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The extinction probability of descendants in bisexual models of fixed population size

Published online by Cambridge University Press:  14 July 2016

K. Kämmerle
K. Kämmerle*
Affiliation:
Johannes Gutenberg-Universität Mainz
*
∗ Postal address: Johannes Gutenberg-Universität Mainz, Fachbereich 17 Mathematik, Saarstraße 21, D-W 6500 Mainz, Germany.
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Abstract

In this paper exchangeable bisexual models with fixed population size and non-overlapping generations are introduced. Each generation consists of N pairs of individuals. The pairs of a generation have altogether 2N children. These individuals form randomly the N pairs of the next generation. The extinction probability of the descendants of a fixed number of pairs of generation 0 is discussed. Under suitable conditions it can be approximately described by the extinction probability of a Galton–Watson process, if the population size is large. Special examples are a bisexual Wright–Fisher model and models with a uniformly bounded number of children of a pair.

Keywords

GALTON-WATSON PROCESSWRIGHT–FISHER MODELEXCHANGEABLE PROCESSES

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 3 , September 1991 , pp. 489 - 502
Copyright
Copyright © Applied Probability Trust 1991 

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