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MrBayes 3.2: Efficient Bayesian Phylogenetic Inference and Model Choice Across a Large Model Space

MrBayes 3.2: Efficient Bayesian Phylogenetic Inference and Model Choice Across a Large Model Space Software for Systematics and Evolution Syst. Biol. 61(3):539–542, 2012 The Author(s) 2012. Published by Oxford University Press, on behalf of the Society of Systematic Biologists. All rights reserved. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. DOI:10.1093/sysbio/sys029 Advance Access publication on February 22, 2012 MrBayes 3.2: Efficient Bayesian Phylogenetic Inference and Model Choice Across a Large Model Space 1,∗ 1 2 3 4 F REDRIK R ONQUIST , M AXIM T ESLENKO , PAUL VAN DER M ARK , D ANIEL L. AYRES , A ARON D ARLING , 5 6 7 8 9 S EBASTIAN H OHNA , B RET L ARGET , L IANG L IU , M ARC A. S UCHARD , AND J OHN P. H UELSENBECK 1 2 Department of Biodiversity Informatics, Swedish Museum of Natural History, SE-10405 Stockholm, Sweden; Department of Scientific Computing, Florida State University, FL 32306, USA; Center for Bioinformatics and Computational Biology, University of Maryland, College Park, MD 20742, 4 5 USA; Genome Center, University of California, Davis, CA 95616, USA; Department of Mathematics, Stockholm University, SE-10691 Stockholm, 6 7 Sweden; Departments of Statistics and Botany, University of Wisconsin, Madison, WI 53706, USA; Departments of Agriculture and Natural Resources, Delaware State University, Dover, DE 19901, USA; Departments of Biomathematics, Biostatistics and Human Genetics, University of California, Los Angeles, CA 90095, USA; and Department of Integrative Biology, University of California, Berkeley, CA 94720, USA; Correspondence to be sent to: Department of Biodiversity Informatics, Swedish Museum of Natural History, SE-10405 Stockholm, Sweden; E-mail: [email protected]. Received 13 August 2011; reviews returned 20 September 2011; accepted 6 February 2012 Associate Editor: David Posada Abstract.—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 prob- lems. 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 incor- poration 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 d /d rations, branch rates, and node N S dates. A wide range of statistics on tree parameters can also be output for visualization in FigTree and compatible software. [Bayes factor; Bayesian inference; MCMC; model averaging; model choice.] Bayesian Markov chain Monte Carlo (MCMC) meth- machinery has led to an explosion in the develop- ods quickly gained in popularity after they were intro- ment of probabilistic evolutionary models (for a re- duced in statistical phylogenetics in the late 1990’s (Mau view, see Ronquist and Deans 2010). We have also seen the appearance of better MCMC algorithms and more and Newton 1997; Yang and Rannala 1997; Larget and sophisticated convergence diagnostics for phylogenetic Simon 1999; Mau et al. 1999). This was due to the inherent advantages of the approach but also to the models, and methods for Bayesian model choice have availability of easy-to-use software packages, such as improved considerably. MrBayes (Huelsenbeck and Ronquist 2001). Originally, With this note, we announce the official release of ver- MrBayes only supported simple phylogenetic models, sion 3.2 of MrBayes. Version 3.2 was originally intended but the model space expanded considerably in version as a relatively modest expansion of version 3.1, which 3.0 (Ronquist and Huelsenbeck 2003). In addition to a added convergence diagnostics to the original features wide range of models on binary, “standard” (morphol- in version 3.0. Over the years, however, a number of ogy), nucleotide and amino acid data, version 3.0 also significant new features were added to version 3.2, supported mixed models. The latter allow different data and large parts of the program were rewritten. When partitions to be combined in the same model, with pa- we now officially release version 3.2, it is every bit as rameters linked or unlinked across partitions according significant in the evolution of the program as the release to user specifications. MrBayes 3.0 was apparently the of version 3.0 almost a decade ago. first statistical phylogenetics package to support such models (Rannala and Yang 2008). D ESCRIPTION OF N EW F EATURES Bayesian phylogenetic inference using MCMC has Convergence developed in leaps and bounds since the release of The phylogenetics community has come to ac- MrBayes 3.0. In particular, the relative ease with which complex models can be tackled using the MCMC cept as good practice that Bayesian MCMC results 539 540 SYSTEMATIC BIOLOGY VOL. 61 be accompanied by a critical assessment of conver- Faster and More Convenient Computation gence. Arguably, the best way of accomplishing this Much of the computational effort in a phylogenetic is to compare samples obtained from independent MCMC analysis is spent calculating likelihoods. To MCMC analyses. It is typically the tree samples that improve speed, MrBayes 3.2 now employs streaming are most divergent in phylogenetic analyses, and we single-instruction-multiple-data extensions (SSE) for all therefore introduced the average standard deviation likelihood calculations. SSE instructions are supported of split frequencies (ASDSF) in MrBayes to allow by most current CPUs and provide low-level paralleliza- quantitative assessment of the similarity among such tion of arithmetic operations. Importantly, MrBayes 3.2 samples. also supports the use of the BEAGLE library for likeli- ASDSF is calculated by comparing split or clade