In silico sequence evolution with site-specific interactions along phylogenetic trees

A biological sequence usually has many sites whose evolution depends on other positions of the sequence, but this is not accounted for by commonly used models of sequence evolution. Here we introduce a Markov model of nucleotide sequence evolution in which the instantaneous substitution rate at a site depends on the states of other sites. Based on the concept of neighbourhood systems, our model represents a universal description of arbitrarily complex dependencies among sites.