Home

MrBayes 3.1 Manual - molecularevolution.org

Contents

1. Nuezmsee Pan 4 100 SSSSSSeSs 555555 Gorilla 5 100 NeERGUHCQAOUOHHATTSEPBEE SASS Pongo 6 100 S S555 535558552 SSs2s5555 S5552 5 Hylobates 7 Fennah S acaca_fuscata 8 100 100 Accu mulatta 9 100 eSSa Sars sae fascicularis 10 100 s Ses 100 Necosesedosucecsuedececnenu sylvanus 11 P D E Saimiri sciureus 12 Phylogram RR eMe EeEUec dnt incedens Tarsius syrichta 1 CLSILoPRSSULICCUSERAMSADSRE Lemur catta 2 Homo sapiens 3 Nessec Pan 4 Aem Gorilla 5 t NesseeeneeRE Pongo 6 d 4 5 t NE E A Hylobates 7 Macaca _ fuscata 8 A F f M mulatta 9 jie NEST M fascicularis 10 NaS SSS gt SsSeeosess S SSsSi55es55S gt SS5S55 Nessa M sylvanus 11 XNemeseeescesccccecccencounueeelueum Saimiri sciureus 12 per site MrBayes 3 1 Manual 5 26 2005 27 In the background the sumt command creates three additional files The first is a parts file which contains the list of taxon bipartitions their posterior probability the proportion of sampled trees containing them and the branch lengths associated with them if branch lengths have been saved The branch length values are based only on those trees containing the relevant bipartition The second generated file has the suffix con and includes two consensus trees The first on
2. 3 charset pos2 2 3 charset pos3 3 3 partition by codon 3 posl pos2 pos3 set partition by codon The character sets are first defined using the dot sign to mark the last character in the data set and the 3 sequence to include every third character in the specified range Then a partitioning scheme called by codon is defined using the previously named character sets Finally the partitioning scheme called by codon is invoked using the set command When we process these commands in MrBayes using the execute command the characters are divided into three sets corresponding to the codon positions By default however all model parameters including the rate will be shared across partitions To allow the rates to differ across partitions we need to change the prior for rates using prset Specifically prset ratepr variable invokes partition specific rates The partition specific rate parameter is referred to as ratemult and the individual rates are labeled m 1 m 2 etc for the rate multiplier of character division 1 2 etc See below for more information on how to set up partitioned models 4 6 5 Inferring Site Rates When you are allowing rate variation across sites you may be interested in inferring the rates at each individual site By default the site rates are not sampled during a MCMC run You need to request the sampling of these values using report siterates yes The rates will be referred to as r site num
3. Drag the pMrBayes 3 1 application and the nexus file you wish to run to Pooch s Job Window 7 Click the Launch Job button MrBayes 3 1 Manual 5 26 2005 62 From this point on MrBayes behaves just like the serial version of the program 7 2 2 The MPI Version for Unix Clusters The MPI version for Unix clusters including Xserve clusters has to be compiled before you can run it To tell the compiler that you want the MPI version you need to change a line in the top section the configuration section of the Makefile The line originally reads MPT nmo Change this to MPI yes If your system is set up correctly among other things you need to have mpicc with the relevant libraries installed you should now be able to compile the MPI version of MrBayes A typical make session would look as follows after the Makefile has been appropriately edited ronquist petal036 mpi_mbdev make mpicc DUNIX VERSION DMPI ENABLED 03 Wall Wno uninitialized c bayes c mpicc DUNIX VERSION DMPI ENABLED 03 Wall Wno uninitialized c command c mpicc DUNIX VERSION DMPI ENABLED 03 Wall Wno uninitialized c mbmath c mpicc DUNIX VERSION DMPI ENABLED 03 Wall Wno uninitialized c mcmc c mpicc DUNIX VERSION DMPI ENABLED 03 Wall Wno uninitialized c model c mpicc DUNIX VERSION DMPI ENABLED 03 Wall Wno uninitialized c
4. For trees without a molecular clock unconstrained the branch length prior can be set either to exponential or uniform The default exponential prior with parameter 10 0 should work well for most analyses It has an expectation of 1 10 0 1 but allows a wide range of branch length values theoretically from 0 to infinity Because the likelihood values vary much more rapidly for short branches than for long branches an exponential prior on branch lengths is closer to being uninformative than a uniform prior 2 5 Checking the Model To check the model before we start the analysis type showmodel This will give an overview of the model settings In our case the output will be as follows Model settings Datatype DNA Nucmodel 4by4 Nst 6 Substitution rates expressed as proportions of the rate sum have a Dirichlet prior 1 00 1 00 1 00 1 00 1 00 1 00 Covarion No States 4 State frequencies have a Dirichlet prior 1 00 1 00 1 00 1 00 Rates Invgamma Gamma shape parameter is uniformly dist ributed on the interval 0 05 50 00 Proportion of invariable sites is uniformly dist ributed on the interval 0 00 1 00 Gamma distribution is approximated using 4 categories MrBayes 3 1 Manual 5 26 2005 16 Active parameters Parameters Revmat 1 Statefreq 2 Shape 3 Pinvar 4 Topology 5 Brlens 6 1 Parameter Revmat Prior Dirichlet 1 00 1 00 1 00 1 00 1 00 1 00 2 Parameter Statefreq Prior D
5. parameters stationary state frequencies in this case If you want to allow transition rate stationary frequency asymmetry in standard data then simply select another hyper prior For instance you can fix the parameter to 1 0 which would result in a uniform prior on the proportions of the state frequencies In practice MrBayes uses a discrete approximation of the Dirichlet distribution for binary characters five categories are used by default change this with lset nbetacat For instance assume that we fix the hyperprior to 1 0 and then evaluate the likelihood of one binary character using five discrete beta categories MrBayes would then calculate the likelihood of the character assuming that the stationary state frequencies of the two states were 0 1 0 9 0 3 0 7 0 5 0 5 0 7 0 3 and 0 1 0 9 The five category likelihoods would then be multiplied by 0 20 there is a probability of 0 20 of being in each of the categories and then summed up to give the total likelihood of the character For multi state characters MrBayes does not use the discrete approximation instead it uses the MCMC procedure to explore different stationary state frequency proportions MrBayes 3 1 Manual 5 26 2005 42 4 5 Parsimony Model MrBayes implements an incredibly parameter rich model first described by Tuffley and Steel 1997 It orders trees in terms of their maximum likelihood in the same way as the parsimony method would order them in terms of their p
6. 4 0 079300 3 0 049876 2 0 066929 0 040517 0 103191 5 0 1382 20 0 105224 0 147212 10 0 059671 8 0 035939 7 0 012332 0 037992 9 0 06947 7 0 060859 0 221336 0 149243 11 0 627561 0 180115 12 0 525606 1 0 339476 end To summarize the tree and branch length information type sumt burnin 250 The sumt and sump commands each have separate burn in settings so it is necessary to give MrBayes 3 1 Manual 5 26 2005 25 the burn in here again Otherwise many of the settings in MrBayes are persistent and need not be repeated every time a command is executed To make sure the settings for a particular command are correct you can always use help lt command gt before issuing the command The sumt command will output among other things summary statistics for the taxon bipartitions a tree with clade credibility posterior probability values and a phylogram if branch lengths have been saved The summary statistics see below describes each partition in the dot star format dots for the taxa that are on one side of the partition and stars for the taxa on the other side for instance the first partition ID 1 is the terminal branch leading to taxon 8 since it has a star in the 8 position and a dot in all other positions Then it gives the number of times the partition was sampled obs the probability of the partition Probab the standard deviation of the partition frequency Stdev s the mean Mean v
7. 57 You can calculate the amount of memory needed to store the conditional likelihoods for an analysis roughly as 2 taxa states in the Q matrix gamma categories 4 bytes for the single precision float version of the code double the memory requirement for the double precision code The program will need slightly more memory for various book keeping purposes but the bulk of the memory required for an analysis is typically occupied by the conditional likelihoods How do I fix the tree topology during an analysis In principle one can fix a tree topology by specifying constraints for all of the nodes in the tree However we do not recommend doing this because it is computationally very inefficient A better way is to set the proposal probability of all topology moves to 0 using the props command Then you need to switch on one proposal that changes branch lengths but not topology by increasing its proposal probability from 0 to some reasonable positive value like 5 The node slider is in our experience the best of these proposals 6 Differences Between Version 2 and Version 3 We have discontinued the development of version 2 of MrBayes and recommend all users to switch over to version 3 With the release of version 3 1 virtually all models implemented in version 2 are available in version 3 plus many more The only exception is the time irreversible model of nucleotide evolution which is still not implemented in
8. 5731 738 0 00 01 5736 484 0 00 00 5726 322 0 00 00 5798 728 5839 5722 2063 5730 0 000000 5720 361 5737 7 9720 670 5731 5720 408 5728 5724 562 5728 5727 405 5727 7 572 132 25728 5724 199 5728 5728 466 5723 5731 803 5727 5727 599 5728 0 000000 268 926 343 852 016 739 274 393 102 404 082 776 20 If you have the terminal window wide enough each generation of the chain will print on a single line like this we have decreased the font size to show the layout Chain results 1 7812 831 7523 685 100 6771 532 6857 529 200 6321 464 6179 561 300 6201 285 6084 899 400 6015 429 5924 177 500 5963 069 5851 415 600 5931 545 5802 472 700 5852 405 5782 934 800 5844 426 5754 416 900 5814 885 5741 101 1000 5811 949 5737 884 Average standard deviation of split frequencies 1100 5784 586 5730 069 9000 5728 228 5737 756 Average standard deviation of split frequencies 9100 5732 093 5733 215 9200 5731 412 5728 251 9300 5739 416 5734 909 9400 5720 648 5732 631 9500 5730 870 5729 773 9600 5736 460 5734 016 9700 5740 378 5733 312 9800 5739 019 5735 541 9900 5743 556 5724 246 10000 5738 1
9. B Rannala 1997 Bayesian phylogenetic inference using DNA sequences a Markov chain Monte carlo method Molecular Biology and Evolution 14 717 724 Yang Z R Nielsen and M Hasegawa 1998 Models of amino acid substitution and applications to mitochondrial protein evolution Molecular Biology and Evolution 15 1600 1611 Models supported by MrBayes 3 simplified State Frequencies Across Site Coding Bias Misc Pata Type Substitution Rates Rate Variation all variable nopresencesites noabsencesites Iset coding Restriction fixed estimated Dirichlet equal gamma 0 1 prset statefreqpr Iset rates Standard equal estimated SymmDir equal gamma all variable informative unordered ordered 0 9 prset symdirihyperpr Iset rates Iset coding ctype Across Site Across Tree Data Type Model Type State Frequencies Substitution Rates Rate Variation Rate Variation DNA 4by4 fixed est Dirichlet F81 HKY GTR equal gamma yes no ACGT Iset nucmodel prset statefreqpr Iset nst 1 2 6 propinv invgamma Iset covarion adgamma Iset rates doublet fixed est Dirichlet F81 HKY GTR equal gamma Iset nucmodel over 16 states Iset nst 1 2 6 propinv invgamma prset statefreqpr Iset rates Across Site Omega Variation codon fixed est Dirichlet F81 HKY GTR equal Ny98 M3 Iset omegavar Iset nucmodel over 61 states Iset nst 1 2 6 prset statefreqpr Models supported by MrBayes 3 simplified page 2 Across Site Across Tr
