Abstract
A branching process method is employed to study the survival probability of a slightly advantageous mutant gene with a general distribution of progeny size in a large population. A counter-example to a classic proposition is given. A somewhat weaker result is proved.
Similar content being viewed by others
References
Evens, W. J.: Population Genetics. London: Methuen 1969
Fisher, R. A.: The genetical theory of natural selection. (Rev. 2nd ed.) New York: Dover 1930, 1958
Gillespie, J. H.: Natural selection for within-generation variance in offspring, number I: Genetics 76, 601–606 (1974)
Gillespie, J H.: Natural selection for within generation variance in offspring, Number II: Direct haploid model. Genetics 81, 2, 403–413 (1975)
Haldane, J. B. S.: A mathematical theory of natural and artificial selection, Part V: Selection and mutation. Proc. Camb. Phil. Soc. 26, 220–230 (1927)
Harris, T. E.: The theory of branching processes. Berlin: Springer 1963.
Kimura, N.: Diffusion models in population genetics. J. Appl. Probabil. 1, 177–232 (1964)
Author information
Authors and Affiliations
Additional information
Supported in part by NIH Grant 5R01 GM10452-18
Rights and permissions
About this article
Cite this article
Eshel, I. On the survival probability of a slightly advantageous mutant gene with a general distribution of progeny size—A branching process model. J. Math. Biology 12, 355–362 (1981). https://doi.org/10.1007/BF00276922
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00276922