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.
We show that the combination of a dependency scheme at the ancestral root sequence and a context-dependent evolutionary model across the remainder of the tree allows for accurate estimation of the model's parameters.
Indeed, while the context-dependent models presented in the two previous sections impose a dependency scheme at the third codon position across the underlying tree, it does not in any way impose a dependency pattern at the ancestral root of the underlying phylogenetic tree.
However, it is realistic to expect that this approach will be less optimal in terms of model fit, so we did not attempt to include this dependency scheme.
To ensure a dependency scheme across the entire underlying phylogenetic tree, we therefore allow for different ancestral root distributions for the third codon position.
This completes the dependency scheme across the entire tree so that the evolution at every nucleotide, ancestral or observed, is allowed to depend on other nucleotides.