10. Works best when the effect on the probability of the data is similar throughout the parameter range Multiplier Proposal x a x ax New values are picked from the equivalent of a sliding window on the log transformed x axis Tuning parameter 2 ln a Bolder proposals increase X More modest proposals decrease Works well when changes in small values of x have a larger effect on the probability of data than changes in large values of x Example branch lengths LOCAL B Three internal branches a 5 and c are chosen at random Their total length is changed using a multiplier with tuning paremeter One of the subtrees A or B is picked at random It is randomly reinserted on a b c according to a uni form distribution Bolder proposals increase X More modest proposals decrease Changing has little effect on the boldness of the proposal Dirichlet proposal New values are picked from a Dirichlet or Beta distribution centered on x Tuning parameter amp Bolder proposals decrease o More modest proposals increase o Works well for proportions such as revmat and statefreqs Node Slider X Two adjacent branches a and b are chosen at random The length of a b is changed using a multiplier with tuning paremeter The node x is randomly inserted on a b according to a uniform distribution Bolder proposals increase X More modest proposals decrease The boldness of the proposa
11. a version for running the program in parallel on clusters of Macintoshes named MrBayes3 1p program icon four portraits of Reverend Bayes For more information on the parallel Macintosh version of MrBayes which requires the installation of POOCH see section 7 of this user manual The Windows package only contains the serial version of the program and is ready to run after unzipping just like the Macintosh serial version If you decide to run the program under Unix Linux then you need to compile the program from the source code In the latter case simply unpack the file mrbayes3 1 src tar gz by typing gunzip MrBayes 3 1 src tar gz and then tar xf MrBayes 3 1 src tar Thegunzip command unzips the compressed file and the tar xf command extracts all of the files from the tar archive that resulted from the unzip operation note that the gz suffix is dropped in the unzip operation You then need to compile the program We have included a Makefile that contains compiler instructions producing the serial version of the program You simply type make to compile the program according to these instructions A typical compile session would look like this ronquistg5 mrbayes gt ls mrbayes3 1 src tar gz ronquistg5 mrbayes gt gunzip MrBayes 3 1 src tar gz ronquistg5 mrbayes ls mrbayes3 1 src tar ronquistg5 mrbayes tar xf MrBayes 3 1 src tar ronquistg5 mrbayes make gcc DUNIX VERSION 03 Wall Wno unin
12. and variance Var v of the branch length the Potential Scale Reduction Factor PSRF and finally the number of runs in which the partition was sampled Nruns In our analysis there is overwhelming support for a single tree so all partitions have a posterior probability of 1 0 Summary statistics for taxon bipartitions Partition kckckckck kck kk kk kckck ck ck kk kk obs Probab 000000 C3 CO C93 ONS C96 OO OP 9 e ce ce c IO OGO GOGO OO C CO G O0 C 1 000000 0 999334 0 999334 Stdev s 00000 00000 058828 082206 030594 049234 063670 271433 472390 113412 165887 122957 022199 018330 070973 329111 429012 056534 248962 139867 035640 054652 049466 000235 000426 000152 000104 000207 003850 007137 002208 000861 001186 000039 000042 000449 003588 004224 000137 002162 000708 000107 000435 000355 The clade credibility tree upper tree next page gives the probability of each partition or clade in the tree and the phylogram lower tree next page gives the branch lengths measured in expected substitutions per site MrBayes 3 1 Manual 5 26 2005 26 Clade credibility values Pare aa Sse sae SS ss ee SSS FS se Sees Sn ss5 Tarsius syrichta 1 CinpumeeemesC Stes a e See ase Lemur catta 2 esce Homo sapiens 3 100
13. default topologies are not constrained in the prior prset topologypr uniform resulting in equal prior probability being associated with all possible labeled trees unless a different topology prior is induced by the branch length model see below There are two instances in which you might want to constrain the topology 1 when you want to contrast a hypothesis of monophyly for a group with the more general hypothesis with no topological constraints and 2 when you want to infer ancestral states for a particular node in the tree In both cases you specify the constraint s first by listing the taxa that should form a monophyletic group For instance if you wanted to constrain taxa 4 5 and 6 to be monophyletic you would use constraint my constraint 1 4 5 6 This defines a constraint called my constraint forcing taxa 4 5 and 6 to form a monophyletic group in all trees that are sampled from the chain In future versions of MrBayes the value following the name of the constraint 1 here will give the relative probability of trees having the constrained partition A negative number will force the constraint to always be present in the sampled trees a positive number will specify how many times more likely the trees with the constraint are compared to the trees not having it In version 3 1 however MrBayes ignores this value and always treats the constraint as absolute When you define constraints make sure that you have the ou
14. different codons that a i is the amino acid coded for by codon i that dj is the minimum number of nucleotide changes involved in changing between them and that w is the ratio of the non synonymous to the synonymous substitution rate The off diagonal elements of the instantaneous rate matrix can now be defined as 0 i d qd 4 Tr if d 1 and a i a J mn T rn 0 if d 1 and ali a j with the diagonal elements being defined to balance the rows of the instantaneous rate matrix as usual The single nucleotide substitution rates can be modeled using the GTR the F81 or the JC model as before Use 1set nst to change among those options for instance use set nst 6 to choose the GTR model The default model is the F81 model 1set nst 1 Invoking the codon model is easy just make sure that the aligned DNA or RNA sequences start with a nucleotide in codon position 1 and that they end with a nucleotide in codon position 3 Also make sure that the sequences do not contain any stop codons To figure out whether a codon is a stop codon and whether a particular single nucleotide change involves an amino acid change MrBayes uses one of several genetic codes By default MrBayes uses the universal code but you can select other codes by using the lset code command Note that the codon models are computationally demanding Whereas the computations for the simple four by four models need to deal with only 16 Q matrix and transition probability el
15. from the MrBayes CVS repository at SourceForge 8 Acknowledgements We would like to acknowledge the invaluable help we have received from students colleagues and numerous users of MrBayes they are too many to name them all here Often we have been overwhelmed by the generosity with which people have shared ideas bug fixes and other valuable tips with us This feedback alone makes all the hours we have put into developing MrBayes worthwhile Thank you all of you 9 References Adachi J and M Hasegawa 1996 MOLPHY version 2 3 programs for molecular phylogenetics based on maximum likelihood Computer Science Monographs of Institute of Statistical Mathematics 28 1 150 Adachi J P Waddell W Martin and M Hasegawa 2000 Plastid genome phylogeny and a model of amino acid substitution for proteins encoded by chloroplast DNA Journal of Molecular Evolution 50 348 358 Altekar G S Dwarkadas J P Huelsenbeck and F Ronquist 2004 Parallel Metropolis coupled Markov chain Monte Carlo for Bayesian phylogenetic inference Bioinformatics 20 407 415 Bishop M J and A E Friday 1987 Tetropad relationships the molecular evidence Pp 123 139 in Molecules and morphology in evolution conflict or compromise C Patterson ed Cambridge University Press Cambridge England Cao Y A Janke P J Waddell M Westerman O Takenaka S Murata N Okada S Paabo and M Hasegawa 1998 Conflict amongst individual mitochon
16. models of nucleotide evolution The Doublet model is intended for stem regions of ribosomal DNA where nucleotides evolve in pairs Finally the Codon models group the nucleotides in triplets and model evolution based on these The type of nucleotide model is set in MrBayes with lset nucmodel for instance if you want to use the doublet model the command is lset nucmodel doublet The default setting is 4by4 4 1 1 Simple Nucleotide Models There has been more work based on the simple four by four nucleotide models than on any other type of evolutionary model for molecular data MrBayes 3 implements three main types of models you select among those by setting the number of substitution types using lset nst to 1 2 or 6 The widely used General Time Reversible GTR model has six substitution types lset nst 6 one for each pair of nucleotides The instantaneous rate matrix for the GTR model is note that we order the rows and columns alphabetically A C G T unlike some other authors A C IG IT A Tol JW Url gr Q C Trc z Wolf Trcr G Airie Tereg x W T mro So ep Jg The GTR model Tavar 1986 has four stationary state frequencies 14 7tc Mac Wr and six rate parameters r4c FAG FAT FCG rcn rar In total there are eight free parameters since one of the stationary state frequencies and one of the substitution rates are determined by the others By default MrBayes uses a flat Diric
17. partitions have been correctly set up MrBayes allows you to set models for individual partitions using the lset applytoandprset applyto mechanism For MrBayes 3 1 Manual 5 26 2005 50 instance assume that we have two partitions a standard data partition partition 1 and a nucleotide partition partition 2 and want to apply a GTR model to the nucleotide data gamma shaped rate variation to both partitions and allow the partition rates to be different Then we would use the commands lset applyto 2 nst 6 lset applyto all rates gamma prset applyto all ratepr variable By default all model parameters that are identical and have the same prior probability distribution associated with them are linked across partitions they are assumed to be one and the same parameter To unlink parameters use the unlink command For instance assume that we want to unlink the shape parameter across the partitions discussed above after all why should the standard data and the molecular data have the same distribution of rates across sites This would be achieved using unlink shape all If you unlink parameters by mistake they can be linked again using the 1 ink command All of the commands mentioned above and given as they would appear in a MrBayes block in a Nexus file can of course be entered from the command line as well without the trailing semicolon However it is often more convenient to have them in either your data file or in a se
18. plot c mpicc DUNIX VERSION DMPI ENABLED 03 Wall Wno uninitialized c sump c mpicc DUNIX VERSION DMPI ENABLED 03 Wall Wno uninitialized c sumt c mpicc DUNIX VERSION DMPI ENABLED 03 Wall Wno uninitialized bayes o command o mbmath o mcmc o model o plot o sump o sumt o lm o mb and produces an MPI enabled version of MrBayes called mb Make sure that the mpicc compiler is invoked and that the MPI ENABLED flag is set It is perfectly normal if the build process stops for a few minutes on the memc c file this is the largest source file and it takes the compiler some time to optimize the code How you run the resulting executable depends on the MPI implementation on your cluster At FSU we typically run MrBayes using LAM MPI First the LAM virtual machine is set up as usual Then the parallel MrBayes job is started with a line such as Smpirun np 4 mb batch nex gt log txt amp to have MrBayes process the file batch nex and run all analyses on four processors np 4 saving screen output to the file 1og txt If you keep both a serial and a parallel version of MrBayes on your system make sure you are using the parallel version with your mpirun command 7 3 Working with the Source Code MrBayes 3 is written entirely in ANSI C If you are interested in investigating or working with the source code you can download the latest bleeding edge version from the MrBayes 3 1 Manual 5 26 2005 63 MrBayes CVS repository at SourceF
