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The total number of heterozygotes before fixation

Published online by Cambridge University Press:  14 July 2016

P. Holgate
P. Holgate*
Affiliation:
Birkbeck College, London
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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 

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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