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Duality Between the Two-Locus Wright–Fisher Diffusion Model and the Ancestral Process with Recombination

Part of: Markov processes Special processes

Published online by Cambridge University Press:  30 January 2018

Shuhei Mano
Shuhei Mano*
Affiliation:
The Institute of Statistical Mathematics
*
∗ Postal address: The Institute of Statistical Mathematics and The Japan Science and Technology Agency, 10-3 Midori-cho, Tachikawa, Tokyo 190-8562, Japan. Email address: smano@ism.ac.jp
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Abstract

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Known results on the moments of the distribution generated by the two-locus Wright–Fisher diffusion model, and the duality between the diffusion process and the ancestral process with recombination are briefly summarized. A numerical method for computing moments using a Markov chain Monte Carlo simulation and a method to compute closed-form expressions of the moments are presented. By applying the duality argument, the properties of the ancestral recombination graph are studied in terms of the moments.

Keywords

dualitydiffusion processancestral graphrecombinationpopulation genetics

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) 92D15: Problems related to evolution 92D25: Population dynamics (general)
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 1 , March 2013 , pp. 256 - 271
Copyright
Copyright © Applied Probability Trust 2013 

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