fre- hood calculations (Ayres et al. 2012). With BEAGLE, the quencies across multiple independent MCMC runs that likelihood calculations can be farmed out to one or more ideally should be started from different randomly cho- graphics processing units (GPUs) on compatible hard- sen starting trees (Lakner et al. 2008). ASDSF should ware, resulting in significant speedups for codon and approach 0.0 as runs converge to the same distribution. amino acid models in particular. BEAGLE can also be The frequencies of rare splits or clades are difficult to used for likelihood computation on the CPU. estimate accurately and these groupings are usually of MrBayes 3.2 does not support multithreading, but it marginal interest. Therefore, it may be advantageous to does implement the message passing interface (MPI) for exclude them from the diagnostic. MrBayes allows the efficient parallel processing across large computer clus- user to set a cutoff frequency (default value 0.10); all ters (Altekar et al. 2004). On many hardware platforms, splits or clades occurring minimally at that frequency including Mac OS and Linux, it is possible to use the in at least one of the runs will be incorporated in the MPI-enabled Unix version of MrBayes to take advan- ASDSF. tage of multiple cores. However, MPI parallelization is To allow users to monitor MCMC progress, MrBayes across chains, which means that the maximum number can run several analyses in parallel and report the av- of cores or processors that can be used by MrBayes is erage (ASDSF) or maximum standard deviation of split the same as the total number of heated and nonheated frequencies at regular intervals. More detailed diag- chains across all simultaneous runs. For instance, two nostics can be obtained using the “sump” and “sumt” runs of four chains each would be maximally acceler- commands after the run has completed. They include ated on a system with eight processors or cores. The MPI ASDSF across runs for each of the sampled clades in version can be combined with BEAGLE to further ex- addition to the potential scale reduction factor (PSRF; pand the opportunity for computational parallelization. Gelman and Rubin 1992) for branch lengths, node times, Finally, to facilitate long runs, MrBayes 3.2 imple- and substitution model parameters. PSRF compares the ments checkpointing across all models. At a frequency variance within and between runs and should approach determined by the user, all parameter samples are 1.0 as runs converge. MrBayes 3.2 also reports the ef- printed to a “.ckp” file. If desired, the analysis can later fective sample size, widely used for single-run conver- be restarted from the checkpoint file, and the final re- gence diagnostics. sults will appear as if the run had never been stopped. MrBayes 3.2 also introduces several new features intended to improve MCMC convergence rates. A number of new tree proposal mechanisms have been New Models added, including subtree-swapping moves and extend- Many phylogenetic hypotheses concern the structure ing subtree-pruning-and-regrafting moves, and the de- of the phylogenetic tree. To facilitate such analyses, fault mix of proposals has been optimized (Lakner MrBayes 3.2 implements three types of constraints on et al. 2008). MrBayes 3.2 further includes a completely the tree: hard, negative, and partial. A hard constraint new type of tree proposal that is guided using forces a split or clade to be present in all trees sampled parsimony scores. The details of the parsimony- in the MCMC analysis, whereas a negative constraint biased proposals will be presented elsewhere; how- forces a split or clade to be absent. Unlike hard and ever, tentative empirical results show that they can negative constraints, a partial constraint (or backbone improve the speed of convergence by an order of constraint) can leave the position of some taxa indeter- magnitude on some problems (see also Hohna ¨ and minate. The indeterminate taxa are allowed to appear on Drummond 2012). For nontree proposals, MrBayes 3.2 either side of the specified split if the tree is unrooted, implements auto-tuning that automatically adjusts tun- or either within or outside the specified clade if the tree ing parameters such that a target acceptance frequency is rooted. Several hard, negative, and partial constraints is reached (Roberts and Rosenthal 2009). Since previ- can be combined into complicated priors on the shape ous versions, MrBayes supports Metropolis coupling of the tree. However, constraints are either on or off; (heated chains) to accelerate convergence. To sim- they cannot be associated with probabilities in the cur- plify monitoring of convergence, MrBayes 3.2 prints rent version. ASDSF values, acceptance rates of moves, and ac- Unlike previous versions, MrBayes 3.2 supports re- ceptance rates of swaps between Metropolis-coupled laxed clock models and dating. Three different relaxed chains to a separate file with a “.mcmc” suffix during clock models are available: the Compound Poisson runs. 2012 SOFTWARE FOR SYSTEMATICS AND EVOLUTION 541 Process (CPP; Huelsenbeck et al. 2000), the Thorne– to integrate out the uncertainty concerning the correct Kishino 2002 (TK02; Thorne and Kishino 2002), and substitution model (Huelsenbeck et al. 2004). The latter the Independent Gamma Rate (IGR; Lepage et al. 2007) procedure is now implemented in MrBayes 3.2. Rather models. than selecting a substitution model before the analy- The CPP model is a discrete autocorrelated model, in sis, the user can now sample across all 203 possible which rate multipliers appear on the