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Asymptotic rates of growth of the extinction probability of a mutant gene

โœ Scribed by Fred M. Hoppe

Publisher
Springer
Year
1992
Tongue
English
Weight
876 KB
Volume
30
Category
Article
ISSN
0303-6812

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โœฆ Synopsis

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 Bienaym6-G a l t o n -W a t s o n 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.

๐Ÿ“œ SIMILAR VOLUMES

Rates of decay for the survival probabil
Rates of decay for the survival probability of a mutant gene
โœ K. B. Athreya ๐Ÿ“‚ Article ๐Ÿ“… 1992 ๐Ÿ› Springer ๐ŸŒ English โš– 203 KB

If q~ is the extinction probability of a slightly supercritical branching process with offspring distribution (Pgr "r = 0, 1, 2 . . . . }, then it is shown that if 2 This provides a simple set of sufficient condi- tions for the validity of a conjecture of Ewens (1969) for the survival probability

The survival probability of a mutant in
The survival probability of a mutant in a multidimensional population
โœ Fred M. Hoppe ๐Ÿ“‚ Article ๐Ÿ“… 1992 ๐Ÿ› Springer ๐ŸŒ English โš– 379 KB

We prove a general result about the asymptotic behaviour of the survival probability of a slightly supercritical multitype Bienaym6-Galton-Watson branching process. This is the complete analogue of a result which Ewens (1968) obtained for a Poisson branching process.