Context-dependent codon partition models provide significant increases in model fit in atpB and rbcL protein-coding genes

Background: Accurate modelling of substitution processes in protein-coding sequences is often hampered by the computational burdens associated with full codon models. Lately, codon partition models have been proposed as a viable alternative, mimicking the substitution behaviour of codon models at a low computational cost. Such codon partition models however impose independent evolution of the different codon positions, which is overly restrictive from a biological point of view. Given that empirical research has provided indications of context-dependent substitution patterns at four-fold degenerate sites, we take those indications into account in this paper. Results: We present so-called context-dependent codon partition models to assess previous empirical claims that the evolution of four-fold degenerate sites is strongly dependent on the composition of its two flanking bases. To this end, we have estimated and compared various existing independent models, codon models, codon partition models and context-dependent codon partition models for the atpB and rbcL genes of the chloroplast genome, which are frequently used in plant systematics. Such context-dependent codon partition models employ a full dependency scheme for four-fold degenerate sites, whilst maintaining the independence assumption for the first and second codon positions. Conclusions: We show that, both in the atpB and rbcL alignments of a collection of land plants, these context-dependent codon partition models significantly improve model fit over existing codon partition models. Using Bayes factors based on thermodynamic integration, we show that in both datasets the same context-dependent codon partition model yields the largest increase in model fit compared to an independent evolutionary model. Context-dependent codon partition models hence perform closer to codon models, which remain the best performing models at a drastically increased computational cost, compared to codon partition models, but remain computationally interesting alternatives to codon models. Finally, we observe that the substitution patterns in both datasets are drastically different, leading to the conclusion that combined analysis of these two genes using a single model may not be advisable from a context-dependent point of view.