tree according to time-reversible rate matrices according to their posterior a Poisson process. The MrBayes implementation uses a probability. The model-jumping approach is available in lognormal distribution for the rate multipliers instead all models where a four-by-four nucleotide model is a of the modified gamma distribution proposed originally component, including doublet and codon models in ad- (Huelsenbeck et al. 2000). It also includes novel algo- dition to the ordinary nucleotide models. rithms to allow sampling across tree space since the Bayesian model choice using Bayes factors is rapidly original paper only dealt with fixed trees. gaining in popularity. Since earlier versions, MrBayes The TK02 model is a continuous autocorrelated has reported the harmonic mean of the likelihoods from model. In the particular version we implemented the MCMC sample, which can be used as a rough esti- (Thorne and Kishino 2002), the rate of a descendant mate of the model likelihood from which the Bayes factor node is drawn from a lognormal distribution, the mean is calculated (Newton and Raftery 1994). However, there of which is the same as the ancestral rate and the vari- are now considerably more accurate, albeit computation- ance of which is proportional to the length of the branch ally more demanding, methods (Lartillot and Philippe (measured in expected substitutions per site at the base 2006). Of these, MrBayes 3.2 implements the recently rate of the clock). proposed stepping stone method (Xie et al. 2011) that The IGR model is a continuous uncorrelated model. uses MCMC to sample from a series of so-called power First published as the “white noise” model (Lepage posterior distributions connecting the posterior distribu- et al. 2007), it is similar to the uncorrelated gamma tion with the prior distribution. The samples across these model (Drummond et al. 2006) but is mathematically distributions are then used to estimate the model likeli- more elegant in that it truly lacks time structure. In the hood. The stepping stone algorithm in MrBayes 3.2 uses IGR model, effective branch lengths are drawn from a the full MCMC machinery, including convergence diag- gamma distribution, in which the mean is the same as, nostics and Metropolis coupling, and can be applied to and the variance proportional to, the branch length. any model available in the program. For instance, it can Dating can be achieved in MrBayes 3.2 by calibrat- be used to test various topological hypotheses or substi- ing interior or tip nodes in the tree; calibrated interior tution models against each other. nodes need to be associated with hard constraints to be valid. Calibration points can be either fixed or associated More Output Options with uncertainty. The birth–death prior model on clock MrBayes 3.2 provides more extensive output options trees has been expanded to incorporate recent progress than previous versions. The user can now request sam- in the understanding of the linear constant birth–death pling of site rates, site selection coefficients, site positive process with complete sampling (Gernhard 2008), with selection probabilities, and ancestral states of particu- random incomplete sampling (Stadler 2009), or with lar nodes. A wide range of tree statistics, including the clustered or diversified sampling ( Hohna et al. 2011). mean and variance of split or clade frequencies, node The tree moves on clock and relaxed clock trees have times, and branch rates, are now added as annotations also been improved considerably over those that were to the consensus tree by the “sumt” command and can available in previous versions. be displayed using FigTree and compatible tree viewers. Bayesian phylogenetic inference of species trees from multiple gene trees was first accomplished in the Bayesian estimation of species trees (BEST) software BENCHMARK AND B IOLOGICAL E XAMPLES using a complex computational machinery, in which Benchmark data on the GPU-accelerated code are pro- MrBayes was one of the components (Edwards et al. vided by Ayres et al. (2012). A number of example data 2007; Liu and Pearl 2007). Despite later improvements sets are distributed with the program, and tutorials illus- to BEST, the analyses remained slow and computation- trating most of the new features are included in the pro- ally demanding. The multispecies coalescent model has gram manual. Many of the dating features in MrBayes now been fully integrated in MrBayes 3.2, and several of 3.2 are discussed in some detail and used in an empiri- the original algorithms have been rewritten to speed up cal context in Ronquist et al. (2012). the calculations. Model Averaging and Model Choice AVAILABILITY It is standard practice today to select a substitution MrBayes 3.2 is freely available under the GNU Gen- model for Bayesian phylogenetic inference using a pri- eral Public License version 3.0. The program web site ori model selection procedures (Goldman 1993; Posada (http://www.mrbayes.net) provides download links to 1998, 2008; Suchard et al. 2001). An alternative is to use both source code for compilation on Unix systems Bayesian model jumping during the MCMC simulation and to convenient installers for Windows and Mac OS 542 SYSTEMATIC BIOLOGY VOL. 61 systems. The installers include both MrBayes and the re- Gelman A., Rubin D. 1992. Inference from iterative simulation using multiple sequences. Stat. Sci. 7:457–472. quired BEAGLE libraries, but the BEAGLE libraries can Gernhard T. 2008. The conditioned reconstructed process. J. Theor. also be installed separately using the BEAGLE installer, Biol. 