A Markov chain model of coalescence with recombination
type: Item
instance of: scholarly article
title: A Markov chain model of coalescence with recombination
zbMATH Open document ID: 0908.92024
author: Katy L. Simonsen
author: Gary A. Churchill
published in: Theoretical Population Biology
publication date: 1999-03-02T00:00:00Z
full work available at URL: https://hdl.handle.net/1813/31986
review text: A model of sequence evolution is described that includes the recombination rate as a free parameter and which is applied to study the effects of recombination on the sampling properties of DNA sequences. A Markov chain model to derive the exact probability distribution of the number of recombination events for a sample of size two (n=2) in the two-locus case (m=2) was used. This case was amenable to exact analytic results because it involves only nine sites. A similar approach might be used to derive results for other small values of ''m'' and ''n'', but the number of states, and the complexity of the analysis, grow very quickly. For n=2 and m=2 a discrete-time Markov chain was used and a key result is the probability distribution of the number to each state. From this distribution the probability distribution of the number of recombination events in the the history of the sample is derived, and the joint distribution of tree times at two loci. Both of these have implications for statistical properties of DNA sequences. The Markov chain model generalizes to any ''n'' and ''m''; this model is a straightforward and computationally useful tool. The computer program consists of repeating three basic steps: 1. In the current state, determine the probabilities of moving to any other state; 2. Randomly choose the next state; 3. Update the current state. Many interesting properties of DNA sequences, such as those depending on tree times or the number of recombination events, may be studied using simulations of the simpler Markov chain, with no topology information.
Mathematics Subject Classification ID: 92D15
Mathematics Subject Classification ID: 60J20
Mathematics Subject Classification ID: 92D20
zbMATH DE Number: 1092892
zbMATH Keywords: DNA sequences
zbMATH Keywords: recombination
zbMATH Keywords: Markov chains
zbMATH Keywords: statistical properties
reviewed by: Fatima T. Adylova
describes a project that uses: Maple
MaRDI profile type: Publication
OpenAlex ID: W2021773601
Wikidata QID: Q52257964
cites work: Distribution of genome shared IBD by half-sibs: Approximation by the Poisson clumping heuristic
cites work: Q4002421
cites work: Neutral two-locus multiple allele models with recombination
cites work: Properties of a neutral allele model with intragenic recombination
cites work: The use of sample genealogies for studying a selectively neutral m-loci model with recombination
DOI: 10.1006/TPBI.1997.1307
description: scientific article; zbMATH DE number 1092892