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A genealogical approach to variable-population-size models in population genetics

Published online by Cambridge University Press:  14 July 2016

Peter Donnelly
Peter Donnelly*
Affiliation:
University College of Swansea
*
∗ Present address: Department of Statistical Science, University College London, London, WC1E 6BT, U.K.
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Abstract

A general exchangeable model is introduced to study gene survival in populations whose size changes without density dependence. Necessary and sufficient conditions for the occurrence of fixation (that is the proportion of one of the types tending to 1 with probability 1) are obtained. These are then applied to the Wright–Fisher model, the Moran model, and conditioned branching-process models. For the Wright–Fisher model it is shown that certain fixation is equivalent to certain extinction of one of the types, but that this is not the case for the Moran model.

Keywords

GENE SURVIVALGENEALOGICAL PROCESSESWRIGHT–FISHER MODELMORAN MODELEXCHANGEABLE MODELSOCCUPANCY PROBLEMS

Information

Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 2 , June 1986, pp. 283 - 296
Copyright
Copyright © Applied Probability Trust 1986 

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