19. set ngammacat For instance if you want to use eight discrete rate categories the appropriate command is lset ngammacat 8 The computational complexity is proportional to the number of categories used An analysis with four discrete gamma categories is four times as slow as an analysis with no rate variation across sites and twice as fast as one with eight categories The shape parameter a of the gamma distribution is similar to the shape parameter of the Dirichlet distribution of stationary state frequencies used for standard data see above in that it controls the distribution of another model parameter the site rates Therefore the prior probability distribution used for the shape parameter can be referred to as a hyperprior The default prior used in MrBayes is a uniform distribution on the interval 0 05 50 The sampled values of the shape parameter are found under the column heading alpha in the p file s 4 6 2 Autocorrelated Gamma Model In this model rates vary across sites according to an autocorrelated gamma model where the rate at each site depends to some extent on the rates at adjacent sites Yang 1995 The spatial autocorrelation is measured by the p rho parameter which ranges from 1 negative autocorrelation that is adjacent sites tend to have wildly different rates to 1 adjacent sites have very similar rates The default prior probability for rho is a uniform distribution covering the entire interval 1 1 M
20. sets In principle this can be done from the command line but it is more convenient to do it in a MrBayes block in the data file In your text editor add the following new MrBayes block after the existing block that you just commented out note that each line must be terminated by a semicolon begin mrbayes charset morphology 1 166 charset COI 167 1244 charset EFla 1245 1611 charset LWRh 1612 2092 charset 28S 2093 3246 The charset command simply associates a name with a set of characters For instance the character set COI is defined above to include characters 167 to 1244 The next step is to define a partition of the data according to genes and morphology This is accomplished with the line add it after the lines above partition favored 5 morphology COI EFla LWRh 28S The elements of the partition command are 1 the name of the partitioning scheme favored 2 an equal sign 3 the number of character divisions in the scheme 5 4 a colon and 5 a list of the characters in each division separated by commas The list of characters can simply be an enumeration of the character numbers the above line is equivalent to partition favored 5 1 166 167 1244 1245 1611 1612 2092 2093 3246 but it is often more convenient to use predefined character sets like we did above The final step is to tell MrBayes that we want to work with this partitioning of the data instead of the default partitionin
21. the six GTR rate parameters r A lt gt C r A lt gt G etc 5 the four stationary nucleotide frequencies pi A pi C etc 6 the shape parameter of the gamma distribution of rate variation alpha and 7 the proportion of invariable sites pinvar lf you use a different model for your data set the p files will of course be different MrBayes provides the sump command to summarize the sampled parameter values Before using it we need to decide on the burn in Since the convergence diagnostic we used previously to determine when to stop the analysis discarded the first 25 of the samples and indicated that convergence had been reached after 10 000 generations it makes sense to discard 25 of the samples obtained during the first 10 000 generations Since we sampled every 10 generation there are 1 000 samples 1 001 to be exact since the first generation is always sampled and 25 translates to 250 samples Thus summarize the information in the p file by typing sump burnin 250 By default sump will summarize the information in the p file generated most recently but the filename can be changed if necessary MrBayes 3 1 Manual 5 26 2005 23 The sump command will first generate a plot of the generation versus the log probability of the data the log likelihood values If we are at stationarity this plot should look like white noise that is there should be no tendency of increase or decrease over time The plot
22. to run the local copy of mb in your working directory If you run MrBayes often you will probably want to add the program to your path refer to your Unix manual or your local Unix expert for more information on this All three packages of MrBayes come with example data files These are intended to show various types of analyses you can perform with the program and you can use them as templates for your own analyses Two of the files primates nex and cynmix nex will be used in the tutorial sections of this manual sections 2 and 3 1 3 Getting Started Start MrBayes by double clicking the application icon or typing mb and you will see the information below MrBayes v3 1 Bayesian Analysis of Phylogeny by Fredrik Ronquist and John P Huelsenbeck School of Computational Science Florida State University ronquist csit fsu edu Section of Ecology Behavior and Evolution Division of Biological Sciences University of California San Diego johnh biomail ucsd edu Distributed under the GNU General Public License Type help or help lt command gt for information on the commands that are available MrBayes gt The order of the authors is randomized each time you start the program so don t be surprised if the order differs from the one above Note the MrBayes gt prompt at the bottom which tells you that MrBayes is ready for your commands 1 4 Changing the Size of the MrBayes Window Some MrBayes com
23. version 3 If you are interested in seeing this model reappear let us know An important difference between versions 2 and 3 is found in the way models are defined MrBayes 3 by default estimates most parameters there is no need to specify estimate for any parameter Some things that were previously set using 1set are now set using prset This is true for the amino acid model and for the site specific rates see section 4 of this manual for more information on the site specific rate model in version 3 Thus site specifc rates for instance can no longer be invoked using rates sitespec In more detail the changes are as follows with emphasis on the features in version 2 that are implemented differently in version 3 commands and options in version 2 listed alphabetically calibration Calibration of clock and relaxed clock trees is not yet implemented in MrBayes 3 constraint The format of the constraint now includes a probability value constraint name probability list of taxa The probability value is ignored by version 3 1 of the program but it must be included in the constraint definition The probability value will be used by future versions of the program Iset aamodel The amino acid model is now set using prset aamodelpr MrBayes 3 1 Manual 5 26 2005 58 Iset ancfile Ancestral states are now written to the p file s Iset basefreq Whether this parameters is estimated or fixed to a particular value in v
24. yes MrBayes will overwrite existing files without warning you so make sure that your batch file does not inadvertently cause the deletion of previous result files that should be saved for future reference The UNIX version of MrBayes can execute batch files in the background from the command prompt Just type mb lt file gt gt log txt amp atthe UNIX prompt where file is the name of your Nexus batch file to have MrBayes run in the background logging its output to the file 1og txt If you want MrBayes to process more than one file just list the files one after the other with space between them before the output redirection sign gt When MrBayes is run in this way it will quit automatically when it has processed all files it will also terminate with an error signal if it encounters an error Alternatively the UNIX version of MrBayes can also be run in batch mode using input redirection For that you need a text file containing the commands exactly as you would have typed them from the command line For instance assume that your data set is in primates nex and that you want to perform the same analyses specified above Then typemb lt batch txt gt log txt amp withthe batch txt file containing this text set autoclose yes nowarn yes execute primates nex lset nst 6 rates gamma mcmc ngen 10000 savebrlens yes file primates nexl mcmc file primates nex2 mcmc file primates nex3 quit MrBayes 3 1 Manual 5 26 2005 5
25. 0 20 Brlens 21212121 21 3 4 Running the Analysis When the model has been completely specified we can proceed with the analysis essentially as described above in the previous tutorial for the primates nex data set However in the case ofthe cynmix nex dataset the analysis will have to be run longer before there is any hope of adequate convergence to the stationary distribution When looking at the parameter samples from a partitioned analysis it is useful to know that the names of the parameters are followed by the character division partition number in curly braces For instance pi A 3 is the stationary frequency of nucleotide A in character division 3 which is the EF la division in the above analysis MrBayes 3 1 Manual 5 26 2005 31 4 Evolutionary Models Implemented in MrBayes 3 MrBayes implements a wide variety of evolutionary models for nucleotide amino acid restriction site binary and standard discrete data In addition there are several different ways of modeling the process generating phylogenetic trees An overview of all the models is given in diagrammatic form in the Appendix Here we provide a brief description of each model with some comments on their implementation in MrBayes and advice on how you can apply them successfully to your data 4 1 Nucleotide Models MrBayes implements a large number of DNA substitution models These models are of three different structures The 4by4 models are the usual simple
26. 045924 0 016801 1 048 pi A 0 35530 0 000162 0 329769 0 377153 0 356808 1 092 pi C 0 32083 0 000131 0 299953 0 341757 0 321312 1 152 pi G 0 081154 0 000048 0 068816 0 098442 0 081723 1 014 pi T 0 242714 0 000104 0 226573 0 264684 0 242113 1 000 alpha 0 714405 0 037305 0 419210 1 147286 0 673545 1 007 pinvar 0 18590 0 004887 0 025889 0 307468 0 188027 1 009 Convergence diagnostic PSRF Potential scale reduction factor Gelman and Rubin 1992 uncorrected should approach 1 as runs converge The values may be unreliable if you have a small number of samples PSRF should only be used as a rough guide to convergence since all the assumptions that allow one to interpret it as a scale reduction factor are not met in the phylogenetic context MrBayes 3 1 Manual 5 26 2005 24 For each parameter the table lists the mean and variance of the sampled values the lower and upper boundaries of the 95 credibility interval and the median of the sampled values The parameters are the same as those listed in the p files the total tree length TL the six reversible substitution rates r A lt gt C r A lt gt G etc the four stationary state frequencies pi A pi C etc the shape of the gamma distribution of rate variation across sites alpha and the proportion of invariable sites pinvar Note that the six rate parameters of the GTR model are given as proportions of the rate sum the Dirichlet parameterization This parameter
