RNA sequence evolution with secondary structure constraints: comparison of substitution rate models using maximum-likelihood methods

We test models for the evolution of helical regions of RNA sequences, where the base pairing constraint leads to correlated compensatory substitutions occurring on either side of the pair. These models are of three types: 6-state models include only the four Watson-Crick pairs plus GU and UG; 7-state models include a single mismatch state that combines all of the 10 possible mismatches; 16-state models treat all mismatch states separately. We analyzed a set of eubacterial ribosomal RNA sequences with a well-established phylogenetic tree structure. For each model, the maximum-likelihood values of the parameters were obtained. The models were compared using the Akaike information criterion, the likelihood-ratio test, and Cox's test. With a high significance level, models that permit a nonzero rate of double substitutions performed better than those that assume zero double substitution rate. Some models assume symmetry between GC and CG, between AU and UA, and between GU and UG. Models that relaxed this symmetry assumption performed slightly better, but the tests did not all agree on the significance level. The most general time-reversible model significantly outperformed any of the simplifications. We consider the relative merits of all these models for molecular phylogenetics.