Importance sampling on coalescent histories. II: Subdivided population models

Journal article

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. © Applied Probability Trust 2004.

Authors: De Iorio, M; Griffiths, R

• Publication status: Published
• Journal: ADVANCES IN APPLIED PROBABILITY
• Volume: 36
• Issue: 2
• Pages: 434-454
• Publication date: 2004-06-01
• DOI: 10.1239/aap/1086957580
• ISSN: 0001-8678
• Language: English
• Keywords: diffusion process; coalescent process; subdivided population; migration; importance sampling