27. 06 5871 573 5783 012 5755 608 0 01 20 1000 5811 949 5737 884 5888 234 5819 793 5867 377 5851 693 5784 437 5749 264 0 01 21 Average standard deviation of split frequencies 0 073946 MrBayes 3 1 Manual 1100 5784 586 5836 074 5779 940 9000 5737 756 5740 655 5730 045 Average standard deviation of split frequencies 9100 5732 093 5741 841 5735 730 9200 5731 412 5740 270 5742 079 9300 5739 416 5728 550 5730 645 9400 5720 648 5720 959 5739 326 9500 5730 870 5720 702 5737 968 9600 5736 460 5718 892 5736 313 9700 5740 378 5724 006 5736 798 9800 5739 019 5722 901 5734 184 9900 5743 556 5732 476 5728 482 10000 5738 106 5732 410 5728 515 Average standard deviation of split frequencies Continue with analysis 5 26 2005 5730 069 5739 170 5728 228 5729 487 29733 215 5726 010 5728 251 5729 764 5734 909 5726 709 5732 631 5720 832 5729 773 5726 367 5734 016 5727 928 5733 312 5722 292 5735 541 5722 141 5724 246 5725 045 5723 380 5725 418 yes no 5880 476 0 01 20 25735 78 1 0 00 09 5735 816 0 00 08 5729 846 0 00 07 5723 707 0 00 06 5732 691 0 00 05 5729 010 0 00 04 5737 829 0 00 03 5735 204 0 00 02
28. 06 5723 380 Average standard deviation of split frequencies 7485 569 7700 6766 678 6682 6338 168 6272 6139 200 6049 6074 274 5967 6019 301 5948 5997 276 5927 5966 224 5880 5963 531 5860 5926 666 5855 5888 234 5819 0 5880 476 5798 5735 787 5722 0 5735 816 5720 5729 846 5720 5723 707 5720 5732 691 5724 5729 010 5727 5737 829 5727 5735 204 5724 5731 738 5728 5736 484 5731 5726 322 5727 0 309 7832 527 6506 242 6339 061 6073 236 6002 768 5925 3 204 5899 975 5890 182 5883 916 5870 193 25867 073946 728 5839 263 5730 000000 361 5737 670 5731 408 5728 562 Fe 5728 405 5727 732 25728 199 25728 466 5723 803 95727 599 55728 000000 045 7618 277 6944 400 6715 056 6359 941 6215 423 6072 590 6035 220 6008 474 5902 806 5871 377 5851 268 5836 926 5740 343 5741 852 5740 016 5728 739 5720 274 5720 393 5718 102 5724 404 5722 082 5732 776 5732 074 655 7776 608 7836 826 6784 126 6991 307 6265 329 6599 698 6106 834 6515 348 5980 096 6036 624 5925 549 5963 42
29. 10000 samplefreq 10 This will ensure that you get at least 1 000 samples from the posterior probability distribution For larger data sets you probably want to run the analysis longer and sample less frequently the default sampling frequency is every 100 generation You can find the predicted remaining time to completion of the analysis in the last column printed to screen 3 2 If the standard deviation of split frequencies is below 0 01 after 100 000 generations stop the run by answering no when the program asks Continue the analysis yes no Otherwise keep adding generations until the value falls below 0 01 4 1 Summarize the parameter values by typing sump burnin 250 or whatever value corresponds to 25 of your samples The program will output a table with summaries of the samples of the substitution model parameters including the mean mode and 95 96 credibility interval of each parameter Make sure that the potential scale reduction factor PSRF is reasonably close to 1 0 for all parameters if not you need to run the analysis longer 4 2 Summarize the trees by typing sumt burnin 250 or whatever value corresponds to 25 of your samples The program will output a cladogram with the posterior probabilities for each split and a phylogram with mean branch lengths The trees will also be printed to a file that can be read by tree drawing programs such as TreeView MacClade and Mesquite It does not have to be more compli
30. 3 The quit command forces MrBayes to terminate With previous versions of MrBayes we have had problems with infinite loops when the quit command is not included at the end of the file This problem should have been solved in version 3 1 How are gaps and missing characters treated MrBayes uses the same method as most maximum likelihood programs it treats gaps and missing characters as missing data Thus gaps and missing characters will not contribute any phylogenetic information There is no way in which you can treat gaps as a fifth state in MrBayes but see below for information on how you can use gap information in your analysis How do I use gap information in my analysis Often insertion and deletion events contain phylogenetically useful information Although MrBayes 3 is not able to do statistical multiple sequence alignment treating the insertion deletion process under a realistic stochastic model there is nevertheless a way of using some of the information in the indel events in your MrBayes analysis Code the indel events as binary characters presence absence of the gap and include them as a separate binary restriction data partition in your analysis See more information on this possibility in the section on the binary model in this manual What do I do when it is difficult to get convergence There are several things you can do to improve the efficiency of your analysis The simplest is to just increase the length of th
31. 4 2 2 Estimating the Fixed Rate Model ee i re e aan eet 3T 4233 variable wate MIOGUels os ohh Gy Aer dee staat tco fa dtr fat at coa 37 4 3 Restriction Site Binary Model eee t ee e ie e naeh e e 39 4 4 Standard Discrete Morphology Model sse 40 4 5 Parsimong Modelo osse usine pesa btsuen Qa eo ge ide Ded a td Moog eta d ot sue do 42 4 6 Rate Variation Across Sites es od uera ee eio e e e ie ege wave 43 4 6 1 Gamma distributed Rate Models ea HR M M Me eden 43 4 6 2 Autocorrelated Gamma Model rrt i reno eb oua resign cheval a aee 43 4 6 3 Proportion of Invariable Sites oso FC n retten ted ere rec edet 44 4 6 4 Partitioned Site Specific Rate Model ec eetetetreeet 45 4 6 5 Inferring Site RATES esee Dor dee qeu ien op eb Ote e ds 45 MrBayes 3 1 Manual 5 26 2005 3 4 7 Rate Variation Across the Tree The Covarion Model cccccccceeseceeeesteeeeees 46 4 8 Topology and Branch Length Models sse 47 4 8 1 Unconstrained and Constrained Topology sese 47 4 8 2 Non clock Standard Trees db oa Qa ep b e p ter Hee one 48 4 8 3 Strict Clock Trees so oo e Det e e vicina e tle Rl aes ep ee Re 48 AS Av Relaxed Clock TIES ari ed Dabei essere A bestand E ceriunle riu 49 4 0 Partiioned Models 45 rst spo a ant ees oA eae 49 4 10 Ancestral State Reconstruction cose o e e Ebo ul beu pred acus 50 5 Frequently Asked Questions oeeeere etr
32. 60 174 Hasegawa M T Yano and H Kishino 1984 A new molecular clock of mitochondrial DNA and the evolution of Hominoids Proc Japan Acad Ser B 60 95 98 Hastings W K 1970 Monte Carlo sampling methods using Markov chains and their applications Biometrika 57 97 109 Henikoff S and J G Henikoff 1992 Amino acid substitution matrices from protein blocks Proc Natl Acad Sci U S A 89 10915 10919 Holder M and P O Lewis 2003 Phylogeny estimation Traditional and Bayesian approaches Nature Reviews Genetics 4 275 284 Huelsenbeck J P F Ronquist R Nielsen and J P Bollback 2001 Bayesian inference of phylogeny and its impact on evolutionary biology Science 294 2310 2314 Huelsenbeck J P H B Larget R E Miller and F Ronquist 2002 Potential applications and pitfalls of Bayesian inference of phylogeny Systematic Biology 51 673 688 Huelsenbeck J P 2002 Testing a covariotide model of DNA sub stitution Molecular Biology and Evolution 19 5 698 707 Huelsenbeck J P and F Ronquist 2001 MRBAYES Bayesian inference of phylogeny Bioinformatics 17 754 755 Huelsenbeck J P and J P Bollback 2001 Empirical and hierarchical Bayesian estimation of ancestral states Systematic Biology 50 351 366 Jones D T W R Taylor and J M Thornton 1992 The rapid generation of mutation data matrices from protein sequences Comput Appl Biosci 8 275 282 Jukes T and C Cantor 1969 Evolutio
33. 7 5904 327 5896 520 5876 956 5838 392 5790 765 5789 326 5783 012 5755 608 5784 437 5749 264 5779 940 5739 170 5730 045 5729 487 5735 730 5726 010 5742 079 5729 764 5730 645 5726 709 5739 326 5720 832 5737 968 5726 367 5736 313 5727 928 5736 798 5722 292 5734 184 5722 141 5728 482 5725 045 5728 515 5725 418 oOooooooooo OoOooooooooo 01 01 01 01 01 01 01 01 01 01 00 00 00 00 00 00 00 00 00 00 00 39 38 37 12 16 19 20 20 21 20 09 08 07 06 05 04 03 02 01 00 00 MrBayes 3 1 Manual 5 26 2005 21 Continue with analysis yes no The first column lists the generation number The following four columns with negative numbers each correspond to one chain in the first run Each column corresponds to one physical location in computer memory and the chains actually shift positions in the columns as the run proceeds The numbers are the log likelihood values of the chains The chain that is currently the cold chain has its value surrounded by square brackets whereas the heated chains have their values surrounded by parentheses When two chains successfully change states they trade column positions places in computer memory If the Metropolis coupling works well the cold chain should move around among the columns this means that the cold chain successfully s
34. CGGCGC GCTCTCCCTAAGCTT Gorilla AAGCTTCTCCGGTGC ACTCTCCCTAAGCTT Pongo AAGCTTCACCGGCGC ACTCTCACTAAGCTT Hylobates AAGTTTCATTGGAGC ACTCTCCCTAAGCTT end The file contains only one block a DATA block The DATA block is initialized with begin data followed by the dimensions statement the format statement and the matrix statement The dimensions statement must contain ntax the number of taxa and nchar the number of characters in each aligned sequence The format statement must specify the type of data for instance datat ype DNA or RNA or Protein or Standard or Restriction The format statement may also contain gap or whatever symbol is used for a gap in your alignment mi ssing or whatever symbol is used for missing data in your file interleave yes when the data matrix is interleaved sequences and match or whatever symbol is used for matching characters in the alignment The format statement is followed by the matrix statement usually started by the word mat xix on a separate line followed by the aligned sequences Each sequence begins with the sequence name separated from the sequence itself by at least one space The data block is completed by an end statement Note that the begin dimensions format and end statements all end in a semicolon That semicolon is essential and must not be left out Note that although it occupies many lines in the file the matrix description is also a regular statement a matrix stat
35. MrBayes 3 1 Manual Draft 5 26 2005 Fredrik Ronquist John P Huelsenbeck and Paul van der Mark q School of Computational Science Florida State University Tallahassee FL 32306 4120 U S A Division of Biological Sciences University of California at San Diego La Jolla CA 92093 USA ronquist csit fsu edu johnh gbiomail ucsd edu gt paulvdm esit fsu edu MrBayes 3 1 Manual 5 26 2005 2 Contents Vnirar iR 2 DIC hO Mae HOM ec 4 1 1 Conventions Used in this Manual cer ee Rn Rees i FRE XE et et tens 4 1 2 Acquiring and Installing MrBayes ccccccccessceceeseneeeeeeeneeeeeeseneeeeeeseneeeeeneaaes 4 1 3 Getting St rted oo sae one testo Ende re uisus tse ed pops opel er gu EID 6 1 4 Changing the Size of the MrBayes Window ssssssssseeeeeeeneens 6 EKETA n E 1 o do taie ot M bua EEN er tK y 1 6 Reporting and Fixing BUBSu coi ee p t ed Rode d e i ee ie du aei de M Rud 7 Iz Licenseand Warranty ecce eit oie tie nie Lie ban m bre ER on ud ees etn Lud bae B E 8 2 Tutorial A Simple Analysis ccssscsssccsvasscessvcsasscavscsvassveuasassvassuusawevassdavcessesavavavadsvasseads 8 2 1 Quick Start Versions S o o d pP eb Ho vag Poi aae T dus 8 2 2 Get ng Data into MT Bayes a uS ano a REN ELI DN Nek Sas 9 2 3 Specifying a Model neresno tates to hai etai ada besx us tox usa nox ua obeunda aed 11 24 Settine tlie PTOI Sects ca vs tor be etel erie neutrogena dd 13 2 9 Checkinethe M
