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Computation 2015, 3(4), 701-713;

Exact Likelihood Calculation under the Infinite Sites Model

Faculty of Health Studies, University of Bradford, Bradford BD71DP, UK
Bradford Institute for Health Research, Bradford Teaching Hospitals NHS Foundation Trust, Bradford BD96RJ, UK
Department of Statistics and Operations Research, University of Vienna, 1090 Vienna, Austria
Institute of Applied Statistics, Johannes Kepler University Linz, 4040 Linz, Austria
Institute of Animal Breeding and Genetics, University of Veterinary Medicine Vienna, Veterinärplatz 1, 1210 Vienna, Austria
Author to whom correspondence should be addressed.
Academic Editor: Rainer Breitling
Received: 1 September 2015 / Revised: 30 November 2015 / Accepted: 2 December 2015 / Published: 11 December 2015
(This article belongs to the Section Computational Biology)
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A key parameter in population genetics is the scaled mutation rate θ = 4 N μ , where N is the effective haploid population size and μ is the mutation rate per haplotype per generation. While exact likelihood inference is notoriously difficult in population genetics, we propose a novel approach to compute a first order accurate likelihood of θ that is based on dynamic programming under the infinite sites model without recombination. The parameter θ may be either constant, i.e., time-independent, or time-dependent, which allows for changes of demography and deviations from neutral equilibrium. For time-independent θ, the performance is compared to the approach in Griffiths and Tavaré’s work “Simulating Probability Distributions in the Coalescent” (Theor. Popul. Biol. 1994, 46, 131–159) that is based on importance sampling and implemented in the “genetree” program. Roughly, the proposed method is computationally fast when n × θ < 100 , where n is the sample size. For time-dependent θ ( t ) , we analyze a simple demographic model with a single change in θ ( t ) . In this case, the ancestral and current θ need to be estimated, as well as the time of change. To our knowledge, this is the first accurate computation of a likelihood in the infinite sites model with non-equilibrium demography. View Full-Text
Keywords: likelihood inference; population genetics; dynamic programming; scaled mutation rate; population demography likelihood inference; population genetics; dynamic programming; scaled mutation rate; population demography

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Faisal, M.; Futschik, A.; Vogl, C. Exact Likelihood Calculation under the Infinite Sites Model. Computation 2015, 3, 701-713.

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