Journal of Applied Probability

Ancestral graph with bias in gene conversion

Shuhei Mano

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Gene conversion is a genetic mechanism by which one gene is `copied and pasted' onto another gene, where the direction can be biased between the different types. In this paper, a stochastic model for biased gene conversion within a d-unlinked multigene family and its diffusion approximation are developed for a finite Moran population. A connection with a d-island model is made. A formula for the fixation probability in the absence of mutation is given. A two-timescale argument is applied in the case of the strong conversion limit. The dual process is generally shown to be a biased voter model, which generates an ancestral bias graph for a given sample. An importance sampling algorithm for computing the likelihood of the sample is deduced.

Article information

J. Appl. Probab., Volume 50, Number 1 (2013), 239-255.

First available in Project Euclid: 20 March 2013

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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)

biased gene conversion diffusion process ancestral graph biased voter model


Mano, Shuhei. Ancestral graph with bias in gene conversion. J. Appl. Probab. 50 (2013), no. 1, 239--255. doi:10.1239/jap/1363784436.

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