36. MrBayes 3 1 Manual 5 26 2005 18 default Nchains is set to 4 meaning that MrBayes will use 3 heated chains and one cold chain In our experience heating is essential for problems with more than about 50 taxa whereas smaller problems often can be analyzed successfully without heating Adding more than three heated chains may be helpful in analyzing large and difficult data sets The time complexity of the analysis is directly proportional to the number of chains used unless MrBayes runs out of physical RAM memory in which case the analysis will suddenly become much slower but the cold and heated chains can be distributed among processors in a cluster of computers using the MPI version of the program see below greatly speeding up the calculations MrBayes uses an incremental heating scheme in which chain i is heated by raising its posterior probability to the power 1 1 iA where A is the temperature controlled by the Temp parameter The effect of the heating is to flatten out the posterior probability such that the heated chains more easily find isolated peaks in the posterior distribution and can help the cold chain move more rapidly between these peaks Every Swapfreq generation two chains are picked at random and an attempt is made to swap their states For many analyses the default settings should work nicely If you are running many more than three heated chains however you may want to increase the number of swaps Nswaps that
37. Muller and Vingron 2000 and the Blosum62 model Henikoff and Henikoff 1992 Each model is appropriate for a particular type of proteins For instance if you are analyzing mammal mitochondrial proteins you might want to use the Mtmam model Invoke that model by typing prset aamodelpr fixed mtmam 4 2 2 Estimating the Fixed Rate Model MrBayes allows a convenient way of estimating the fixed rate model for your amino acid data instead of specifying it prior to the analysis If you choose this option MrBayes will allow the MCMC sampler to explore all of the fixed rate models listed above including the Poisson model by regularly proposing new models When the MCMC procedure has converged each model will contribute to your results in proportion to its posterior probability For instance if you are analyzing mammal mitochondrial proteins it is likely that the Mtmam model will contribute most to the posterior distribution but it is possible that some other models for instance the Mtrev model will contribute significantly too A nice feature of the MCMC model estimation is that the extra computational cost is negligible To allow so called model jumping between fixed rate amino acid models simply set the prior for the amino acid model to mixed prset aamodelpr mixed prior to analysis During the run MrBayes will print the index of the current model to the p file s in the aamodel column The indices of the models are as follows 0 Poisso
38. OSels s to deca n f es ede sc et difci 15 2 6 Setting up THE ATalY SIS a a aoi esca nha oue ERG 2A BUR Gada MS MIRO ORAE 16 2 T Running the Analysis ior eoe Cis rer er e il e e e HN amen Ha re Ie ee 19 2 5 When fO SItOD th Analysis nai cud eet none ai Woe a P eMe eR 21 2 9 Summarizing Samples of Substitution Model Parameters ssssss 22 2 10 Summarizing Samples of Trees and Branch Lengths sess 24 3 Analyzing a Partitioned Data Set eeeee eee eee eee eese eee eee eene eene ee teet annes ane 27 3 1 Getting Mixed Data into MEBAVES c en re et X ge Ure S e teu vt tava eed 27 3 2 Dividing the Data into ParBtiotisa 2c duas emeret oret decet s ne dua Tes 28 3 3 Specifying a Partitioned Model ciis tontos Sabaensetsnonde labsoncsassauscts 29 34 R nning the AMAIVSIS bete pce Un e dn eiua Ue d qi ort cial 30 4 Evolutionary Models Implemented in MrBayes 3 eee 31 4 1 Nucleotide Models naro nira rore rode gates vt sette av gea lend 31 4 1 1 Simple Nucleotide Models uu rrt er ete e c ae rh 31 41 2 The Doublet Model 5 0 bas cyenssnecsehakivenstsdnwavetabsaatesddnonte dol ec ugik gox deduce det uec 33 4 1 3 Codon Models ossi E hue ER DE dite telle ie b e Up Ne nd Ge REN en du eG 35 2 2 Amino actd IMGT Sess uoc ect tit ft t ito Data nese tae Sed reto e sheds 36 42 LPIxedRale MOelgc c eie potete cis qub tsubek da bee eee ekle og ud dea edu uet eias ES id 37
39. able at the end of the help information reads MrBayes 3 1 Manual 5 26 2005 14 Model settings for partition 1 Parameter Options Current Setting Tratiopr Beta Fixed Beta 1 0 1 0 Revmatpr Dirichlet Fixed Dirichlet 1 0 1 0 1 0 1 0 1 0 1 0 Aamodelpr Fixed Mixed Fixed Poisson Aarevmatpr Dirichlet Fixed DrirTYchle t l 0 l 0 4 Omegapr Dirichlet Fixed Dirichlet 1 0 1 0 Ny98omegalpr Beta Fixed Beta 1 0 1 0 Ny98omega3pr Uniform Exponential Fixed Exponential 1 0 3omegapr Exponential Fixed Exponential Codoncatfreqs Dirichlet Fixed Dirichlet 1 0 1 0 1 0 Statefreqpr Dirichlet Fixed Dirichlet 1 0 1 0 1 0 1 0 Ratepr Fixed Variable Dirichlet Fixed Shapepr Uniform Exponential Fixed Uniform 0 0 50 0 Ratecorrpr Uniform Fixed Uniform 1 0 1 0 Pinvarpr Uniform Fixed Uniform 0 0 1 0 Covswitchpr Uniform Exponential Fixed Uniform 0 0 100 0 Symmetricbetapr Uniform Exponential Fixed Fixed Infinity Topologypr Uniform Constraints Uniform Brlenspr Unconstrained Clock Unconstrained Exp 10 0 Speciationpr Uniform Exponential Fixed Uniform 0 0 10 0 Extinctionpr Uniform Exponential Fixed Uniform 0 0 10 0 Sampleprob number 1 00 Thetapr Uniform Exponential Fixed Uniform 0 0 10 0 Growthpr Uniform Exponential Fixed Normal Fixed 0 0 We need to focus on Revmatpr for the six substitution rates of the GTR rate matrix Statefreqpr for the stationary nucleotide frequencies of the GTR rate matrix Shapepr for t
40. aking MrBayes 3 1 Manual 5 26 2005 8 sure the bug can be reproduced reliably using a fixed seed and swapseed for the memc command and ideally also with a small data set The Tracker software at SourceForge will make sure that you get email notification when the bug has been fixed in the source code on the MrBayes CVS repository at SourceForge Note however that there may be some time before new executables containing the bug fix will be released Advanced users may be interested in fixing bugs themselves in the source code Refer to section 7 of this manual for information on how to contribute bug fixes improved algorithms or expanded functionality to other users of MrBayes 1 7 License and Warranty MrBayes is free software you can redistribute it and or modify it under the terms of the GNU General Public License as published by the Free Software Foundation either version 2 of the License or at your option any later version The program is distributed in the hope that it will be useful but WITHOUT ANY WARRANTY without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE See the GNU General Public License for more details http www gnu org copyleft gpl html 2 Tutorial A Simple Analysis This section is a tutorial based on the primates nex data file It will guide you through a basic Bayesian MCMC analysis of phylogeny explaining the most important features of the program There are two ve
41. all characters evolve at the same rate measured in expected changes per site over the tree There are four ways in which you can allow rate variation across sites The simplest method is to assume that rates vary over sites according to a gamma distribution Yang 1993 The gamma model can be combined with spatial autocorrelation between the rates at adjacent sites the autocorrelated gamma model A completely different approach to rate variation across sites is to allow a proportion of sites to be invariable This model can be combined with the gamma model but not with the autocorrelated gamma model Finally it is possible to divide characters into groups evolving at different rates the partitioned or site specific rate model 4 6 1 Gamma distributed Rate Model The commonly used model of gamma shaped rate variation across sites is invoked using lset rates gamma The shape of the gamma distribution is determined by the so called alpha parameter When this parameter is small below 1 the distribution takes on an L shaped form with a few sites evolving rapidly while most sites are conserved Conversely when a is above 1 the distribution becomes similar to a normal distribution with less and less variation in rates across sites as becomes larger In practice the gamma distribution is approximated using a small number of discrete rate categories Yang 1994 By default four rate categories are used you can change this setting by using
42. alue If you have a posterior of this kind you should not be surprised 1f Metropolis coupling results in rapid instantaneous shifts from one mode to the other during the stationary phase of the analysis The reason for this is that different chains are likely to explore different peaks in the posterior and successful swapping MrBayes 3 1 Manual 5 26 2005 45 involving the cold chain is likely to result in mode jumping Also you should consider presenting the entire distribution of the sampled alpha and pinvar parameters since simple point estimates of each parameter would be misleading 4 6 4 Partitioned Site Specific Rate Model For protein coding nucleotide sequences a site specific rate model is often used allowing each codon position first second and third codon position sites to have its own rate This results in a model with three rates two of which are free to vary since the average rate is 1 0 by definition More generally we might have different character divisions separate genes morphology etc which potentially evolve at very different rates In MrBayes 3 we provide a general mechanism for setting up these models based on partitioning the data set and then unlinking parameters across the partitions Assume for instance that we want to set up a site specific rate model for a data set with one sequence We first set up the codon site partitioning scheme using the following lines in a MrBayes block charset posl 1
43. ameter 2 Then there is also a topology parameter 3 and a set of branch length parameters 4 Both the topology and branch lengths are the same for all partitions Now assume we want a separate GTR T I model for each gene partition All the parameters should be estimated separately for the individual genes Assume further that we want the overall evolutionary rate to be potentially different across partitions and that we want to assume gamma shaped rate variation for the morphological data We can obtain this model by using 1set and prset with the applyto mechanism which allows us to apply the settings to specific partitions For instance to apply a GTR I model to the molecular partitions we type 1set applyto 2 3 4 5 nst 6 rates invgamma This will produce the following table when showmodel is invoked Active parameters Partition s Parameters 1 2 3 4 5 Revmat z uh mW TR al Statefreq 2 3 23 35 43 Shape 4 4 4 4 Pinvar ma 8 08 125 o5 Topology 6 6 6 6 6 Brlens Es wb XR Ug vb As you can see all molecular partitions now evolve under the correct model but all parameters statefreq revmat shape pinvar are shared across partitions To MrBayes 3 1 Manual 5 26 2005 30 unlink them such that each partition has its own set of parameters type unlink statefreq all revmat all shape all pinvar all Gamma shaped rate variation for the morphological data is enforced with 1set applyto 1 rate