253:769–778. available at http://beagle-lib.googlecode.com. The pro- Goldman N. 1993. Statistical tests of models of DNA substitution. gram comes with a manual and example files. Further J. Mol. Evol. 36:182–198. help is available on the program web site, which also Hohna S., Drummond A.J. 2012. Guided tree topology proposal for Bayesian phylogenetic inference. Syst. Biol. 61:1–11. provides instructions for reporting bugs and signing up Hohna ¨ S., Stadler T., Ronquist F., Britton T. 2011. Inferring speciation for the MrBayes e-mail list. Instructions for accessing and extinction rates under different species sampling schemes. Mol. the MrBayes source code repository can be found at Biol. Evol. 28:2577–2589. http://sourceforge.net/projects/mrbayes/develop. Huelsenbeck J., Larget B., Swofford D. 2000. A compound Poisson pro- cess for relaxing the molecular clock. Genetics. 154:1879–1892. Huelsenbeck J.P., Larget B., Alfaro M.E. 2004. Bayesian phylogenetic FUNDING model selection using reversible jump Markov chain Monte Carlo. Mol. Biol. Evol. 21:1123–1133. The development of version 3.2 of MrBayes would Huelsenbeck J.P., Ronquist F. 2001. MRBAYES: Bayesian inference of not have been possible without generous support from phylogenetic trees. Bioinformatics. 17:754–755. the Swedish Research Council [2008-5629 to F.R.]; the Lakner C., van der Mark P., Huelsenbeck J., Larget B., Ronquist F. 2008. Efficiency of Markov chain Monte Carlo tree proposals in Bayesian National Institutes of Health [GM-069801 to J.P.H. and phylogenetics. Syst. Biol. 57:86–103. GM-086887, HG-006139 to M.A.S.]; and the National Sci- Larget B., Simon D. 1999. Markov chain Monte Carlo algorithms for ence Foundation [DEB-0445453 to J.P.H., DEB-0949121 the Bayesian analysis of phylogenetic trees. Mol. Biol. Evol. 16: and DEB-0936214 to B.L., and DBI-0755048 to D.L.A.]. 750–759. Incorporation of the BEST algorithms and support Lartillot N., Philippe H. 2006. Computing Bayes factors using thermo- dynamic integration. Syst. Biol. 55:195–207. for the BEAGLE library was greatly facilitated by a Lepage T., Bryant D., Philippe H., Lartillot N. 2007. A general compar- workshop in October 2010 sponsored by the Mathe- ison of relaxed molecular clock models. Mol. Biol. Evol. 24:2669– matical Biosciences Institute at Ohio State University [NSF-DMS-0931642], hosted by Dennis Pearl and Marty Liu L., Pearl D.K. 2007. Species trees from gene trees: reconstructing Bayesian posterior distributions of a species phylogeny using esti- Golubitsky. mated gene tree distributions. Syst. Biol. 56:504–514. Mau B., Newton M.A. 1997. Phylogenetic inference for binary data on A CKNOWLEDGMENTS dendograms using Markov chain Monte Carlo. J. Comput. Graph. Stat. 6:122–131. F.R., with the assistance of M.T. and P.v.d.M., did most Mau B., Newton M.A., Larget B. 1999. Bayesian phylogenetic inference of the programming for version 3.2, whereas J.P.H., as- via Markov chain Monte Carlo methods. Biometrics. 55:1–12. Newton M., Raftery A. 1994. Approximate Bayesian inference with sisted by F.R., was responsible for the software archi- the weighted likelihood bootstrap. J. R. Stat. Soc. B Stat. Methodol. tecture and initial code base. D.L.A., A.D., and M.A.S. 56:3–48. helped with the BEAGLE integration and the related Posada D. 1998. Modeltest: testing the model of DNA substitution. performance testing. L.L. assisted in the incorporation of Bioinformatics. 14:817–818. Posada D. 2008. jModelTest: phylogenetic model averaging. Mol. Biol. the BEST algorithms, whereas B.L. and S.H. contributed Evol. 25:1253–1256. to the implementation of particular models. We would Rannala B., Yang Z. 2008. Phylogenetic inference using whole like to thank Chris Anderson for additional assistance genomes. Annu. Rev. Genomics Hum. Genet. 9:217–231. with the BEST algorithms. We would also like to express Roberts G., Rosenthal J. 2009. Examples of adaptive MCMC. J. Com- our deep gratitude to the many MrBayes users, who put. Graph. Stat. 18:349–367. Ronquist F., Deans A.R. 2010. Bayesian phylogenetics and its influence have generously contributed to the project by submit- on insect systematics. Annu. Rev. Entomol. 55:189–206. ting bug reports, bug fixes, feature requests, and other Ronquist F., Huelsenbeck J.P. 2003. Mrbayes 3: Bayesian phylogenetic comments on the software. David Posada, Leonardo inference under mixed models. Bioinformatics. 19:1572–1574. Martins, and Jeremy Brown provided constructive criti- Ronquist F., Klopfstein S., Vilhelmsen L., Schulmeister S., Murray D.L., cism that helped improve the manuscript. Rasnitsyn A.P. Forthcoming 2012. A total-evidence approach to dat- ing with fossils, applied to the early radiation of the Hymenoptera. Syst. Biol. Stadler T. 2009. On incomplete sampling under birth-death models R EFERENCES and connections to the sampling-based coalescent. J. Theor. Biol. Altekar G., Dwarkadas S., Huelsenbeck J. 2004. Parallel metropolis 261:58–66. coupled Markov chain Monte Carlo for Bayesian phylogenetic in- Suchard M.A., Weiss R.E., Sinsheimer J.S. 2001. Bayesian selection ference. Bioinformatics. 20:407–425. of continuous-time Markov chain evolutionary models. Mol. Biol. Ayres D.L., Darling A., Zwickl D.J., Beerli P., Holder M.T., Lewis P.O., Evol. 18:1001–1013. Huelsenbeck J.P., Ronquist F., Swofford D.L., Cummings M.P., Ram- Thorne J.L., Kishino H. 2002. Divergence time and evolutionary rate baut A., Suchard M.A. 2012. BEAGLE: an application programming estimation with multilocus data. Syst. Biol. 51:689–702. interface and high-performance computing library for statistical Xie W., Lewis P.O., Fan Y., Kuo L., Chen M.-H. 2011. Improving phylogenetics. Syst. Biol. 61:170–173. marginal likelihood estimation for Bayesian phylogenetic model se- Drummond A.J., Ho S.Y.W., Phillips M.J., Rambaut A. 2006. Relaxed lection. Syst. Biol. 60:150–160. phylogenetics and dating with confidence. PLoS Biol. 4:e88. Yang Z., Rannala B. 1997. Bayesian phylogenetic inference using DNA Edwards S.V., Liu L., Pearl D.K. 2007. High-resolution species trees sequences: a Markov chain Monte Carlo method. Mol. Biol. Evol. without concatenation. Proc. Natl. Acad. Sci. U.S.A. 104:5936–5941. 14:717–724. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Systematic Biology Pubmed Central

