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Probabilistic models of DNA sequence evolution with context dependent rates of substitution

Part of: Markov processes

Published online by Cambridge University Press:  19 February 2016

Jens Ledet Jensen  and
Anne-Mette Krabbe Pedersen
Jens Ledet Jensen*
Affiliation:
Aarhus University
Anne-Mette Krabbe Pedersen*
Affiliation:
Aarhus University
*
∗ Postal address: Department of Theoretical Statistics, Institute of Mathematics, Ny Munkegade, DK-8000 Aarhus C, Denmark. Email address: [email protected]
∗∗ Postal address: Department of Genetics and Ecology, Institute of Biological Sciences, Ny Munkegade, DK-8000 Aarhus C, Denmark. Email address: [email protected]
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Abstract

We consider Markov processes of DNA sequence evolution in which the instantaneous rates of substitution at a site are allowed to depend upon the states at the sites in a neighbourhood of the site at the instant of the substitution. We characterize the class of Markov process models of DNA sequence evolution for which the stationary distribution is a Gibbs measure, and give a procedure for calculating the normalizing constant of the measure. We develop an MCMC method for estimating the transition probability between sequences under models of this type. Finally, we analyse an alignment of two HIV-1 gene sequences using the developed theory and methodology.

Keywords

Dependent substitution ratesDNA sequencesGibbs samplerMarkov dynamicsMCMCstationary distribution

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 92D20: Protein sequences, DNA sequences
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 32 , Issue 2 , June 2000 , pp. 499 - 517
Copyright
Copyright © Applied Probability Trust 2000 

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