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The transient distribution of allele frequencies under mutation pressure

Published online by Cambridge University Press:  14 April 2009

Masatoshi Nei  and
Wen-Hsiung Li
Masatoshi Nei
Affiliation:
Center for Demographic and Population Genetics, University of Texas at Houston, Texas 77030
Wen-Hsiung Li
Affiliation:
Center for Demographic and Population Genetics, University of Texas at Houston, Texas 77030
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Summary

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The transient distribution of allele frequencies in a finite population is derived under the assumption that there are k possible alleic states at a locus and mutation occurs in all directions. At steady state this distribution becomes identical with the distribution obtained by Wright, Kimura and Crow when k = ∞. The rate of approach to the steady state distribution is generally very slow, the asymptotic rate being 2v + 1/(2N), where v and N are the mutation rate and effective population size, respectively. Using this distribution it is shown that when population size is suddenly increased, the expected number of alleles increases more rapidly than the expected heterozygosity. Implications of the present study on testing hypotheses for the maintenance of genetic variability in populations are discussed.

Type
Research Article
Information
Genetics Research , Volume 28 , Issue 3 , December 1976 , pp. 205 - 214
Copyright
Copyright © Cambridge University Press 1976

References

REFERENCES

Crow, J. F. & Kimura, M. (1956). Some genetic problems in natural populations. Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability 4, 1–22.Google Scholar
Crow, J. F. & Kimura, M. (1970). An Introduction to Population Genetics Theory. New York: Harper & Row.Google Scholar
Ewens, W. J. (1964). The maintenance of alleles by mutation. Genetics 50, 891–898.CrossRefGoogle ScholarPubMed
Ewens, W. J. (1972). The sampling theory of selectively neutral alleles. Theoretical Population Biology 3, 87–112.CrossRefGoogle ScholarPubMed
Ewens, W. J. & Gillespie, J. H. (1974). Some simulation results for the neutral allele model, with interpretations. Theoretical Population Biology 6, 35–57.CrossRefGoogle ScholarPubMed
Ewens, W. J. & Kirby, K. (1975). The eigenvalues of the neutral alleles process. Theoretical Population Biology 7, 212–220.CrossRefGoogle ScholarPubMed
Karlin, S. & Avni, H. (1975). Derivation of the eigenvalues of the configuration process induced by a labeled direct product branching process. Theoretical Population Biology 7, 221–228.CrossRefGoogle ScholarPubMed
Kimura, M. (1968). Genetic variability maintained in a finite population due to mutational production of neutral and nearly neutral isoalleles. Genetical Research 11, 247–269.CrossRefGoogle Scholar
Kimura, M. (1971). Theoretical foundation of population genetics at the molecular level. Theoretical Population Biology 2, 174–208.CrossRefGoogle ScholarPubMed
Kimura, M. & Crow, J. F. (1964). The number of alleles that can be maintained in a finite population. Genetics 49, 725–738.CrossRefGoogle Scholar
Kimura, M. & Ohta, T. (1971). Protein polymorphism as a phase of molecular evolution. Nature 229, 467–469.CrossRefGoogle ScholarPubMed
Kimura, M. & Ohta, T. (1975). Distribution of allelic frequencies in a finite population under stepwise production of neutral alleles. Proceedings of the National Academy of Sciences U.S.A. 72, 2761–2764.CrossRefGoogle Scholar
Latter, B. D. H. (1975). Enzyme polymorphisms: gene frequency distributions with mutation and selection for optimal activity. Genetics 79, 325–331.CrossRefGoogle ScholarPubMed
Li, W.-H. & Nei, M. (1975). Drift variances of heterozygosity and genetic distance in transient states. Genetical Research 25, 229–247.CrossRefGoogle ScholarPubMed
Malécot, G. (1948). Les Mathématiques de l'hérédité. Paris: Masson et Cie.Google Scholar
Maruyama, T. & Yamazaki, T. (1974). Analysis of heterozygosity in regard to the neutrality theory of protein polymorphism. Journal of Molecular Evolution 4, 195–199.CrossRefGoogle Scholar
Nei, M. (1975). Molecular Population Genetics and Evolution. Amsterdam and New York: North Holland.Google ScholarPubMed
Nei, M. (1976). Comments on B. D. H. Latter's paper. In Population Genetics and Ecology (ed. Karlin, S. and Nevo, E.), p. 408. New York: Academic Press.Google Scholar
Nei, M. & Feldman, M. W. (1972). Identity of genes by descent within and between populations under mutation and migration pressures. Theoretical Population Biology 3, 460–465.CrossRefGoogle ScholarPubMed
Nei, M. & Li, W.-H. (1975). Probability of identical monomorphism in related species. Genetical Research 26, 31–43.CrossRefGoogle ScholarPubMed
Ohta, T. (1975). Statistical analyses of Drosophila and human protein polymorphisms. Proceedings of the National Academy of Sciences U.S.A. 72, 3194–3196.CrossRefGoogle Scholar
Wright, S. (1949). Genetics of populations. Encyclopedia Britannica 10, 111, 111A–D, 112.Google Scholar
Yamazaki, T. & Maruyama, T. (1972). Evidence for the neutral hypothesis of protein polymorphism. Science 178, 56–58.CrossRefGoogle ScholarPubMed