2012 SOFTWARE FOR SYSTEMATICS AND EVOLUTION 541 Process (CPP; Huelsenbeck et al. 2000), the Thorne– Kishino 2002 (TK02; Thorne and Kishino 2002), and the Independent Gamma Rate (IGR; Lepage et al. 2007) models. The CPP model is a discrete autocorrelated model, in which rate multipliers appear on the tree according to a Poisson process. The MrBayes implementation uses a lognormal distribution for the rate multipliers instead of the modified gamma distribution proposed originally (Huelsenbeck et al. 2000). It also includes novel algo- rithms to allow sampling across tree space since the original paper only dealt with fixed trees. The TK02 model is a continuous autocorrelated model. In the particular version we implemented (Thorne and Kishino 2002), the rate of a descendant node is drawn from a lognormal distribution, the mean of which is the same as the ancestral rate and the vari- ance of which is proportional to the length of the branch (measured in expected substitutions per site at the base rate of the clock). The IGR model is a continuous uncorrelated model. First published as the “white noise” model (Lepage et al. 2007), it is similar to the uncorrelated gamma model (Drummond et al. 2006) but is mathematically more elegant in that it truly lacks time structure. In the IGR model, effective branch lengths are drawn from a gamma distribution, in which the mean is the same as, and the variance proportional to, the branch length. Dating can be achieved in MrBayes 3.2 by calibrat- ing interior or tip nodes in the tree; calibrated interior nodes need to be associated with hard constraints to be valid. Calibration points can be either fixed or associated with uncertainty. The birth–death prior model on clock trees has been expanded to incorporate recent progress in the understanding of the linear constant birth–death process with complete sampling (Gernhard 2008), with random incomplete sampling (Stadler 2009), or with clustered or diversified sampling (Ho¨ hna et al. 2011). The tree moves on clock and relaxed clock trees have also been improved considerably over those that were available in previous versions. Bayesian phylogenetic inference of species trees from multiple gene trees was first accomplished in the Bayesian estimation of species trees (BEST) software using a complex computational machinery, in which MrBayes was one of the components (Edwards et al. 2007; Liu and Pearl 2007). Despite later improvements to BEST, the analyses remained slow and computation- ally demanding. The multispecies coalescent model has now been fully integrated in MrBayes 3.2, and several of the original algorithms have been rewritten to speed up the calculations. to integrate out the uncertainty concerning the correct substitution model (Huelsenbeck et al. 2004). The latter procedure is now implemented in MrBayes 3.2. Rather than selecting a substitution model before the analy- sis, the user can now sample across all 203 possible time-reversible rate matrices according to their posterior probability. The model-jumping approach is available in all models where a four-by-four nucleotide model is a component, including doublet and codon models in ad- dition to the ordinary nucleotide models. Bayesian model choice using Bayes factors is rapidly gaining in popularity. Since earlier versions, MrBayes has reported the harmonic mean of the likelihoods from the MCMC sample, which can be used as a rough esti- mate of the model likelihood from which the Bayes factor is calculated (Newton and Raftery 1994). However, there are now considerably more accurate, albeit computation- ally more demanding, methods (Lartillot and Philippe 2006). Of these, MrBayes 3.2 implements the recently proposed stepping stone method (Xie et al. 2011) that uses MCMC to sample from a series of so-called power posterior distributions connecting the posterior distribu- tion with the prior distribution. The samples across these distributions are then used to estimate the model likeli- hood. The stepping stone algorithm in MrBayes 3.2 uses the full MCMC machinery, including convergence diag- nostics and Metropolis coupling, and can be applied to any model available in the program. For instance, it can be used to test various topological hypotheses or substi- tution models against each other. More Output Options MrBayes 3.2 provides more extensive output options than previous versions. The user can now request sam- pling of site rates, site selection coefficients, site positive selection probabilities, and ancestral states of particu- lar nodes. A wide range of tree statistics, including the mean and variance of split or clade frequencies, node times, and branch rates, are now added as annotations to the consensus tree by the “sumt” command and can be displayed using FigTree and compatible tree viewers. BENCHMARK AND BIOLOGICAL EXAMPLES Benchmark data on the GPU-accelerated code are pro- vided by Ayres et al. (2012). A number of example data sets are distributed with the program, and tutorials illus- trating most of the new features are included in the pro- gram manual. Many of the dating features in MrBayes 3.2 are discussed in some detail and used in an empiri- cal context in Ronquist et al. (2012). Model Averaging and Model Choice AVAILABILITY It is standard practice today to select a substitution model for Bayesian phylogenetic inference using a pri- ori model selection procedures (Goldman 1993; Posada 1998, 2008; Suchard et al. 2001). An alternative is to use Bayesian model jumping during the MCMC simulation MrBayes 3.2 is freely available under the GNU Gen- eral Public License version 3.0. The program web site (http://www.mrbayes.net) provides download links to both source code for compilation on Unix systems and to convenient installers for Windows and Mac OS