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The common ancestor at a nonneutral locus

Part of: Stochastic processes Markov processes

Published online by Cambridge University Press:  14 July 2016

Paul Fearnhead
Paul Fearnhead*
Affiliation:
University of Oxford
*
∗ Postal address: Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster LA1 4YW, UK. Email address: p.fearnhead@lancaster.ac.uk
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Abstract

We consider a nonneutral population genetics model with parent-independent mutations and two selective classes. We calculate the stationary distribution of the type of the common ancestor of a sample of genes from this model. The expected fitness of any ancestor (including the most recent common ancestor of any sample) is shown to be greater than the expected fitness of a randomly chosen gene from the population. The process of mutations to the common ancestor is also analysed. Our results are related to, but more general than, results obtained from diffusion theory.

Keywords

Ancestral selection graphcommon ancestorfitnessfixationparent-independent mutations

MSC classification

Primary: 60J05: Discrete-time Markov processes on general state spaces 92D10: Genetics
Secondary: 60G10: Stationary processes

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 1 , March 2002 , pp. 38 - 54
Copyright
Copyright © Applied Probability Trust 2002 

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