Summary
This note pertains to a generalized model for random fluctuation of allele frequency, where the population size is permitted to fluctuate randomly from generation to generation. Martingale methods are applied to discuss in two propositions, respectively, necessary and sufficient conditions for P (Y(11−Y)>0)>0, where Y is the (almost sure) limiting frequency of one allele. Under an additional restriction a necessary and sufficient condition results. Some simple remarks are made on further description of the distribution of Y.
Received October 28, 1974
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References
Neveu, J.: Mathematical Foundations of the Calculus of Probability. San Francisco: Holden-Day 1965.
Seneta, E.: A note on the balance between random sampling and population size. (On the 30th anniversary of G. Malecot’s paper.) Genetics 77, 607–610 (1974).
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Heyde, C.C., Seneta, E. (2010). The Genetic Balance between Random Sampling and Random Population Size. In: Maller, R., Basawa, I., Hall, P., Seneta, E. (eds) Selected Works of C.C. Heyde. Selected Works in Probability and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-5823-5_39
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DOI: https://doi.org/10.1007/978-1-4419-5823-5_39
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