44. are tried each time the chain stops for swapping The Samplefreq setting determines how often the chain is sampled By default the chain is sampled every 100th generation and this works well for most analyses However our analysis is so small that we are likely to get convergence quickly so it makes sense to sample the chain more frequently say every 10 generation this will ensure that we get at least 1 000 samples when the number of generations is set to 10 000 To change the sampling frequency type mcmcp samplefreq 10 When the chain is sampled the current values of the model parameters are printed to file The substitution model parameters are printed to a p file in our case there will be one file for each independent analysis and they will be called primates nex runl p and primates nex run2 p The p files are tab delimited text files that can be imported into most statistics and graphing programs The topology and branch lengths are printed to a t file in our case there will be two files called primates nex runl tandprimates nex run2 t The t files are Nexus tree files that can be imported into programs like PAUP and TreeView The root of the p and t file names can be altered using the Filename setting The Printfreq parameter controls the frequency with which the state of the chains is printed to screen Leave Printfreq at the default value print to screen every 100th generation The default behavior of MrBayes is
45. are using the MPI version of the program you may also want to cite Altekar et al 2004 How do I run MrBayes in batch mode When you become more familiar with MrBayes you will undoubtedly want to run it in batch mode instead of typing all commands at the prompt This is done by adding a MrBayes 3 1 Manual 5 26 2005 52 MRBAYES block to a Nexus file either the same file containing the DATA block or a separate Nexus file The MRBAYES block simply contains the commands as you would have given them from the command line with the difference that each command line is ended with a semi colon For instance a MRBAYES block that performs three single run analyses of the data set primates nex under the GTR model and stores each result in a separate file is given below begin mrbayes set autoclose yes nowarn yes execute primates nex lset nst 6 rates gamma mcme nruns 1 ngen 10000 samplefreq 10 file primates nexl mcmc file primates nex2 mcmc file primates nex3 end Since this file contains the execute command it must be in a file separate from the primates nex file You start the analysis simply by typing execute filename where filename is the name of the file containing the MRBAYES block The set command is needed to change the behavior of MrBayes such that it is appropriate for batch mode When autoclose yes MrBayes will finish the MCMC analysis without asking you whether you want to add more generations When nowarn
46. arsimony score hence we call it the parsimony model The model is also referred to as the No Common Mechanism model because it treats each branch length for each character as a separate completely independent parameter In principle a Bayesian MCMC analysis using the parsimony model should integrate out the branch lengths but MrBayes 3 uses a simpler approach in which the branch lengths are fixed to their maximum likelihood values infinity if there is a change on the branch and zero otherwise This type of approach where some parameters are fixed prior to the Bayesian analysis according to some non Bayesian estimate is typically referred to as an empirical Bayes method Future versions of MrBayes may implement the true hierarchical Bayesian approach to the parsimony model but we expect the results to be very similar under both approaches The parsimony model is much less parsimonious with respect to parameters than any other model implemented in MrBayes Consider for instance an analysis of 1 000 characters and 100 taxa The parsimony model would have about 200 000 free parameters 200 branches times 1 000 characters A more typical GTR T I model would have only little more than 200 parameters about 1 000 times fewer parameters In this sense the standard stochastic models are much more parsimonious than the parsimony model Several problems are associated with the excessive number of parameters Statistical inconcistency is perhaps the
47. ate unequal stationary state frequencies or substitution rates recall that the stationary state frequencies are an important factor in determining the latter However it is still possible to allow the state frequencies rates to vary over sites according to some appropriate distribution MrBayes uses a symmetric Dirichlet distribution for this purpose For binary data the analogy of the Dirichlet distribution is called the beta distribution MrBayes uses Dirichlet and beta interchangeably for the distribution depending on context The approach is similar to the one used to allow rate variation across sites according to a gamma distribution we calculate the likelihood of a site assuming different discrete categories of asymmetry and then we sum the values to obtain the site likelihood The symmetric Dirichlet distribution has one parameter that determines its shape just like the alpha parameter determines the shape of the gamma distribution The larger the parameter of the symmetric Dirichlet the less transition rate stationary frequency asymmetry there is across sites By default the parameter is fixed to infinity prset symdirihyperpr fixed infinity this corresponds to the standard assumption of no transition rate asymmetry across sites the rate of going from 0 to 1 is equal to the rate of going from 1 to 0 for all characters The prior is called a hyperprior because it concerns a distribution that controls the distributions of other model
48. ave concatenated nucleotide sequences from three genes in your data set of length 1962 1050 and 2082 sites respectively Then you create character sets for those three genes using charset genel 1 1962 charset gene2 1963 3012 charset gene3 3013 in a MrBayes block Note the use of the dot as a synonym of the last site You can also use the backslash n sequence to include every nth character in the preceding range of characters see the description of the site specific rate model above Once the character sets are defined the partitioning scheme based on the genes is defined with the partition command and selected using the set command partition by gene 3 genel gene2 gene3 set partition by gene Here by gene is the name we chose for the partitioning scheme The name is followed by an equal sign the number of partitions and then a comma separated list of characters to include in each partition Note that MrBayes requires the partitioning scheme to include all characters Say for instance that you wanted to run an analysis with only gene 1 and gene 2 Then define a two partition scheme and exclude the characters represented by gene 3 partition genel amp 2 2 genel gene2 gene3 exclude gene3 set partition genel amp 2 If the only purpose of the partition gene1 amp 2 is to allow exclusion of gene 3 then gene 3 can of course be included in either of the two partitions before being excluded Once the
49. ber gt For instance r 45 is the inferred rate at site character 45 of your data set MrBayes 3 1 Manual 5 26 2005 46 4 7 Rate Variation Across the Tree The Covarion Model For both nucleotide sequence and amino acid data MrBayes allows rates to change across the tree under a covarion like model Tuffley and Steel 1998 Huelsenbeck 2002 see also Galtier 2001 Specifically the covarion like model assumes that a site is either on or off When it is on it evolves under a standard four by four nucleotide or 20 by 20 amino acid model but when it is off it does not change at all The switching between on and off states is controlled by two rate parameters s01 from off to on and s10 from on to off The instantaneous rate matrix of the nucleotide variant also referred to as the covariotide model assuming a GTR model for the on state is Au Cor Gor Me An Col Ga Ta Aa 0 0 0 s 0 0 0 a 0 0 0 0 S l 0 0 G oer 0 0 0 0 0 Big 0 Q Us 0 0 0 0 0 0 Sos s As Sio 0 0 0 B Work morak mrqk Con 0 Sio 0 O Taik Wghgk Wink Gon 0 0 Sio O Ayk mongk Turk Ton 0 0 0 Sio ark monk monk B where k is a scaling constant determined by the proportion of time the sites spend in the on state The matrix can be simplified into Q D R R KR where each R element is a four by four matrix R contains the rates in the off state all rates are 0 Rz and R describe the switching process the d
50. best known of these but more fundamentally a model like the parsimony model does not offer much in terms of generalities that can be inferred about the evolutionary process The Goldman 1993 model is another example of a parameter rich stochastic model that orders trees in the same way as the parsimony method In this model the branch lengths are the same but the ancestral states are estimated for all characters and all nodes in the tree For an analysis of 100 taxa and 1 000 characters this results in approximately 100 000 free parameters The Goldman model is actually very similar to the No Common Mechanism model it makes little difference if the character specific and tree section specific parameters are introduced at the nodes or at the branches The Goldman model is not implemented in MrBayes We would like to emphasize that we do not recommend the use of the parsimony model We have included it in MrBayes only to allow users to explore its properties and contrast it with the other models implemented in the program The parsimony model is not the default model used for standard morphological data in MrBayes The default standard data model is described above and is similar to the models used for nucleotide and amino acid data By default MrBayes does not use the parsimony model at all you have to invoke it using lset parsmodel yes MrBayes 3 1 Manual 5 26 2005 43 4 6 Rate Variation Across Sites By default MrBayes assumes that
51. bluth A H Teller and E Teller 1953 Equations of state calculations by fast computing machines J Chem Phys 21 1087 1091 Muller T and M Vingron 2000 Modeling amino acid replacement Journal of Computational Biology 7 761 776 Muse S and B Gaut 1994 A likelihood approach for comparing synonymous and non synonymous substitution rates with application to the chloroplast genome Molecular Biology and Evolution 11 715 724 Newton M B Mau and B Larget 1999 Markov chain Monte Carlo for the Bayesian analysis of evolutionary trees from aligned molecular sequences In Statistics in molecular biology F Seillier Moseiwitch T P Speed and M Waterman eds Monograph Series of the Institute of Mathematical Statistics Newton M A and A E Raftery 1994 Approximate Bayesian inference by the weighted likelihood bootstrap with discussion Journal of the Royal Statistical Society Series B 56 3 48 Nielsen R and Z Yang 1998 Likelihood models for detecting positively selected amino acid sites and applications to the HIV 1 envelope gene Genetics 148 929 936 Nylander J A A F Ronquist J P Huelsenbeck and J L Nieves Aldrey 2004 Bayesian Phylogenetic analysis of combined data Systematic Biology 53 47 67 Rannala B and Z Yang 1996 Probability distribution of molecular evolutionary trees a new method of phylogenetic inference J Mol Evol 43 304 311 Ronquist F 2004 Bayesian inference of
52. cated than this however as you get more proficient you will probably want to know more about what is happening behind the scenes The rest of this section explains each of the steps in more detail and introduces you to all the implicit assumptions you are making and the machinery that MrBayes uses in order to perform your analysis 2 2 Getting Data into MrBayes To get data into MrBayes you need a so called Nexus file that contains aligned nucleotide or amino acid sequences morphological standard data restriction site binary data or any mix of these four data types The Nexus file that we will use for this tutorial primates nex contains 12 mitochondrial DNA sequences of primates A Nexus file is a simple text ASCII file that begins with NEXUS on the first line The rest of the file is divided into different blocks The primates nex file looks like this NEXUS MrBayes 3 1 Manual 5 26 2005 10 begin data dimensions ntax 12 nchar 898 format datatype dna interleave no gap matrix Saimiri sciureus AAGCTTCATAGGAGC ACTATCCCTAAGCTT Tarsius syrichta AAGCTTCACCGGCGC ATTATGCCTAAGCTT Lemur catta AAGCTTCACCGGCGC ACTATCTATTAGCTT Macaca fuscata AAGCTTCACCGGCGC CCTAACGCTAAGCTT M mulatta AAGCTTCACCGGCGC CCTAACACTAAGCTT M fascicularis AAGCTTTACAGGTGC CCTAACACTAAGCTT M sylvanus AAGCTTTTCCGGCGC CCTAACATTAAGCTT Homo sapiens AAGCTTTTCTGGCGC GCTCTCCCTAAGCTT Pan AAGCTTCTC
