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Coalescence times and FST values in subdivided populations with symmetric structure

Part of: Markov processes Graph theory

Published online by Cambridge University Press:  01 July 2016

Hilde M. Wilkinson-Herbots
Hilde M. Wilkinson-Herbots*
Affiliation:
University College London
*
∗ Postal address: Department of Statistical Science, University College London, Gower Street, London WC1E 6BT, UK. Email address: hh@stats.ucl.ac.uk
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Abstract

The structured coalescent is a continuous-time Markov chain which describes the genealogy of a sample of homologous genes from a subdivided population. Assuming this model, some results are proved relating to the genealogy of a pair of genes and the extent of subpopulation differentiation, which are valid under certain graph-theoretic symmetry and regularity conditions on the structure of the population. We first review and extend earlier results stating conditions under which the mean time since the most recent common ancestor of a pair of genes from any single subpopulation is independent of the migration rate and equal to that of two genes from an unstructured population of the same total size. Assuming the infinite alleles model of neutral mutation with a small mutation rate, we then prove a simple relationship between the migration rate and the value of Wright's coefficient FST for a pair of neighbouring subpopulations, which does not depend on the precise structure of the population provided that this is sufficiently symmetric.

Keywords

Structured coalescentgenealogysubpopulation differentiationF-statisticsgraph theoryMarkov chain

MSC classification

Primary: 92D10: Genetics
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 05C90: Applications
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 35 , Issue 3 , September 2003 , pp. 665 - 690
Copyright
Copyright © Applied Probability Trust 2003 

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