Models of sequence evolution for DNA sequences containing gaps.

Most evolutionary tree estimation methods for DNA sequences ignore or inefficiently use the phylogenetic information contained within shared patterns of gaps. This is largely due to the computational difficulties in implementing models for insertions and deletions. A simple way to incorporate this information is to treat a gap as a fifth character (with the four nucleotides being the other four) and to incorporate it within a Markov model of nucleotide substitution. This idea has been dismissed in the past, since it treats a multiple-site insertion or deletion as a sequence of independent events rather than a single event. While this is true, we have found that under many circumstances it is better to incorporate gap information inadequately than to ignore it, at least for topology estimation. We propose an extension to a class of nucleotide substitution models to incorporate the gap character and show that, for data sets (both real and simulated) with short and medium gaps, these models do lead to effective use of the information contained within insertions and deletions. We also implement an ad hoc method in which the likelihood at columns containing multiple-site gaps is downweighted in order to avoid giving them undue influence. The precision of the estimated tree, assessed using Markov chain Monte Carlo techniques to find the posterior distribution over tree space, improves under these five-state models compared with standard methods which effectively ignore gaps.