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The survival of a mutant gene under selection. II

Published online by Cambridge University Press:  09 April 2009

P. A. P. Moran
P. A. P. Moran
Affiliation:
The Australian National University, Canberra.
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R. A. Fisher (1930) has obtained approximate expressions for the probability of survival of a new mutant in a finite population of haploid individuals in which the generations are non-overlapping. Suppose that we have M haploid individuals which are either of genotype a or A, and suppose that a has a small selective advantage over A so that the relative numbers of offspring have expectations proportional to 1 + s and 1 respectively, where s is small and positive. If each generation is produced by binomial sampling with probabilities proportional to the numbers of a and A individuals in the previous generation multiplied by their respective selective values, and if initially there is only one individual of type a, the probability of the population ultimately becoming entirely of this type is approximately so long as s2M is small. This also holds when s is small and negative.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 1 , Issue 4 , December 1960 , pp. 485 - 491
Copyright
Copyright © Australian Mathematical Society 1960

References

[1] Fisher, R. A., The Genetícal Theory of Natural Selection, Oxford, (1930).CrossRefGoogle Scholar
[2] Moran, P. A. P., The survival of a mutant gene under selection. Jour. Australian Math. Soc. I (1959) 121–126.CrossRefGoogle Scholar