Bioinformatics Advance Access published online on February 24, 2005
Bioinformatics, doi:10.1093/bioinformatics/bti177
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1 Department of Statistics, 1 South Parks Road, Oxford OX1 3TG, UK
* To whom correspondence should be addressed.
Motivation: The Expectation Maximisation algorithm, in the form of the Baum-Welch algorithm (for HMMs) or the Inside-Outside algorithm (for SCFGs), is a powerful way to estimate the parameters of stochastic grammars for biological sequence analysis. To use this algorithm for multiplesequence evolutionary modeling, it would be useful to apply the EM algorithm to estimate not just the probability parameters of the stochastic grammar, but also the instantaneous mutation rates of the underlying evolutionary model (to facilitate the development of stochastic grammars based on phylogenetic trees, also known as Statistical Alignment). Recently, we showed how to do this for the point substitution component of the evolutionary process; here, we extend these results to the indel process. Results: We present an algorithm for maximum likelihood estimation of insertion and deletion rates from multiple sequence alignments, using Expectation Maximisation, under the single-residue indel model due to Thorne, Kishino and Felsenstein (the "TKF91" model). The algorithm converges extremely rapidly, gives accurate results on simulated data that are an improvement over parsimonious estimates (which are shown to underestimate the true indel rate), and gives plausible results on experimental data (coronavirus envelope domains). Due to the algorithm's close similarity to the Baum-Welch algorithm for training Hidden Markov Models, it can be used in an "unsupervised" fashion to estimate rates for unaligned sequences, or estimate several sets of rates for sequences with heterogenous rates. Availability: Software implementing the algorithm and the benchmark is available under GPL from http://www.biowiki.org/.
Received July 20, 2004
Revised November 19, 2004
Accepted November 22, 2004
Article
Using evolutionary Expectation Maximisation to estimate indel rates
Ian Holmes, E-mail: ihh{at}berkeley.edu
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