Asymptotic rates of growth of the extinction probability of a mutant gene
Copyright policy )Asymptotic rates of growth of the extinction probability of a mutant gene
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.
- McMaster University Canada
second factorial moment, supercritical Bienaymé-Galton-Watson branching processes, Gene Frequency, Poisson-distributed offspring distribution, Applications of branching processes, Branching processes (Galton-Watson, birth-and-death, etc.), mutant gene, Probability, selection advantage, Models, Genetic, Taylor expansion, probability generating functions, nonlinear behavior, asymptotic expansions, branching process, Population dynamics (general), Genes, extinction probability, remainder term, Mutation, Genetics and epigenetics, Mathematics
second factorial moment, supercritical Bienaymé-Galton-Watson branching processes, Gene Frequency, Poisson-distributed offspring distribution, Applications of branching processes, Branching processes (Galton-Watson, birth-and-death, etc.), mutant gene, Probability, selection advantage, Models, Genetic, Taylor expansion, probability generating functions, nonlinear behavior, asymptotic expansions, branching process, Population dynamics (general), Genes, extinction probability, remainder term, Mutation, Genetics and epigenetics, Mathematics
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