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 σ^{2} k > 0, and m _{k} → 1, then 1 -q _{k} ~ 2(m _{k} -1)σ k ^{-2}, where m_{ k} = ∑ r rp kr , σ^{2} 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 |
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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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