossRefGoogle Scholar