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Drift in haploid models

Published online by Cambridge University Press:  01 July 2016

C. Cannings
C. Cannings*
Affiliation:
Department of Probability and Statistics, University of Sheffield
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Extract

The classical models for genetic drift of Wright (1931) and Moran (1958) have been generalized by Karlin and McGregor (1965), and Chia and Watterson (1969), this last treatment including the other three. The basic technique for the generalized models was to consider the change of certain expectations of the underlying random variables, the generalization being in terms of the conditional branching process.

Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 1 , March 1975 , pp. 4 - 5
Copyright
Copyright © Applied Probability Trust 1975 

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References

Cannings, C. (1973) The equivalence of some overlapping and non-overlapping generation models for genetic drift. J. Appl. Prob. 10, 432–436.Google Scholar
Cannings, C. (1974) The latent roots of certain Markov chains arising in genetics: A new approach, I. Haploid models. Adv. Appl. Prob. 6, 260–290.Google Scholar
Chia, A. B. and Watterson, G. A. (1969) Demographic effects on the rate of genetic evolution. I. Constant size populations with two genotypes. J. Appl. Prob. 6, 231–249.Google Scholar
Karlin, S. and McGregor, J. (1965) Direct product branching processes and related induced Markoff chains. I. Calculation of rates of approach to homozygosity. Bernouilli, Bayes, Laplace Anniversary Volume. Springer-Verlag, Berlin 111–145.Google Scholar
Moran, P. A. P. (1958). Random processes in genetics. Proc. Camb. Phil. Soc. 34, 60–71.CrossRefGoogle Scholar
Wright, S. W. (1931) Evolution in Mendelian populations. Genetics 16, 97–159.Google Scholar