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MBE Advance Access published online on August 5, 2008
Molecular Biology and Evolution, doi:10.1093/molbev/msn169
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© The Author 2008. 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

Research Article

Quantifying the Stationarity and Time Reversibility of the Nucleotide Substitution Process

Federico Squartini and Peter F. Arndt

Department of Computational Molecular Biology, Max Planck Institute for Molecular Genetics, Ihnestr. 63-73, 14195 Berlin, Germany

Corresponding author: Federico Squartini, tel: +49-30-8413-1157, fax: +49-30-8413-1152, email: squartin{at}molgen.mpg.de

Received for publication April 9, 2008. Revision received July 9, 2008. Accepted for publication July 27, 2008.

Markov models describing the evolution of the nucleotide substitution process, widely used in phylogeny reconstruction, usually assume the hypotheses of stationarity and time reversibility. Although these models give meaningful results when applied to biological data, it is not clear if the two assumptions mentioned above hold and, if not, how much sequence evolution processes deviate from them. To this aim we introduce two sets of indices which can be calculated from the nucleotide distribution and the substitution rates. The stationarity indices (STIs) can be used to test the validity of the equilibrium assumption. The irreversibility indices (IRIs) are derived from the Kolmogorov cycle conditions for time reversibility and quantify the degree of non time reversibility of a process. We have computed STIs and IRIs for the evolutionary process of two lineages, Drosophila simulans and Homo sapiens. In the latter case we use a modified form of the indices which takes into account the CpG decay process. In both cases we find statistically significant deviations from the ideal case of a process which has reached stationarity and is time reversible.

Key Words: Markov Models of Nucleotide Substitutions • Stationarity • Time Reversibility • Maximum Likelihood Estimation • CpG Effect


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