MrBayes 3.2: Efficient Bayesian Phylogenetic Inference and Model Choice Across a Large Model Space

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Abstract

Software for Systematics and Evolution Syst. Biol. 61(3):539–542, 2012 The Author(s) 2012. Published by Oxford University Press, on behalf of the Society of Systematic Biologists. All rights reserved. This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0), which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. DOI:10.1093/sysbio/sys029 Advance Access publication on February 22, 2012 MrBayes 3.2: Efficient Bayesian Phylogenetic Inference and Model Choice Across a Large Model Space 1,∗ 1 2 3 4 F REDRIK R ONQUIST , M AXIM T ESLENKO , PAUL VAN DER M ARK , D ANIEL L. AYRES , A ARON D ARLING , 5 6 7 8 9 S EBASTIAN H OHNA , B RET L ARGET , L IANG L IU , M ARC A. S UCHARD , AND J OHN P. H UELSENBECK 1 2 Department of Biodiversity Informatics, Swedish Museum of Natural History, SE-10405 Stockholm, Sweden; Department of Scientific Computing, Florida State University, FL 32306, USA; Center for Bioinformatics and Computational Biology, University of Maryland, College Park, MD 20742, 4 5 USA; Genome Center, University of California, Davis, CA 95616, USA; Department of Mathematics, Stockholm University, SE-10691 Stockholm, 6 7 Sweden; Departments of Statistics and Botany, University of Wisconsin, Madison, WI 53706, USA; Departments of Agriculture and Natural Resources, Delaware State University, Dover, DE 19901, USA; Departments of Biomathematics, Biostatistics and Human Genetics, University of California, Los Angeles, CA 90095, USA; and Department of Integrative Biology, University of California, Berkeley, CA 94720, USA; Correspondence to be sent to: Department of Biodiversity Informatics, Swedish Museum of Natural History, SE-10405 Stockholm, Sweden; E-mail: [email protected]. Received 13 August 2011; reviews returned 20 September 2011; accepted 6 February 2012 Associate Editor: David Posada Abstract.—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 prob- lems. 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 incor- poration 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 d /d rations, branch rates, and node N S dates. A wide range of statistics on tree parameters can also be output for visualization in FigTree and compatible software. [Bayes factor; Bayesian inference; MCMC; model averaging; model choice.] Bayesian Markov chain Monte Carlo (MCMC) meth- machinery has led to an explosion in the develop- ods quickly gained in popularity after they were intro- ment of probabilistic evolutionary models (for a re- duced in statistical phylogenetics in the late 1990’s (Mau view, see Ronquist and Deans 2010). We have also seen the appearance of better MCMC algorithms and more and Newton 1997; Yang and Rannala 1997; Larget and sophisticated convergence diagnostics for phylogenetic Simon 1999; Mau et al. 1999). This was due to the inherent advantages of the approach but also to the models, and methods for Bayesian model choice have availability of easy-to-use software packages, such as improved considerably. MrBayes (Huelsenbeck and Ronquist 2001). Originally, With this note, we announce the official release of ver- MrBayes only supported simple phylogenetic models, sion 3.2 of MrBayes. Version 3.2 was originally intended but the model space expanded considerably in version as a relatively modest expansion of version 3.1, which 3.0 (Ronquist and Huelsenbeck 2003). In addition to a added convergence diagnostics to the original features wide range of models on binary, “standard” (morphol- in version 3.0. Over the years, however, a number of ogy), nucleotide and amino acid data, version 3.0 also significant new features were added to version 3.2, supported mixed models. The latter allow different data and large parts of the program were rewritten. When partitions to be combined in the same model, with pa- we now officially release version 3.2, it is every bit as rameters linked or unlinked across partitions according significant in the evolution of the program as the release to user specifications. MrBayes 3.0 was apparently the of version 3.0 almost a decade ago. first statistical phylogenetics package to support such models (Rannala and Yang 2008). D ESCRIPTION OF N EW F EATURES Bayesian phylogenetic inference using MCMC has Convergence developed in leaps and bounds since the release of The phylogenetics community has come to ac- MrBayes 3.0. In particular, the relative ease with which complex models can be tackled using the MCMC cept as good practice that Bayesian MCMC results 539 540 SYSTEMATIC BIOLOGY VOL. 61 be accompanied by a critical assessment of conver- Faster and More Convenient Computation gence. Arguably, the best way of accomplishing this Much of the computational effort in a phylogenetic is to compare samples obtained from independent MCMC analysis is spent