SUMMARY: The program MRBAYES performs Bayesian inference of phylogeny using a variant of Markov chain Monte Carlo. AVAILABILITY: MRBAYES, including the source code, documentation, sample data files, and an executable, is available at http://brahms.biology.rochester.edu/software.html.

A new method is presented for inferring evolutionary trees using nucleotide sequence data. The birth-death process is used as a model of speciation and extinction to specify the prior distribution of phylogenies and branching times. Nucleotide substitution is modeled by a continuous-time Markov process. Parameters of the branching model and the substitution model are estimated by maximum likelihood. The posterior probabilities of different phylogenies are calculated and the phylogeny with the highest posterior probability is chosen as the best estimate of the evolutionary relationship among species. We refer to this as the maximum posterior probability (MAP) tree. The posterior probability provides a natural measure of the reliability of the estimated phylogeny. Two example data sets are analyzed to infer the phylogenetic relationship of human, chimpanzee, gorilla, and orangutan. The best trees estimated by the new method are the same as those from the maximum likelihood analysis of separate topologies, but the posterior probabilities are quite different from the bootstrap proportions. The results of the method are found to be insensitive to changes in the rate parameter of the branching process.

We present a statistical graphical model to infer specific molecular function for unannotated protein sequences using homology. Based on phylogenomic principles, SIFTER (Statistical Inference of Function Through Evolutionary Relationships) accurately predicts molecular function for members of a protein family given a reconciled phylogeny and available function annotations, even when the data are sparse or noisy. Our method produced specific and consistent molecular function predictions across 100 Pfam families in comparison to the Gene Ontology annotation database, BLAST, GOtcha, and Orthostrapper. We performed a more detailed exploration of functional predictions on the adenosine-5′-monophosphate/adenosine deaminase family and the lactate/malate dehydrogenase family, in the former case comparing the predictions against a gold standard set of published functional characterizations. Given function annotations for 3% of the proteins in the deaminase family, SIFTER achieves 96% accuracy in predicting molecular function for experimentally characterized proteins as reported in the literature. The accuracy of SIFTER on this dataset is a significant improvement over other currently available methods such as BLAST (75%), GeneQuiz (64%), GOtcha (89%), and Orthostrapper (11%). We also experimentally characterized the adenosine deaminase from Plasmodium falciparum, confirming SIFTER?s prediction. The results illustrate the predictive power of exploiting a statistical model of function evolution in phylogenomic problems. A software implementation of SIFTER is available from the authors.

Several methods have been proposed to infer the states at the ancestral nodes on a phylogeny. These methods assume a specific tree and set of branch lengths when estimating the ancestral character state. Inferences of the ancestral states, then, are conditioned on the tree and branch lengths being true. We develop a hierarchical Bayes method for inferring the ancestral states on a tree. The method integrates over uncertainty in the tree, branch lengths, and substitution model parameters by using Markov chain Monte Carlo. We compare the hierarchical Bayes inferences of ancestral states with inferences of ancestral states made under the assumption that a specific tree is correct. We find that the methods are correlated, but that accommodating uncertainty in parameters of the phylogenetic model can make inferences of ancestral states even more uncertain than they would be in an empirical Bayes analysis.