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Ancestral Graph with Bias in Gene Conversion

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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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.

Keywords

biased gene conversiondiffusion processancestral graphbiased voter model

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. 239 - 255
Copyright
Copyright © Applied Probability Trust 2013 

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