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Originally published as Genetics Published Articles Ahead of Print on September 2, 2005.
Genetics, Vol. 171, 1419-1436, November 2005, Copyright © 2005
doi:10.1534/genetics.104.040402
Likelihoods From Summary Statistics: Recent Divergence Between Species
Scotland C. Leman*,
Yuguo Chen*,1,
Jason E. Stajich
,
Mohamed A. F. Noor
and
Marcy K. Uyenoyama,2
* Institute of Statistics and Decision Sciences, Department of Molecular Genetics and Microbiology and Department of Biology, Duke University, Durham, North Carolina 27708
2 Corresponding author: Department of Biology, Duke University, Box 90338, Durham, NC 27708-0338.
E-mail: marcy{at}duke.edu
We describe an importance-sampling method for approximating likelihoods of population parameters based on multiple summary statistics. In this first application, we address the demographic history of closely related members of the Drosophila pseudoobscura group. We base the maximum-likelihood estimation of the time since speciation and the effective population sizes of the extant and ancestral populations on the pattern of nucleotide variation at DPS2002, a noncoding region tightly linked to a paracentric inversion that strongly contributes to reproductive isolation. Consideration of summary statistics rather than entire nucleotide sequences permits a compact description of the genealogy of the sample. We use importance sampling first to propose a genealogical and mutational history consistent with the observed array of summary statistics and then to correct the likelihood with the exact probability of the history determined from a system of recursions. Analysis of a subset of the data, for which recursive computation of the exact likelihood was feasible, indicated close agreement between the approximate and exact likelihoods. Our results for the complete data set also compare well with those obtained through Metropolis-Hastings sampling of fully resolved genealogies of entire nucleotide sequences.
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