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A fundamental problem in evolutionary biology is determining evolutionary relationships among different taxa. Genome arrangement data is potentially more informative than DNA sequence data in cases where alignment of DNA sequences is highly uncertain. We describe a Bayesian framework for phylogenetic inference from mitochondrial genome arrangement data that uses Markov chain Monte Carlo (MCMC) as the computational engine for inference. Our approach is to model mitochondrial data as a circular signed permutation which is subject to reversals. We calculate the likelihood of one arrangement mutating into another along a single branch by counting the number of possible sequences of reversals which transform the first to the second. We calculate the likelihood of the entire tree by augmenting the state space with the arrangements at the branching points of the tree. We use MCMC to update both the tree and the arrangement data at the branching points.

Phylogenetic Inference from Mitochondrial Genome Arrangement Data