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Importance sampling on coalescent histories. II: Subdivided population models

Part of: Stochastic processes Stochastic systems and control

Published online by Cambridge University Press:  01 July 2016

Maria De Iorio  and
Robert C. Griffiths
Maria De Iorio*
Affiliation:
Imperial College London
Robert C. Griffiths*
Affiliation:
University of Oxford
*
∗ Postal address: Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2BZ, UK
∗∗ Postal address: Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, UK. Email address: griff@stats.ox.ac.uk
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Abstract

De Iorio and Griffiths (2004) developed a new method of constructing sequential importance-sampling proposal distributions on coalescent histories of a sample of genes for computing the likelihood of a type configuration of genes in the sample by simulation. The method is based on approximating the diffusion-process generator describing the distribution of population gene frequencies, leading to an approximate sample distribution and finally to importance-sampling proposal distributions. This paper applies that method to construct an importance-sampling algorithm for computing the likelihood of samples of genes in subdivided population models. The importance-sampling technique of Stephens and Donnelly (2000) is thus extended to models with a Markov chain mutation mechanism between gene types and migration of genes between subpopulations. An algorithm for computing the likelihood of a sample configuration of genes from a subdivided population in an infinitely-many-alleles model of mutation is derived, extending Ewens's (1972) sampling formula in a single population. Likelihood calculation and ancestral inference in gene trees constructed from DNA sequences under the infinitely-many-sites model are also studied. The Griffiths-Tavaré method of likelihood calculation in gene trees of Bahlo and Griffiths (2000) is improved for subdivided populations.

Keywords

Coalescent processdiffusion processimportance samplingmigrationsubdivided population

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Secondary: 93E25: Other computational methods 92D25: Population dynamics (general)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 36 , Issue 2 , June 2004 , pp. 434 - 454
Copyright
Copyright © Applied Probability Trust 2004 

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Footnotes

Supported by BBSRC Bioinformatics grant 43/BIO14435.

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