Review: A General Empirical Model of Protein Evolution Derived from Multiple Protein Families Using a Maximum-Likelihood Approach

Citation

• Whelan, S., & Goldman, N. (2001). A general empirical model of protein evolution derived from multiple protein families using a maximum-likelihood approach. Molecular Biology and Evolution, 18(5), 691–699.
• DOI

Abstract

An empirical model of amino acid substitution, WAG, is estimated from a large collection of protein families using a maximum-likelihood approach. The model provides a better fit than the widely used JTT matrix and is recommended for general use in protein phylogenetics.

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The WAG (Whelan and Goldman) matrix was, at the time of publication, the most statistically rigorous empirically derived amino acid substitution matrix available. It was estimated from a training set of 182 protein families and 182,926 aligned amino acid pairs, using maximum-likelihood estimation under the general time-reversible model.

The WAG matrix improved on JTT in two respects: it was derived from a much larger dataset, and the estimation method (maximum likelihood rather than counting transitions) better accounts for multiple substitutions along a branch and unequal usage of amino acids. Like all empirical matrices, WAG provides time-reversible exchangeabilities \( r_{ij} = r_{ji} \) along with a set of stationary amino acid frequencies.

For several years, WAG was the recommended default for protein phylogenetic analysis. It was superseded for most applications by LG (Le and Gascuel 2008; see Le & Gascuel 2008), which was estimated from a substantially larger and more diverse training set.

In Hifuku, WAG is one of the built-in fixed-rate matrices. It remains useful as a reference model and for datasets from biological contexts (e.g., mitochondrial proteins) where WAG may outperform LG, and for compatibility with analyses previously run with WAG.