Codon and rate variation models in molecular phylogeny

This article generalizes previous models for codon substitution and rate variation in molecular phylogeny. Particular attention is paid to (1) reversibility, (2) acceptance and rejection of proposed codon changes, (3) varying rates of evolution among codon sites, and (4) the interaction of these sites in determining evolutionary rates. To accommodate spatial variation in rates, Markov random fields rather than Markov chains are introduced. Because these innovations complicate maximum likelihood estimation in phylogeny reconstruction, it is necessary to formulate new algorithms for the evaluation of the likelihood and its derivatives with respect to the underlying kinetic, acceptance, and spatial parameters. To derive the most from maximum likelihood analysis of sequence data, it is useful to compute posterior probabilities assigning residues to internal nodes and evolutionary rate classes to codon sites. It is also helpful to search through tree space in a way that respects accepted phylogenetic relationships. Our phylogeny program LINNAEUS implements algorithms realizing these goals. Readers may consult our companion article in this issue for several examples.