Asymptotic rates of growth of the extinction probability of a mutant gene
- 1 January 1992
- journal article
- Published by Springer Nature in Journal of Mathematical Biology
- Vol. 30 (6) , 547-566
- https://doi.org/10.1007/bf00948890
Abstract
We prove that a result of Haldane (1927) that relates the asymptotic behaviour of the extinction probability of a slightly supercritical Poisson branching process to the mean number of offspring is true for a general Bienaymé-Galton-Watson branching process, provided that the second derivatives of the probability-generating functions converge uniformly to a non-zero limit. We show also by examples that such a result is true more widely than our proof suggests and exhibit some counter-examples.Keywords
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