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MBE Advance Access published online on October 20, 2006

Molecular Biology and Evolution, doi:10.1093/molbev/msl155
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© The Author 2006. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org
Accepted October 17, 2006

Research Article

Testing for Covarion-like Evolution in Protein Sequences

Huai-Chun Wang 1 *, Matthew Spencer 2, Edward Susko 3, and Andrew J. Roger 4

1 Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 3J5; Department of Biochemistry and Molecular Biology, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 4H7; Canadian Institute for Advanced Research, Program in Evolutionary Biology
2 Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 3J5; Department of Biochemistry and Molecular Biology, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 4H7; Canadian Institute for Advanced Research, Program in Evolutionary Biology; School of Biological Sciences, University of Liverpool, Crown Street, Liverpool, L69 7ZB, UK
3 Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 3J5; Canadian Institute for Advanced Research, Program in Evolutionary Biology
4 Department of Biochemistry and Molecular Biology, Dalhousie University, Halifax, Nova Scotia, Canada, B3H 4H7; Canadian Institute for Advanced Research, Program in Evolutionary Biology

* To whom correspondence should be addressed.
Huai-Chun Wang, E-mail: hcwang{at}mathstat.dal.ca


   Abstract

The covarion hypothesis of molecular evolution proposes that selective pressures on an amino acid or nucleotide site change through time, thus causing changes of evolutionary rate along the edges of a phylogenetic tree. Several kinds of Markov models for the covarion process have been proposed. One, proposed by Huelsenbeck (2002), has two substitution rate classes: the substitution process at a site can switch between a single variable rate, drawn from a discrete gamma distribution, and a zero invariable rate. A second model, suggested by Galtier (2001), assumes rate switches among an arbitrary number of rate classes but switching to and from the invariable rate class is not allowed. The latter model allows for some sites that do not participate in the rate switching process. Here we propose a general covarion model that combines features of both models, allowing evolutionary rates not only to switch between variable and invariable classes, but also to switch among different rates when they are in a variable state. We have implemented all three covarion models in a maximum likelihood framework for amino acid sequences and tested them on 23 protein data sets. We found significant likelihood increases for all data sets for the three models, compared to a model that does not allow site-specific rate switches along the tree. Furthermore, we found that the general model fit the data better than the simpler covarion models in the majority of the cases, highlighting the complexity in modeling the covarion process. The general covarion model can be used for comparing tree topologies, molecular dating studies and the investigation of protein adaptation.

Keywords: covarion; heterotachy; evolutionary rate; Markov model; maximum likelihood; likelihood ratio.
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