calculating likelihoods. To MCMC analyses. It is typically the tree samples that improve speed, MrBayes 3.2 now employs streaming are most divergent in phylogenetic analyses, and we single-instruction-multiple-data extensions (SSE) for all therefore introduced the average standard deviation likelihood calculations. SSE instructions are supported of split frequencies (ASDSF) in MrBayes to allow by most current CPUs and provide low-level paralleliza- quantitative assessment of the similarity among such tion of arithmetic operations. Importantly, MrBayes 3.2 samples. also supports the use of the BEAGLE library for likeli- ASDSF is calculated by comparing split or clade fre- hood calculations (Ayres et al. 2012). With BEAGLE, the quencies across multiple independent MCMC runs that likelihood calculations can be farmed out to one or more ideally should be started from different randomly cho- graphics processing units (GPUs) on compatible hard- sen starting trees (Lakner et al. 2008). ASDSF should ware, resulting in significant speedups for codon and approach 0.0 as runs converge to the same distribution. amino acid models in particular. BEAGLE can also be The frequencies of rare splits or clades are difficult to used for likelihood computation on the CPU. estimate accurately and these groupings are usually of MrBayes 3.2 does not support multithreading, but it marginal interest. Therefore, it may be advantageous to does implement the message passing interface (MPI) for exclude them from the diagnostic. MrBayes allows the efficient parallel processing across large computer clus- user to set a cutoff frequency (default value 0.10); all ters (Altekar et al. 2004). On many hardware platforms, splits or clades occurring minimally at that frequency including Mac OS and Linux, it is possible to use the in at least one of the runs will be incorporated in the MPI-enabled Unix version of MrBayes to take advan- ASDSF. tage of multiple cores. However, MPI parallelization is To allow users to monitor MCMC progress, MrBayes across chains, which means that the maximum number can run several analyses in parallel and report the av- of cores or processors that can be used by MrBayes is erage (ASDSF) or maximum standard deviation of split the same as the total number of heated and nonheated frequencies at regular intervals. More detailed diag- chains across all simultaneous runs. For instance, two nostics can be obtained using the “sump” and “sumt” runs of four chains each would be maximally acceler- commands after the run has completed. They include ated on a system with eight processors or cores. The MPI ASDSF across runs for each of the sampled clades in version can be combined with BEAGLE to further ex- addition to the potential scale reduction factor (PSRF; pand the opportunity for computational parallelization. Gelman and Rubin 1992) for branch lengths, node times, Finally, to facilitate long runs, MrBayes 3.2 imple- and substitution model parameters. PSRF compares the ments checkpointing across all models. At a frequency variance within and between runs and should approach determined by the user, all parameter samples are 1.0 as runs converge. MrBayes 3.2 also reports the ef- printed to a “.ckp” file. If desired, the analysis can later fective sample size, widely used for single-run conver- be restarted from the checkpoint file, and the final re- gence diagnostics. sults will appear as if the run had never been stopped. MrBayes 3.2 also introduces several new features intended to improve MCMC convergence rates. A number of new tree proposal mechanisms have been New Models added, including subtree-swapping moves and extend- Many phylogenetic hypotheses concern the structure ing subtree-pruning-and-regrafting moves, and the de- of the phylogenetic tree. To facilitate such analyses, fault mix of proposals has been optimized (Lakner MrBayes 3.2 implements three types of constraints on et al. 2008). MrBayes 3.2 further includes a completely the tree: hard, negative, and partial. A hard constraint new type of tree proposal that is guided using forces a split or clade to be present in all trees sampled parsimony scores. The details of the parsimony- in the MCMC analysis, whereas a negative constraint biased proposals will be presented elsewhere; how- forces a split or clade to be absent. Unlike hard and ever, tentative empirical results show that they can negative constraints, a partial constraint (or backbone improve the speed of convergence by an order of constraint) can leave the position of some taxa indeter- magnitude on some problems (see also Hohna ¨ and minate. The indeterminate taxa are allowed to appear on Drummond 2012). For nontree proposals, MrBayes 3.2 either side of the specified split if the tree is unrooted, implements auto-tuning that automatically adjusts tun- or either within or outside the specified clade if the tree ing parameters such that a target acceptance frequency is rooted. Several hard, negative, and partial constraints is reached (Roberts and Rosenthal 2009). Since previ- can be combined into complicated priors on the shape ous versions, MrBayes supports Metropolis coupling of the tree. However, constraints are either on or off; (heated chains) to accelerate convergence. To sim- they cannot be associated with probabilities in the cur- plify monitoring of convergence, MrBayes 3.2 prints rent version. ASDSF values, acceptance rates of moves, and ac- Unlike previous versions, MrBayes 3.2 supports re- ceptance rates of swaps between Metropolis-coupled laxed clock models and dating. Three different relaxed chains to