Abstract
This note extends to an arbitrary offspring distribution the generalized model for random fluctuation of allele frequency, where population size is permitted to fluctuate randomly from generation to generation. Martingale methods analogous to those of Seneta (1974) and Heyde and Seneta (1975) are applied to discuss conditions for Pr(Y(1−Y)>0)>0, where Y is the (almost sure) limiting frequency of one allele. An overlapping generation study of the same phenomenon has recently been made by Heyde (1981).
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References
Cannings, C.: The latent roots of certain Markov chains arising in genetics: A new approach, I. Haploid models. Adv. Appl. Prob. 6, 260–290 (1974)
Ewens, W. J.: Population genetics. London: Methuen 1969
Ewens, W. J.: Mathematical population genetics. Berlin-Heidelberg-New York: Springer 1979
Heyde, C. C.: On the survival of a gene represented in a founder population. J. Math. Biol. 12, 91–99 (1981)
Heyde, C. C., Seneta, E.: The genetic balance between random sampling and random population size. J. Math. Biol. 1, 317–320 (1975)
Karlin, S., McGregor, J.: Direct product branching processes and related Markov chains. Proc. Natl. Acad. Sci. USA 51, 598–602 (1964)
Seneta, E.: A note on the balance between random sampling and population size (on the 30th anniversary of G. Malécot's paper). Genetics 77, 607–610 (1974)
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Buckley, M.J., Seneta, E. The genetic balance between varying population size and selective neutrality. J. Math. Biology 17, 217–222 (1983). https://doi.org/10.1007/BF00305760
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DOI: https://doi.org/10.1007/BF00305760