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An alternative approach to asymptotic results on genetic composition when the population size is varying

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Abstract

This paper is concerned with methodology for studying the long-term genetic composition of a population of haploid individuals in the case where the population size is varying. A general approach requiring a minimum of assumptions is described based on constructing martingales out of expressions for the means of the numbers of allelic types, conditional on the past. Earlier investigations were based on studying the asymptotic behaviour of the proportion of alleles of a certain type in the population. Several applications demonstrate that the approach suggested in the paper provides results which usefully complement ones obtained previously.

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References

  • Daley, D. J., Hall, P., Heyde, C. C.: Further results on the survival of a gene represented in a founder population. J. Math. Biology 14, 355–363 (1982)

    Google Scholar 

  • Ewens, W. J.: Mathematical population genetics, Berlin-Heidelberg-New York: Springer 1979

    Google Scholar 

  • Heyde, C. C.: The effect of selection on genetic balance when the population size is varying. Theoret. Population Biology 11, 249–251 (1977)

    Google Scholar 

  • Heyde, C. C.: On the survival of a gene represented in a founder population. J. Math. Biology 12, 91–99 (1981)

    Google Scholar 

  • Heyde, C. C.: The effect of differential reproductive rates on the survival of a gene represented in a founder population. In: (Gani, J., Hannan, E. J., eds.) Essays in statistical science. J. Applied Prob. 19A, 19–25 (1982)

  • Heyde, C. C.: On limit theorems for gene survival. Colloquia Mathematica János Bolyai (1983) in press

  • Heyde, C. C., Seneta, E.: The genetic balance between random sampling and random population size. J. Math. Biology 1, 317–320 (1975)

    Google Scholar 

  • Seneta, E.: A note on the balance between random sampling and population size. Genetics 77, 607–610 (1974)

    Google Scholar 

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Authors and Affiliations

  1. CSIRO Division of Mathematics and Statistics, Box 1965, P.O., 2601, Canberra City, A.C.T., Australia

    C. C. Heyde

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  1. C. C. Heyde
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Heyde, C.C. An alternative approach to asymptotic results on genetic composition when the population size is varying. J. Math. Biology 18, 163–168 (1983). https://doi.org/10.1007/BF00280664

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  • DOI: https://doi.org/10.1007/BF00280664

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