Rates of decay for the survival probability of a mutant gene

Athreya, K. B. (1991) Rates of decay for the survival probability of a mutant gene Journal of Mathematical Biology, 30 (6). pp. 577-581. ISSN 0303-6812

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Official URL: http://www.springerlink.com/content/770u16p3242078...

Related URL: http://dx.doi.org/10.1007/BF00175607

Abstract

If qk is the extinction probability of a slightly supercritical branching process with offspring distributionP kr :r = 0, 1, 2,..., then it is shown that if sup ∑r r 3 p kr , <∞, inf σ2 k > 0, and m k → 1, then 1 -q k ~ 2(m k -1)σ k -2, where m k = ∑ r rp kr , σ2 k = ∑k r r 2 p kr −m k 2. This provides a simple set of sufficient conditions for the validity of a conjecture of Ewens (1969) for the survival probability of a slightly advantageous mutant gene.

Item Type:Article
Source:Copyright of this article belongs to Springer-Verlag.
Keywords:Mutant Gene; Branching Process; Extinction Probability
ID Code:1145
Deposited On:05 Oct 2010 18:22
Last Modified:12 May 2011 15:30

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