MrBayes 3 performs Bayesian phylogenetic analysis combining information from different data partitions or subsets evolving under different stochastic evolutionary models. This allows the user to analyze heterogeneous data sets consisting of different data types-e.g. morphological, nucleotide, and protein-and to explore a wide variety of structured models mixing partition-unique and shared parameters. The program employs MPI to parallelize Metropolis coupling on Macintosh or UNIX clusters.

Since its introduction in 2001, MrBayes has grown in popularity as a software package for Bayesian phylogenetic inference using Markov chain Monte Carlo (MCMC) methods. With this note, we announce the release of version 3.2, a major upgrade to the latest official release presented in 2003. The new version provides convergence diagnostics and allows multiple analyses to be run in parallel with convergence progress monitored on the fly. The introduction of new proposals and automatic optimization of tuning parameters has improved convergence for many problems. The new version also sports significantly faster likelihood calculations through streaming single-instruction-multiple-data extensions (SSE) and support of the BEAGLE library, allowing likelihood calculations to be delegated to graphics processing units (GPUs) on compatible hardware. Speedup factors range from around 2 with SSE code to more than 50 with BEAGLE for codon problems. Checkpointing across all models allows long runs to be completed even when an analysis is prematurely terminated. New models include relaxed clocks, dating, model averaging across time-reversible substitution models, and support for hard, negative, and partial (backbone) tree constraints. Inference of species trees from gene trees is supported by full incorporation of the Bayesian estimation of species trees (BEST) algorithms. Marginal model likelihoods for Bayes factor tests can be estimated accurately across the entire model space using the stepping stone method. The new version provides more output options than previously, including samples of ancestral states, site rates, site dN/dS rations, branch rates, and node dates. A wide range of statistics on tree parameters can also be output for visualization in FigTree and compatible software.

MRBAYES, including the source code, documentation, sample data files, and an executable, is available at http://brahms.biology.rochester.edu/software.html.

As a discipline, phylogenetics is becoming transformed by a flood of molecular data. These data allow broad questions to be asked about the history of life, but also present difficult statistical and computational problems. Bayesian inference of phylogeny brings a new perspective to a number of outstanding issues in evolutionary biology, including the analysis of large phylogenetic trees and complex evolutionary models and the detection of the footprint of natural selection in DNA sequences.

The recent development of Bayesian phylogenetic inference using Markov chain Monte Carlo (MCMC) techniques has facilitated the exploration of parameter-rich evolutionary models. At the same time, stochastic models have become more realistic (and complex) and have been extended to new types of data, such as morphology. Based on this foundation, we developed a Bayesian MCMC approach to the analysis of combined data sets and explored its utility in inferring relationships among gall wasps based on data from morphology and four genes (nuclear and mitochondrial, ribosomal and protein coding). Examined models range in complexity from those recognizing only a morphological and a molecular partition to those having complex substitution models with independent parameters for each gene. Bayesian MCMC analysis deals efficiently with complex models: convergence occurs faster and more predictably for complex models, mixing is adequate for all parameters even under very complex models, and the parameter update cycle is virtually unaffected by model partitioning across sites. Morphology contributed only 5% of the characters in the data set but nevertheless influenced the combined-data tree, supporting the utility of morphological data in multigene analyses. We used Bayesian criteria (Bayes factors) to show that process heterogeneity across data partitions is a significant model component, although not as important as among-site rate variation. More complex evolutionary models are associated with more topological uncertainty and less conflict between morphology and molecules. Bayes factors sometimes favor simpler models over considerably more parameter-rich models, but the best model overall is also the most complex and Bayes factors do not support exclusion of apparently weak parameters from this model. Thus, Bayes factors appear to be useful for selecting among complex models, but it is still unclear whether their use strikes a reasonable balance between model complexity and error in parameter estimates.

