A population genetic model incorporating the evolutionary forces of zygotic selection, gametic selection and non-Mendelian segregation has been analyzed for the case in which all selection coefficients and the segregation parameter are assumed to be random variables that are uncorrelated from generation to generation. The diffusion approximation of the model is developed, and the subsequent analysis shows that one of four limiting outcomes of the stochastic process may obtain — an allele may be fixed or lost almost surely and irrespective of the initial gene frequency, the gene frequency may converge to a unique stationary distribution, or an allele may be fixed or lost with probabilities depending on the initial gene frequency. These outcomes correspond rather closely with the possible outcomes of the deterministic model — fixation or loss of an allele, convergence to a stable equilibrium, or the existence of an unstable equilibrium.
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Work supported by N. I. H. grants GM21732 and GM21623. The author is supported by Research Career Award GM2301.
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Hartl, D.L. Stochastic selection in both haplophase and diplophase. J. Math. Biol. 3, 263–269 (1976). https://doi.org/10.1007/BF00275059
- Stationary Distribution
- Mathematical Biology
- Genetic Model
- Matrix Theory
- Gene Frequency