Model Averaging and Bayes Factor Calculation of Relaxed Molecular Clocks in Bayesian Phylogenetics

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Abstract
We describe a procedure for model averaging of relaxed molecular clock models in Bayesian phylogenetics. Our approach allows us to model the distribution of rates of substitution across branches, averaged over a set of models, rather than conditioned on a single model. We implement this procedure and test it on simulated data to show that our method can accurately recover the true underlying distribution of rates. We applied the method to a set of alignments taken from a data set of 12 mammalian species and uncovered evidence that lognormally distributed rates better describe this data set than do exponentially distributed rates. Additionally, our implementation of model averaging permits accurate calculation of the Bayes factor(s) between two or more relaxed molecular clock models. Finally, we introduce a new computational approach for sampling rates of substitution across branches that improves the convergence of our Markov chain Monte Carlo algorithms in this context. Our methods are implemented under the BEAST 1.6 software package, available at http://beast-mcmc.googlecode.com.