DNA sequences and other molecular data compared among organisms may contain phylogenetic signal, or they may be randomized with respect to phylogenetic history. Some method is needed to distinguish phylogenetic signal from random noise to avoid analysis of data that have been randomized with respect to the historical relationships of the taxa being compared. We analyzed 8,000 random data matrices consisting of 10-500 binary or four-state characters and 5-25 taxa to study several options for detecting signal in systematic data bases. Analysis of random data often yields a single most-parsimonious tree, especially if the number of characters examined is large and the number of taxa examined is small (both often true in molecular studies). The most-parsimonious tree inferred from random data may also be considerably shorter than the second-best alternative. The distribution of tree lengths of all tree topologies (or a random sample thereof) provides a sensitive measure of phylogenetic signal: data matrices with phylogenetic signal produce tree-length distributions that are strongly skewed to the left, whereas those composed of random noise are closer to symmetrical. In simulations of phylogeny with varying rates of mutation (up to levels that produce random variation among taxa), the skewness of tree-length distributions is closely related to the success of parsimony in finding the true phylogeny. Tables of critical values of a skewness test statistic, g1, are provided for binary and four-state characters for 10-500 characters and 5-25 taxa. These tables can be used in a rapid and efficient test for significant structure in data matrices for phylogenetic analysis.

Time-calibrated species phylogenies are critical for addressing a wide range of questions in evolutionary biology, such as those that elucidate historical biogeography or uncover patterns of coevolution and diversification. Because molecular sequence data are not informative on absolute time, external data-most commonly, fossil age estimates-are required to calibrate estimates of species divergence dates. For Bayesian divergence time methods, the common practice for calibration using fossil information involves placing arbitrarily chosen parametric distributions on internal nodes, often disregarding most of the information in the fossil record. We introduce the "fossilized birth-death" (FBD) process-a model for calibrating divergence time estimates in a Bayesian framework, explicitly acknowledging that extant species and fossils are part of the same macroevolutionary process. Under this model, absolute node age estimates are calibrated by a single diversification model and arbitrary calibration densities are not necessary. Moreover, the FBD model allows for inclusion of all available fossils. We performed analyses of simulated data and show that node age estimation under the FBD model results in robust and accurate estimates of species divergence times with realistic measures of statistical uncertainty, overcoming major limitations of standard divergence time estimation methods. We used this model to estimate the speciation times for a dataset composed of all living bears, indicating that the genus Ursus diversified in the Late Miocene to Middle Pliocene.A phylogenetic analysis of species has two goals: to infer the evolutionary relationships and the amount of divergence among species. Preferably, divergence is estimated in units proportional to time, thus revealing the times at which speciation events occurred. Once orthologous DNA sequences from the species have been aligned, both goals can be accomplished by assuming that nucleotide substitutions occur at the same rate in all lineages [the "molecular clock" assumption (1)] and that the time of at least one speciation event on the tree is known, i.e., one speciation event acts to "calibrate" the substitution rate.The goal of reconstructing rooted, time-calibrated phylogenies is complicated by substitution rates changing over the tree and by the difficulty of determining the date of any speciation event. Substitution rate variation among lineages is pervasive and has been accommodated in several ways. The most widely used method to account for rate heterogeneity is to assign an independent parameter to each branch of the tree. Branch lengths, then, are the product of substitution rate and time, and usually measured in units of expected number of substitutions per site. This solution allows estimation of the tree topology-which is informative about interspecies relationships-but does not attempt to estimate the rate and time separately. Thus, under this "unconstrained" parameterization, molecular sequence data allow inference of phylogenetic relationships and ge...

Programs for Bayesian inference of phylogeny currently implement a unique and fixed suite of models. Consequently, users of these software packages are simultaneously forced to use a number of programs for a given study, while also lacking the freedom to explore models that have not been implemented by the developers of those programs. We developed a new open-source software package, RevBayes, to address these problems. RevBayes is entirely based on probabilistic graphical models, a powerful generic framework for specifying and analyzing statistical models. Phylogenetic-graphical models can be specified interactively in RevBayes, piece by piece, using a new succinct and intuitive language called Rev. Rev is similar to the R language and the BUGS model-specification language, and should be easy to learn for most users. The strength of RevBayes is the simplicity with which one can design, specify, and implement new and complex models. Fortunately, this tremendous flexibility does not come at the cost of slower computation; as we demonstrate, RevBayes outperforms competing software for several standard analyses. Compared with other programs, RevBayes has fewer black-box elements. Users need to explicitly specify each part of the model and analysis. Although this explicitness may initially be unfamiliar, we are convinced that this transparency will improve understanding of phylogenetic models in our field. Moreover, it will motivate the search for improvements to existing methods by brazenly exposing the model choices that we make to critical scrutiny. RevBayes is freely available at http://www.RevBayes.com. [Bayesian inference; Graphical models; MCMC; statistical phylogenetics.]