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Markov-Modulated Markov Chains and the Covarion Process of Molecular Evolution

Nicolas Galtier 1 Alain Jean-Marie 2, 3
2 MAESTRO - Models for the performance analysis and the control of networks
CRISAM - Inria Sophia Antipolis - Méditerranée
3 APR - Algorithmes et Performance des Réseaux
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : The covarion (or site specific rate variation, SSRV) process of biological sequence evolution is a process by which the evolutionary rate of a nucleotide/amino acid/codon position can change in time. In this paper, we introduce time-continuous, space-discrete, Markov-modulated Markov chains as a model for representing SSRV processes, generalizing existing theory to any model of rate change. We propose a fast algorithm for diagonalizing the generator matrix of relevant Markov-modulated Markov processes. This algorithm makes phylogeny likelihood calculation tractable even for a large number of rate classes and a large number of states, so that SSRV models become applicable to amino acid or codon sequence datasets. Using this algorithm, we investigate the accuracy of the discrete approximation to the Gamma distribution of evolutionary rates, widely used in molecular phylogeny. We show that a relatively large number of classes is required to achieve accurate approximation of the exact likelihood when the number of analyzed sequences exceeds 20, both under the SSRV and among site rate variation (ASRV) models.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00108559
Contributor : Christine Carvalho de Matos <>
Submitted on : Monday, October 23, 2006 - 7:43:12 AM
Last modification on : Friday, September 18, 2020 - 2:34:35 PM

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Nicolas Galtier, Alain Jean-Marie. Markov-Modulated Markov Chains and the Covarion Process of Molecular Evolution. Journal of Computational Biology, Mary Ann Liebert, 2004, 11 (4), pp.727-733. ⟨10.1089/1066527041887339⟩. ⟨lirmm-00108559⟩

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