Open Access Open Badges Research article

Comparison of methods for estimating the nucleotide substitution matrix

Maribeth Oscamou1, Daniel McDonald2, Von Bing Yap3, Gavin A Huttley4, Manuel E Lladser1 and Rob Knight5*

Author Affiliations

1 Department of Applied Mathematics, University of Colorado, Boulder, CO, USA

2 Department of Computer Science, University of Colorado, Boulder, CO, USA

3 Department of Statistics and Applied Probability, National University of Singapore, 21 Lower Kent Ridge Road 119077, Singapore

4 John Curtin School of Medical Research, Australian National University, Canberra, Australia

5 Department of Chemistry & Biochemistry, University of Colorado, Boulder, CO, USA

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BMC Bioinformatics 2008, 9:511  doi:10.1186/1471-2105-9-511

Published: 1 December 2008



The nucleotide substitution rate matrix is a key parameter of molecular evolution. Several methods for inferring this parameter have been proposed, with different mathematical bases. These methods include counting sequence differences and taking the log of the resulting probability matrices, methods based on Markov triples, and maximum likelihood methods that infer the substitution probabilities that lead to the most likely model of evolution. However, the speed and accuracy of these methods has not been compared.


Different methods differ in performance by orders of magnitude (ranging from 1 ms to 10 s per matrix), but differences in accuracy of rate matrix reconstruction appear to be relatively small. Encouragingly, relatively simple and fast methods can provide results at least as accurate as far more complex and computationally intensive methods, especially when the sequences to be compared are relatively short.


Based on the conditions tested, we recommend the use of method of Gojobori et al. (1982) for long sequences (> 600 nucleotides), and the method of Goldman et al. (1996) for shorter sequences (< 600 nucleotides). The method of Barry and Hartigan (1987) can provide somewhat more accuracy, measured as the Euclidean distance between the true and inferred matrices, on long sequences (> 2000 nucleotides) at the expense of substantially longer computation time. The availability of methods that are both fast and accurate will allow us to gain a global picture of change in the nucleotide substitution rate matrix on a genomewide scale across the tree of life.