Abstract
Gene survival in a population which increases without density dependence is considered using a generalization of the Moran model for haploid individuals. It is shown that situations where ultimate homozygosity is certain and where there is a non-zero probability of balanced polymorphism are both possible. Necessary and sufficient conditions in terms of the mean of the population growth distribution are given which determine which of these situations holds.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Athreya, K. B., Karlin, S.: Limit theorems for split times of branching processes. J. Math. Mech. 17, 257–277 (1967)
Ewens, W. J.: Mathematical population genetics. Berlin: Springer 1979
Heyde, C. C., Seneta, E.: The genetic balance between random sampling and random population size. J. Math. Biol. 1, 317–320 (1975)
Mayr, E.: Systematics and the origin of species. New York: Columbia Univ. Press 1942; New York: Reprinted by Dover Publications 1964
Moran, P. A. P.: The statistical processes of evolutionary theory. Oxford: Clarendon Press 1962
Schuh, H.-J.: Sums of i.i.d. random variables and an application to the explanation to the explosion criterion for Markov branching processes. Department of Statistics, University of Melbourne Research Report Series, No. 2, 1980
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Heyde, C.C. On the survival of a gene represented in a founder population. J. Math. Biol. 12, 91–99 (1982). https://doi.org/10.1007/BF00275205
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00275205