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On random genetic drift in a subdivided population

Published online by Cambridge University Press:  14 July 2016

Edward Pollak
Edward Pollak*
Affiliation:
Iowa State University, Ames, Iowa
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Summary

Generations are assumed to be non-overlapping. We consider a haploid population divided into K parts, each of which contain N adults in any generation. These are obtained by a random sampling of the offspring of the previous generation. We assume that the probability of an adult offspring of an individual in one subpopulation being in some other subpopulation is the same small positive number, no matter what two subpopulations are considered.

If the population initially has individuals of two types, A and a, it is of interest to study approximations, if n is large, to

  1. (1) the rate at which A or a is lost between generations n-1 and n,

  2. (2) the probability that A and a are still present in generation n,

  3. (3) the joint distribution of frequencies of A in the subpopulations.

A solution is given for the first problem. It is found that if the mean number of migrants per generation from one subpopulation to another is at least as large as 1, the population behaves almost as if it were not subdivided. But if this number is considerably less that 1, then the rate at which one or the other gene is lost is slower than in an undivided population. The other two problems are discussed for K = 2.

Type
Research Papers
Information
Journal of Applied Probability , Volume 5 , Issue 2 , August 1968 , pp. 314 - 333
Copyright
Copyright © Applied Probability Trust 1968 

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References

Ewens, W. J. (1965) The adequacy of the diffusion approximation to certain distributions in genetics. Biometrics 21, 386–394.CrossRefGoogle ScholarPubMed
Fisher, R. A. (1930) The Genetical Theory of Natural Selection, Oxford University Press, Oxford. Second Edition (1958) Dover Publications, Inc., New York.CrossRefGoogle Scholar
Gantmacher, F. R. (1959) Matrix Theory, Vol. II. The Chelsea Publishing Company, New York.Google Scholar
Kendall, M. G. (1952) The Advanced Theory of Statistics, Vol. I. Hafner Publishing Co., New York.Google Scholar
Kimura, M. (1955) Solution of a process of random genetic drift with a continuous model. Proc. Nat. Acad. Sci. U.S.A. 41, 144–149.CrossRefGoogle ScholarPubMed
Malecot, G. (1944) Sur un problème de probabilités en chaîne que pose la génétique. Comptes Rendus. Acad. Sci. 219, 379–381.Google Scholar
Moran, P. A. P. (1959) The theory of some genetical effects of population subdivision. Aust. J. Biol. Sci. 12, 109–116.CrossRefGoogle Scholar
Wright, S. (1931) Evolution in Mendelian populations. Genetics 16, 97–159.CrossRefGoogle ScholarPubMed