  Traditionally, phylogeny and sequence alignment are estimated separately:
first estimate a multiple sequence alignment and then infer a phylogeny based
on the sequence alignment estimated in the previous step. However, uncertainty
in the alignment estimation is ignored, resulting, possibly, in overstated
certainty in phylogeny estimates. We develop a joint model for co-estimating
phylogeny and sequence alignment which improves estimates from the traditional
approach by accounting for uncertainty in the alignment in phylogenetic
inferences. Our insertion and deletion (indel) model allows arbitrary-length
overlapping indel events and a general distribution for indel fragment size. We
employ a Bayesian approach using MCMC to estimate the joint posterior
distribution of a phylogenetic tree and a multiple sequence alignment. Our
approach has a tree and a complete history of indel events mapped onto the tree
as the state space of the Markov Chain while alternative previous approaches
have a tree and an alignment. A large state space containing a complete history
of indel events makes our MCMC approach more challenging, but it enables us to
infer more information about the indel process. The performances of this joint
method and traditional sequential methods are compared using simulated data as
well as real data. Software named BayesCAT (Bayesian Co-estimation of Alignment
and Tree) is available at https://github.com/heejungshim/BayesCAT.
