A new semiempirical codon substitution model based on principal component analysis of mammalian sequences

Codon substitution models have traditionally been parametric Markov models, but recently, empirical and semiempirical models also have been proposed. Parametric codon models are typically based on 61×61 rate matrices that are derived from a small number of parameters. These parameters are rooted in experience and theoretical considerations and generally show good performance but are still relatively arbitrary. We have previously used principal component analysis (PCA) on data obtained from mammalian sequence alignments to empirically identify the most relevant parameters for codon substitution models, thereby confirming some commonly used parameters but also suggesting new ones. Here, we present a new semiempirical codon substitution model that is directly based on those PCA results. The substitution rate matrix is constructed from linear combinations of the first few (the most important) principal components with the coefficients being free model parameters. Thus, the model is not only based on empirical rates but also uses the empirically determined most relevant parameters for a codon model to adjust to the particularities of individual data sets. In comparisons against established parametric and semiempirical models, the new model consistently achieves the highest likelihood values when applied to sequences of vertebrates, which include the taxonomic class where the model was trained on.