a separate file with a “.mcmc” suffix during clock models are available: the Compound Poisson runs. 2012 SOFTWARE FOR SYSTEMATICS AND EVOLUTION 541 Process (CPP; Huelsenbeck et al. 2000), the Thorne– to integrate out the uncertainty concerning the correct Kishino 2002 (TK02; Thorne and Kishino 2002), and substitution model (Huelsenbeck et al. 2004). The latter the Independent Gamma Rate (IGR; Lepage et al. 2007) procedure is now implemented in MrBayes 3.2. Rather models. than selecting a substitution model before the analy- The CPP model is a discrete autocorrelated model, in sis, the user can now sample across all 203 possible which rate multipliers appear on the tree according to time-reversible rate matrices according to their posterior a Poisson process. The MrBayes implementation uses a probability. The model-jumping approach is available in lognormal distribution for the rate multipliers instead all models where a four-by-four nucleotide model is a of the modified gamma distribution proposed originally component, including doublet and codon models in ad- (Huelsenbeck et al. 2000). It also includes novel algo- dition to the ordinary nucleotide models. rithms to allow sampling across tree space since the Bayesian model choice using Bayes factors is rapidly original paper only dealt with fixed trees. gaining in popularity. Since earlier versions, MrBayes The TK02 model is a continuous autocorrelated has reported the harmonic mean of the likelihoods from model. In the particular version we implemented the MCMC sample, which can be used as a rough esti- (Thorne and Kishino 2002), the rate of a descendant mate of the model likelihood from which the Bayes factor node is drawn from a lognormal distribution, the mean is calculated (Newton and Raftery 1994). However, there of which is the same as the ancestral rate and the vari- are now considerably more accurate, albeit computation- ance of which is proportional to the length of the branch ally more demanding, methods (Lartillot and Philippe (measured in expected substitutions per site at the base 2006). Of these, MrBayes 3.2 implements the recently rate of the clock). proposed stepping stone method (Xie et al. 2011) that The IGR model is a continuous uncorrelated model. uses MCMC to sample from a series of so-called power First published as the “white noise” model (Lepage posterior distributions connecting the posterior distribu- et al. 2007), it is similar to the uncorrelated gamma tion with the prior distribution. The samples across these model (Drummond et al. 2006) but is mathematically distributions are then used to estimate the model likeli- more elegant in that it truly lacks time structure. In the hood. The stepping stone algorithm in MrBayes 3.2 uses IGR model, effective branch lengths are drawn from a the full MCMC machinery, including convergence diag- gamma distribution, in which the mean is the same as, nostics and Metropolis coupling, and can be applied to and the variance proportional to, the branch length. any model available in the program. For instance, it can Dating can be achieved in MrBayes 3.2 by calibrat- be used to test various topological hypotheses or substi- ing interior or tip nodes in the tree; calibrated interior tution models against each other. nodes need to be associated with hard constraints to be valid. Calibration points can be either fixed or associated More Output Options with uncertainty. The birth–death prior model on clock MrBayes 3.2 provides more extensive output options trees has been expanded to incorporate recent progress than previous versions. The user can now request sam- in the understanding of the linear constant birth–death pling of site rates, site selection coefficients, site positive process with complete sampling (Gernhard 2008), with selection probabilities, and ancestral states of particu- random incomplete sampling (Stadler 2009), or with lar nodes. A wide range of tree statistics, including the clustered or diversified sampling ( Hohna et al. 2011). mean and variance of split or clade frequencies, node The tree moves on clock and relaxed clock trees have times, and branch rates, are now added as annotations also been improved considerably over those that were to the consensus tree by the “sumt” command and can available in previous versions. be displayed using FigTree and compatible tree viewers. Bayesian phylogenetic inference of species trees from multiple gene trees was first accomplished in the Bayesian estimation of species trees (BEST) software BENCHMARK AND B IOLOGICAL E XAMPLES using a complex computational machinery, in which Benchmark data on the GPU-accelerated code are pro- MrBayes was one of the components (Edwards et al. vided by Ayres et al. (2012). A number of example data 2007; Liu and Pearl 2007). Despite later improvements sets are distributed with the program, and tutorials illus- to BEST, the analyses remained slow and computation- trating most of the new features are included in the pro- ally demanding. The multispecies coalescent model has gram manual. Many of the dating features in MrBayes now been fully integrated in MrBayes 3.2, and several of 3.2 are discussed in some detail and used in an empiri- the original algorithms have been rewritten to speed up cal context in Ronquist et al. (2012). the calculations. Model Averaging and Model Choice AVAILABILITY It is standard practice today to select a substitution MrBayes 3.2 is freely available under the GNU Gen- model for Bayesian phylogenetic inference using a pri- eral Public License version 3.0. The program web site ori model selection