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Post-data inference of coalescence times and segregating-site distribution in a two-island model with symmetric migration

Part of: Markov processes

Published online by Cambridge University Press:  01 July 2016

Prakash Gorroochurn
Prakash Gorroochurn*
Affiliation:
University of Mauritius
*
∗ Postal address: Department of Mathematics, University of Mauritius, Réduit, Mauritius. Email address: gorroocp@uom.ac.mu
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Abstract

In this paper, we present the distribution of the coalescence time of two DNA sequences (or genes) subject to symmetric migration between two islands, and conditional on the observed number of segregating sites in the sequences. The distribution for the segregating-site pattern is also obtained. Some surprising results emerge when both genes are initially on the same island. First, the post-data mean coalescence time is shown to be dependent on the migration parameter, as opposed to the pre-data mean. Second, both the post-data density and expectation for the coalescence time are shown to converge, in the weak-migration limit, to the corresponding panmictic results, as opposed to the pre-data situation where there is convergence in the density but not in the expectation. Finally, it is shown that there is convergence in the weak-migration limit in the distribution of the number of segregating sites but not in the expectation and variance. Numerical and graphical results for samples of size greater than two are also presented.

Keywords

Structured coalescentsegregating sitestwo-island modelsymmetric migrationmonomorphic

MSC classification

Primary: 92D25: Population dynamics (general)
Secondary: 60J85: Applications of branching processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 33 , Issue 3 , September 2001 , pp. 600 - 616
Copyright
Copyright © Applied Probability Trust 2001 

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