Phylogenetics aims at inferring the tree that better represents the evolutionary relationships among species studying differences and similarities in DNA sequences in different taxonomies. Alternative estimation methods have been proposed from different perspectives (Gascuel, 2004, Swafford, 2003): in this work, we deal with a stochastic model for substitution rates estimating its parameters in a fully Bayesian framework. We focus on computational tools based on MCMC sampling. For a fixed topology we evaluate the evidence of two competing models through Bayes factor. Available computational tools are compared together with a new implementation of the generalized harmonic mean approach via hyperplane inflation recently proposed in Petris and Tardella (2007). When the topology is not known in advance, we will compare more conventional transdimensional MCMC sampler based on the reversible jump approach with the alternative geometric approach proposed in Petris and Tardella (2003).
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