Although the rates at which positions in the genome mutate are known to depend not only on the nucleotide to be mutated, but also on neighboring nucleotides, it remains challenging to do phylogenetic inference using models of context-dependent mutation. In these models, the effects of one mutation may in principle propagate to faraway locations, making it difficult to compute exact likelihoods. This article shows how to use bounds on the propagation of dependency to compute likelihoods of mutation of a given segment of genome by marginalizing over sufficiently long flanking sequence. This can be used for maximum likelihood or Bayesian inference. Protocols examining residuals and iterative model refinement are also discussed. Tools for efficiently working with these models are provided in an R package, which could be used in other applications. The method is used to examine context dependence of mutations since the common ancestor of humans and chimpanzee.
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