Journal of Applied Probability

Ancestral graph with bias in gene conversion

Shuhei Mano

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Abstract

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

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

Dates
First available in Project Euclid: 20 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.jap/1363784436

Digital Object Identifier
doi:10.1239/jap/1363784436

Mathematical Reviews number (MathSciNet)
MR3076784

Zentralblatt MATH identifier
06157741

Subjects
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)

Keywords
biased gene conversion diffusion process ancestral graph biased voter model

Citation

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


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