procedures (Goldman 1993; Posada (http://www.mrbayes.net) provides download links to 1998, 2008; Suchard et al. 2001). An alternative is to use both source code for compilation on Unix systems Bayesian model jumping during the MCMC simulation and to convenient installers for Windows and Mac OS 542 SYSTEMATIC BIOLOGY VOL. 61 systems. The installers include both MrBayes and the re- Gelman A., Rubin D. 1992. Inference from iterative simulation using multiple sequences. Stat. Sci. 7:457–472. quired BEAGLE libraries, but the BEAGLE libraries can Gernhard T. 2008. The conditioned reconstructed process. J. Theor. also be installed separately using the BEAGLE installer, Biol. 253:769–778. available at http://beagle-lib.googlecode.com. The pro- Goldman N. 1993. Statistical tests of models of DNA substitution. gram comes with a manual and example files. Further J. Mol. Evol. 36:182–198. help is available on the program web site, which also Hohna S., Drummond A.J. 2012. Guided tree topology proposal for Bayesian phylogenetic inference. Syst. Biol. 61:1–11. provides instructions for reporting bugs and signing up Hohna ¨ S., Stadler T., Ronquist F., Britton T. 2011. Inferring speciation for the MrBayes e-mail list. Instructions for accessing and extinction rates under different species sampling schemes. Mol. the MrBayes source code repository can be found at Biol. Evol. 28:2577–2589. http://sourceforge.net/projects/mrbayes/develop. Huelsenbeck J., Larget B., Swofford D. 2000. A compound Poisson pro- cess for relaxing the molecular clock. Genetics. 154:1879–1892. Huelsenbeck J.P., Larget B., Alfaro M.E. 2004. Bayesian phylogenetic FUNDING model selection using reversible jump Markov chain Monte Carlo. Mol. Biol. Evol. 21:1123–1133. The development of version 3.2 of MrBayes would Huelsenbeck J.P., Ronquist F. 2001. MRBAYES: Bayesian inference of not have been possible without generous support from phylogenetic trees. Bioinformatics. 17:754–755. the Swedish Research Council [2008-5629 to F.R.]; the Lakner C., van der Mark P., Huelsenbeck J., Larget B., Ronquist F. 2008. Efficiency of Markov chain Monte Carlo tree proposals in Bayesian National Institutes of Health [GM-069801 to J.P.H. and phylogenetics. Syst. Biol. 57:86–103. GM-086887, HG-006139 to M.A.S.]; and the National Sci- Larget B., Simon D. 1999. Markov chain Monte Carlo algorithms for ence Foundation [DEB-0445453 to J.P.H., DEB-0949121 the Bayesian analysis of phylogenetic trees. Mol. Biol. Evol. 16: and DEB-0936214 to B.L., and DBI-0755048 to D.L.A.]. 750–759. Incorporation of the BEST algorithms and support Lartillot N., Philippe H. 2006. Computing Bayes factors using thermo- dynamic integration. Syst. Biol. 55:195–207. for the BEAGLE library was greatly facilitated by a Lepage T., Bryant D., Philippe H., Lartillot N. 2007. A general compar- workshop in October 2010 sponsored by the Mathe- ison of relaxed molecular clock models. Mol. Biol. Evol. 24:2669– matical Biosciences Institute at Ohio State University [NSF-DMS-0931642], hosted by Dennis Pearl and Marty Liu L., Pearl D.K. 2007. Species trees from gene trees: reconstructing Bayesian posterior distributions of a species phylogeny using esti- Golubitsky. mated gene tree distributions. Syst. Biol. 56:504–514. Mau B., Newton M.A. 1997. Phylogenetic inference for binary data on A CKNOWLEDGMENTS dendograms using Markov chain Monte Carlo. J. Comput. Graph. Stat. 6:122–131. F.R., with the assistance of M.T. and P.v.d.M., did most Mau B., Newton M.A., Larget B. 1999. Bayesian phylogenetic inference of the programming for version 3.2, whereas J.P.H., as- via Markov chain Monte Carlo methods. Biometrics. 55:1–12. Newton M., Raftery A. 1994. Approximate Bayesian inference with sisted by F.R., was responsible for the software archi- the weighted likelihood bootstrap. J. R. Stat. Soc. B Stat. Methodol. tecture and initial code base. D.L.A., A.D., and M.A.S. 56:3–48. helped with the BEAGLE integration and the related Posada D. 1998. Modeltest: testing the model of DNA substitution. performance testing. L.L. assisted in the incorporation of Bioinformatics. 14:817–818. Posada D. 2008. jModelTest: phylogenetic model averaging. Mol. Biol. the BEST algorithms, whereas B.L. and S.H. contributed Evol. 25:1253–1256. to the implementation of particular models. We would Rannala B., Yang Z. 2008. Phylogenetic inference using whole like to thank Chris Anderson for additional assistance genomes. Annu. Rev. Genomics Hum. Genet. 9:217–231. with the BEST algorithms. We would also like to express Roberts G., Rosenthal J. 2009. Examples of adaptive MCMC. J. Com- our deep gratitude to the many MrBayes users, who put. Graph. Stat. 18:349–367. Ronquist F., Deans A.R. 2010. Bayesian phylogenetics and its influence have generously contributed to the project by submit- on insect systematics. Annu. Rev. Entomol. 55:189–206. ting bug reports, bug fixes, feature requests, and other Ronquist F., Huelsenbeck J.P. 2003. Mrbayes 3: Bayesian phylogenetic comments on the software. David Posada, Leonardo inference under mixed models. Bioinformatics. 19:1572–1574. Martins, and Jeremy Brown provided constructive criti- Ronquist F., Klopfstein S., Vilhelmsen L., Schulmeister S., Murray D.L., cism that helped improve the manuscript. Rasnitsyn A.P. Forthcoming 2012. A total-evidence approach to dat- ing with fossils, applied to the early radiation of the Hymenoptera. Syst. Biol. Stadler T. 2009. 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Journal

Systematic Biology – Pubmed Central

Published: Feb 22, 2012

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