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The effect of differential reproductive rates on the survival of a gene represented in a founder population

Published online by Cambridge University Press:  14 July 2016

C. C. Heyde
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Abstract

Gene survival in a population which increases without density dependence is considered using a generalization of the Moran model for haploid individuals in which we have differential reproductive rates. It is shown under very mild conditions that ultimate fixation is certain. This provides some mathematical support for the phenomenon of reduced genetic variability in isolated populations established from founder groups.

Keywords

SURVIVAL OF GENEFOUNDER POPULATIONFIXATIONGENETIC VARIABILITY
Type
Part 1 — Genetics
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 19 - 25
Copyright
Copyright © 1982 Applied Probability Trust 

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References

Ewens, W. J. (1979) Mathematical Population Genetics. Springer-Verlag, Berlin.Google Scholar
Hall, P. and Heyde, C. C. (1980) Martingale Limit Theory and its Application. Academic Press, New York.Google Scholar
Heyde, C. C. (1981) On the survival of a gene represented in a founder population. J. Math. Biol. 12, 91–99.CrossRefGoogle Scholar
Mayr, E. (1942) Systematics and the Origin of Species. Columbia Press, New York. (Reprinted (1964) Dover, New York.).Google Scholar
Moran, P. A. P. (1962) The Statistical Processes of Evolutionary Theory. Clarendon Press, Oxford.Google Scholar