Likelihoods from summary statistics: Recent divergence between species

¹ Duke University
² University of Illinois at Urbana-Champaign

^* To whom correspondence should be addressed. E-mail: marcy{at}duke.edu.

Submitted on December 29, 2004
Revised on April 22, 2005
Accepted on 5 August 2005

	Abstract

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 dataset also compare well with those obtained through Metropolis-Hastings sampling of fully resolved genealogies of entire nucleotide sequences.

Key Words: importance sampling, maximum likelihood, population structure, speciation time

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