53. character evolution Trends in Ecology and Evolution 19 475 481 Ronquist F and J P Huelsenbeck 2003 MRBAYES 3 Bayesian phylogenetic inference under mixed models Bioinformatics 19 1572 1574 Schoniger M and A von Haeseler 1994 A stochastic model and the evolution of autocorrelated DNA sequences Molecular Phylogenetics and Evolution 3 240 247 MrBayes 3 1 Manual 5 26 2005 66 Tavare S 1986 Some probabilistic and statisical problems on the analysis of DNA sequences Lect Math Life Sci 17 57 86 Tuffley C and M Steel 1997 Links between maximum likelihood and maximum parsimony under a simple model of site substitution Bull Math Bio 59 581 607 Tuffley C and M Steel 1998 Modeling the covarion hypothesis of nucleotide substitution Mathematical Biosciences 147 63 91 Whelan S and Goldman N 2001 A general empirical model of protein evolution derived from multiple protein families using a maximum likelihood approach Molecular Biology and Evolution 18 691 699 Yang Z 1993 Maximum likelihood estimation of phylogeny from DNA sequences when substitution rates differ over sites Molecular Biology and Evolution 10 1396 1401 Yang Z 1994 Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites Approximate methods Journal of Molecular Evolution 39 306 314 Yang Z 1995 A space time process model for the evolution of DNA sequences Genetics 139 993 1005 Yang Z and
54. dom User Random Nperts lt number gt 0 Savebrlens Yes No Yes Ordertaxa Yes No No The Seed is simply the seed for the random number generator and Swapseed is the seed for the separate random number generator used to generate the chain swapping sequence see below Unless they are set to user specified values these seeds are generated from the system clock so your values are likely to be different from the ones in the screen dump above The Ngen setting is the number of generations for which the analysis will be run It is useful to run a small number of generations first to make sure the analysis is correctly set up and to get an idea of how long it will take to complete a longer analysis We will start with 10 000 generations To change the Ngen setting without starting the analysis we use the mcmcp command which is equivalent to memc except that it does not start the analysis Type mcomcp ngen 10000 to set the number of generations to 10 000 You can type help memc to confirm that the setting was changed appropriately By default MrBayes will run two simultaneous completely independent analyses starting from different random trees Nruns 2 Running more than one analysis simultaneously is very helpful in determining when you have a good sample from the posterior probability distribution so we suggest that you leave this setting as is The idea is to start each run from different randomly chosen trees In the early phases of the run th
55. drial proteins in resolving the phylogeny of eutherian orders Journal of Molecular Evolution MrBayes 3 1 Manual 5 26 2005 64 Dayhoff M O R M Schwartz and B C Orcutt 1978 A model of evolutionary change in proteins Pp 345 352 in Atlas of protein sequence and structure Vol 5 Suppl 3 National Biomedical Research Foundation Washington D C Dimmic M W J S Rest D P Mindell and D Goldstein 2002 RArtREV An amino acid substitution matrix for inference of retrovirus and reverse transcriptase phylogeny Journal of Molecular Evolution 55 65 73 Felsenstein J 1981 Evolutionary trees from DNA sequences A maximum likelihood approach Journal of Molecular Evolution 17 368 376 Felsenstein J 1992 Phylogenies from restriction sites A maximum likelihood approach Evolution 46 159 173 Galtier N 2001 Maximum likelihood phylogenetic analysis under a covarion like model Mol Biol Evol 18 866 873 Geyer C J 1991 Markov chain Monte Carlo maximum likelihood Pages 156 163 in Computing Science and Statistics Proceedings of the 23rd Symposium on the Interface E M Keramidas ed Fairfax Station Interface Foundation Goldman N and Z Yang 1994 A codon based model of nucleotide substitution for protein coding DNA sequences Molecular Biology and Evolution 11 725 736 Hasegawa M H Kishino and T Yano 1985 Dating the human ape split by a molecular clock of mitochondrial DNA Journal of Molecular Evolution 22 1
56. e M3 model also has three classes of values but these values are less constrained in that they only have to be ordered lt z lt w3 If for instance you would like to invoke the M3 model use the command 1set omegavar M3 When you use a model with variation in selection pressure across sites you probably want to infer the positively selected sites If you select report possel yes before you start your analysis MrBayes will calculate the probability of each site being in a positively selected omega class For the M3 model for instance the likelihood of the site is calculated under each of the three categories taking the category frequencies into account and then the likelihoods are summed to yield the total likelihood of the site Finally the proportion of this sum originating from categories that are positively selected those that have an wvalue larger than 1 this is the posterior probability of the site being positively selected Once the probabilities of each site being positively selected are printed to file they can be summarized using the standard sump command When interpreting the output from the Ny98 model it is helpful to know that pi pi N and pi are the frequencies of the negatively selected neutral and positively selected categories respectively and omega omega N and omega are the corresponding w values The M3 model parameters are instead labeled pi 1 pi 2 and pi 3 for the category freq
57. e eee ete epo trn eese as e soe n be een se ea ae ee rp a pape Ce e uaa aea 51 6 Differences Between Version 2 and Version 3 cccccccsssssssseecccssscccsssseeeeeesssees 57 Je POV ANCE VO PICS ET m TT T 59 Tab C mpiline IMAP AY 6 Sot cool nas ite otto et aae aie inb Parvo ios staan seh sates aaa an aas 59 7 1 1 Compiling with GNU MAE nune tr iei tense datas unu Gadd iutaties 59 7 1 2 Compiling with Code Warrior or Visual Studio eseesssssss 61 7 2 Compiling and Running the Parallel Version of MrBayes sesssss 61 7 2 1 The Parallel Macintosh Version eee em ete tr eI Reo lide aa ee dee 61 7 2 2 The MPI Version for Unix Clusters s c eire tre eret fret tnt deri 62 7 3 Working with the Source Code o eset a eser Eri ebes eel mares dove erige deco oua 62 8 Acknowledgements oe sesion areis a oENSUROE Rente sa M YR UNES ane Ua euni QNI Ca sauna sdsaveabeadsedeesdoa 63 9 Referents cmo d LT M EN 63 Appendix Evolutionary models and proposals in MrBayes MrBayes 3 1 Manual 5 26 2005 4 1 Introduction MrBayes 3 is a program for the Bayesian inference of phylogeny The program has a command line interface and should run on a variety of computer platforms including clusters of Macintosh and UNIX computers Note that the computer should be reasonably fast and should have a lot of RAM memory depending on the size of the data matrix the program may require hundreds of megabytes of memory The
58. e has both the posterior probability of clades as interior node labels and the branch lengths if they have been saved in its description A graphical representation of this tree can be generated in Rod Page s program TreeView The second tree only contains the branch lengths and it can be imported into a wide range of tree drawing programs such as MacClade and Mesquite The third file generated by the sumt command is the trprobs file which contains the trees that were found during the MCMC search sorted by posterior probability 3 Analyzing a Partitioned Data Set MrBayes handles a wide variety of data types and models as well as any mix of these models In this example we will look at how to set up a simple analysis of a combined data set consisting of data from four genes and morphology for 30 taxa of gall wasps and outgroups A similar approach can be used e g to set up a partitioned analysis of molecular data coming from different genes The data set for this tutorial is found in the file cynmix nex 3 1 Getting Mixed Data into MrBayes First open up the Nexus data file in a text editor The DATA block of the Nexus file should look familiar but there are some differences compared to the primates nex file in the format statement Format datatype mixed Standard 1 166 DNA 167 3246 interleave yes gap missing First the datatype is specified as datat ype mixed Standard 1 166 DNA 167 3246 This means that the matrix c
59. e run However the computational cost of doing so may be prohibitive A better way is then to try improving the mixing behavior of the chain First examine the acceptance rates of the proposal mechanisms used in your analysis output at the end of the run The Metropolis proposals used by MrBayes work best when their acceptance rate is neither too low nor too high A rough guide is to try to get them within the range of 10 to 70 Rates outside this range are not necessarily a big problem but they typically mean that the analysis is inefficient If the rate is too high you can make the proposal bolder by changing tuning parameters see Appendix using the props command Be warned however that changing tuning parameters of proposals and proposal probabilities may destroy any hope of getting convergence For instance you need at least one move changing each parameter in your model The next step is to examine the heating parameters if you are using Metropolis coupled MCMC If acceptance rates for the swaps between adjacent chains the values close to the diagonal in the swap statistics matrix are low then it might be a good idea to decrease the temperature to make the cold and heated chains more similar to each other so that they can change states more easily The efficiency of the Metropolis coupling can also be improved by increasing the number of parallel chain A good way of improving convergence is to start the analysis from a good tree ins
60. e the other assumes equal rates across sites As stated above models need not be hierarchically nested An interesting property of the Bayes factor comparisons is that it can favor either the more complex model or the simpler model so they need not be corrected for the number of parameters in the models being compared MrBayes 3 1 Manual 5 26 2005 56 Additional discussion of Bayesian model testing with several examples is found in Nylander et al 2004 Can I do model jumping in MrBayes Bayesian MCMC model jumping provides a convenient alternative to model selection prior to the analysis In model jumping the MCMC sampler explores different models and weights the results according to the posterior probability of each model The only model jumping implemented in MrBayes 3 is the estimation of fixed rate amino acid substitution models see the section on those models in this manual General model jumping across models of different dimensionality will be implemented in version 4 of MrBayes ModelTest suggests a model for my data How do I implement it in MrBayes A model selection procedure such as that implemented in ModelTest and MrModelTest often suggests a quite specific model for your analysis including estimates of all parameters This suggestion 1s often based on several simplifications for instance you might have fixed the topology when comparing models and you might have used a small set of the possible models In the Bayes
