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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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

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

First available in Project Euclid: 12 February 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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