Advances in Applied Probability

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

Jens Ledet Jensen and Anne-Mette Krabbe Pedersen

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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.

Article information

Source
Adv. in Appl. Probab. Volume 32, Number 2 (2000), 499-517.

Dates
First available in Project Euclid: 12 February 2002

Permanent link to this document
http://projecteuclid.org/euclid.aap/1013540176

Digital Object Identifier
doi:10.1239/aap/1013540176

Mathematical Reviews number (MathSciNet)
MR1778577

Zentralblatt MATH identifier
0958.92024

Subjects
Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 92D20: Protein sequences, DNA sequences 62E25

Keywords
Dependent substitution rates DNA sequences Gibbs sampler Markov dynamics MCMC stationary distribution

Citation

Jensen, Jens Ledet; Pedersen, Anne-Mette Krabbe. Probabilistic models of DNA sequence evolution with context dependent rates of substitution. Adv. in Appl. Probab. 32 (2000), no. 2, 499--517. doi:10.1239/aap/1013540176. http://projecteuclid.org/euclid.aap/1013540176.


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