Journal of Applied Probability

Duality between the two-locus Wright–Fisher diffusion model and the ancestral process with recombination

Shuhei Mano

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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.

Article information

J. Appl. Probab., Volume 50, Number 1 (2013), 256-271.

First available in Project Euclid: 20 March 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx] 92D15: Problems related to evolution 92D25: Population dynamics (general)

duality diffusion process ancestral graph recombination population genetics


Mano, Shuhei. Duality between the two-locus Wright–Fisher diffusion model and the ancestral process with recombination. J. Appl. Probab. 50 (2013), no. 1, 256--271. doi:10.1239/jap/1363784437.

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