Asymptotic rates of growth of the extinction probability of a mutant gene |
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Authors: | Fred M Hoppe |
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Institution: | (1) Department of Mathematics and Statistics, McMaster University, L8S 4K1 Hamilton, Ontario, Canada |
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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.Research supported by NSERC |
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Keywords: | Branching process Extinction probability Asymptotics Probability-generating function |
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