61. e two MPI versions of MrBayes The first is the parallel version for Macintosh computers distributed as part of the Macintosh package It is intended for use on clusters of Macintosh computers and runs under POOCH which must be installed first The second MPI version of MrBayes is intended for use on clusters running UNIX and must be compiled from the source code 7 2 1 The Parallel Macintosh Version There are several options available for running jobs in parallel on clusters of Macintosh computers For example in OS X you could configure your machine to run jobs using mpich or lam mpi and then compile the regular Unix MPI version of the program as described in the next section However the simplest method is to use Dean Daugger s program Pooch available at www daugerresearch com pooch whatis html to control the jobs The Pooch web site gives a good description of the steps required to run a job in parallel The steps are as follows 1 Configure a network of Macintosh computers You have probably already done this step You simply need more than one computer hooked to the internet 2 Buy and install a copy of Pooch for each computer you intend to run MrBayes on 3 Start Pooch on all of the computers of your cluster If you set Pooch to automatically start on login then this has already been done 4 Select New Job from Pooch on one of the computers 5 Select the nodes computers you want to participate in the parallel job 6
62. e two runs will sample very different trees but when they have reached convergence when they produce a good sample from the posterior probability distribution the two tree samples should be very similar To make sure that MrBayes compares tree samples from the different runs make sure that Mcmcdiagn is set to yes and that Diagnfreq is set to some reasonable value such as every 1000 generation MrBayes will now calculate various run diagnostics every Diagnfreq generation and print them to a file with the name lt Filename gt mcmc The most important diagnostic a measure of the similarity of the tree samples in the different runs will also be printed to screen every Diagnfreq generation Every time the diagnostics are calculated either a fixed number of samples burnin or a percentage of samples burninfrac from the beginning of the chain is discarded The relburnin setting determines whether a fixed burnin relburnin no or a burnin percentage relburnin yes is used If you don t change any settings MrBayes will by default discard the first 25 samples from the cold chain relburnin yes and burninfrac 0 25 By default MrBayes uses Metropolis coupling to improve the MCMC sampling of the target distribution The Swapfreq Nswaps Nchains and Temp settings together control the Metropolis coupling behavior When Nchains is set to 1 no heating is used When Nchains is set to a value n larger than 1 then n 1 heated chains are used By
63. ee Data Type Model Type State Frequencies Substitution Rates Rate Variation Rate Variation Protein GTR fixed est Dirichlet fixed est Dirichlet equal gamma yes no A Y prset aamodelpr prset statefreqpr prset statefreqpr propinv invgamma Iset covarion adgamma Equalin fixed est Dirichlet Iset rates fixed to equal prset aamodelpr prset statefreqpr equal gamma yes no ropinv invgamma d Prop g Iset covarion adgamma Iset rates Poisson Jones Dayhoff Mtrev Mtmam Wag Rtrev Cprev Vt Blossum mixed prset aamodelpr equal gamma propinv invgamma yes no adgamma Iset covarion fixed mixed fixed mixed Iset rates Brlens Variation Across Partitions Tree Type Brlens Type Brlens Prior equal proportional Non clock Unconstrained Exponential Uniform Additional prset ratepr prset brlenspr prset brlenspr parameters see prset Clock Uniform Iset for ploidy prset brlenspr prset brlenspr Treeheight unlinked unlink brlens Theta Ploidy Topology Variation Coalescence Na Growth Across Partitions prset brlenspr Speciation Birth Death Extinction prset brlenspr Sampleprob same unlinked link topology unlink topology The most common proposal types used by MrBayes 3 Sliding Window Proposal New values are picked uniformly from a sliding window of size 6 centered on x Tuning parameter Bolder proposals increase 5 More modest proposals decrease 6
64. ehavioral or ecological trait may be mapped onto trees based on molecular data To do this type of analysis in MrBayes you would set up a mixed data set including both the character to be mapped and the data used to infer the phylogeny with the character to be mapped in a separate data partition How to do this is explained in the tutorial given in section 3 of this manual as well as in the description of partitioned models above Typically you also want to assume that the evolutionary rate for the mapped character is proportional to that of the other data rather than identical This is achieved by setting up a partitioned rate model using prset ratepr variable Then you need to set up a constraint for the node of interest as described above Finally you request that ancestral states are inferred for the partition with the mapped character there is no need to wade through ancestral state probabilities for the other partition s For instance if the character to be mapped is in partition 2 request ancestral state sampling using prset applyto 2 ancstates yes Now only the ancestral states for the character of interest will be printed to the p file s The sampled values can be summarized as usual with the sump command 5 Frequently Asked Questions How do I cite the program If you want to cite the program we suggest you use the two papers published in Bioinformatics Huelsenbeck and Ronquist 2003 Ronquist and Huelsenbeck 2005 If you
65. ement which ends with a semicolon just as any other statement Our example file contains sequences in non interleaved block format Non interleaved is the default but you can put interleave no in the format statement if you want to be sure The Nexus data file can be generated by a program such as MacClade or Mesquite Note however that MrBayes does not support the full Nexus standard so you may have to do a little editing of the file for MrBayes to process it properly In particular MrBayes uses a fixed set of symbols for each data type and does not support the symbols and equate options of the format command The supported symbols are A C G T R Y M K S W H B D Ni for DNA data A C G U R Y M K S W H B V D Nj for RNA data A R N D C Q E G H I L K M F P S T W Y V X for protein data 0 1 for restriction binary data and 0 1 2 3 4 5 6 5 7 8 9 for standard morphology data In addition to the standard one letter ambiguity symbols for DNA and RNA listed above ambiguity can also be expressed using the Nexus parenthesis or curly MrBayes 3 1 Manual 5 26 2005 11 braces notation For instance a taxon polymorphic for states 2 and 3 can be coded as 23 2 3 23 or 2 3 and a taxon with either amino acid A or F can be coded as AF A F AF or A F Like most other statistical phylogenetics programs MrBayes effectively treats polymorphism and
66. ements 4x4 the codon model computations need to process more than 3 600 Q matrix and transition probability elements resulting in these runs being roughly 200 times slower The codon models also require much more memory than the four by four models about 16 times as much The simplest codon model described above assumes that all amino acid sites are subject to the same level of selection the same w factor However MrBayes also implements models accommodating variation in selection across sites This allows you to detect positively selected amino acid sites using a full hierarchical Bayes analysis that is an MrBayes 3 1 Manual 5 26 2005 36 analysis that does not fix tree topology branch lengths or any substitution model parameters but instead integrates out uncertainty in all these factors The variation models work much like the model accommodating rate variation across sites according to a gamma distribution The likelihood of each site is calculated under several different w values and then the values are summed to give the site likelihood A difference is that the stationary frequency of each omega category is estimated instead of being fixed as in the case of the gamma distribution There are two variants implemented in MrBayes and they are invoked using the Lset omegavar option In the Ny98 model Nielsen and Yang 1998 there are three classes with potentially different values 0 lt w lt 1 1 and w gt 1 Th
67. ersion 3 is controlled by setting the prior with prset statefreqpr By default all parameters are estimated There is no basefreq option in the 1set command of version 3 of MrBayes Iset clock Whether the tree is a clock or a non clock tree is now set using prset brlenspr Iset enforcecal Calibrations are not implemented yet in MrBayes 3 Iset enforcecodon The type of nucleotide model is now set using 1set nucmodel 4by4 doublet codon Iset enforcecon Now set using prset topologypr constraints lt list_of_constraints gt Iset inferanc Now set using report ancstates Iset inferpossel Now set using report possel Iset inferrates This is now set with report siterates Iset neat number of categories used to approximate the gamma distribution of site rates Now set using 1set ngammacat to distinguish it from nbetacat the number of categories used to approximate the beta distribution of rate stationary state asymmetry across sites in the standard model Iset nonrevmat Time irreversible models are not implemented in MrBayes 3 Iset omega Whether this parameters is estimated or fixed to a particular value in version 3 is controlled by setting the prior with prset omegapr By default all parameters are estimated There is no omega option in the 1set command of version 3 of MrBayes Iset rates The site specific rate models si tespec ssgamma ssadgamma are now set using the more general partitioning model See sect
68. es if you want to compile the parallel MPI version of MrBayes This variable is set to no by default meaning that a serial version of MrBayes will be built See below for more information on how to compile and run the MPI version of MrBayes CC This variable defines which compiler to use For example gcc for the GNU compiler or icc for the Intel C compiler The default setting is the GNU compiler DEBUG Set this variable to yes if you want to compile a debug version of MrBayes This adds the appropriate flag for the GNU gdb debugger OPTFLAGS Sets the optimization flags for the compiler This option is ignored if DEBUG is set to yes The default is set to O2 which yields good results for every platform It is however possible to perform some tuning with this variable We give a few possibilities below for some common processor types assuming you are using gcc version 3 See the gcc manual for further information on optimization flags Intel x86 Some compiler flags for gcc under unix and for gcc cygwin under windows march X with X one of pentium4 athlon xp or opteron If you have one of these processors this will generate instructions specifically tailored for that processor mfpmath sse attempts to use the SSE extension for numerical calculations This flag is only effective in combination with the above mentioned march flag This flag can provide a big performance gain However using this flag in combination with other o
69. g We do this using the set command Set partition favored Finally we need to add an end statement to close the MrBayes block The entire block should now look like this begin mrbayes charset morphology 1 166 charset COI 167 1244 charset EFla 1245 1611 charset LWRh 1612 2092 charset 28S 2093 3246 partition favored 5 morphology COI EFla LWRh 28S set partition favored end MrBayes 3 1 Manual 5 26 2005 29 When we read this block into MrBayes we will get a partitioned model with the first character division being morphology the second division being the COI gene etc Save the data file exit your text editor and finally launch MrBayes and type execute cynmix nex to read in your data and set up the partitioning scheme 3 3 Specifying a Partitioned Model Before starting to specify the partitioned model it is useful to examine the default model Type showmode1 and you should get this table as part of the output Active parameters Partition s Parameters D c2 795 45 Statefreq le 2 2 42 2 Topology 3 3 39 m 3 Brlens 4 4 4 4 4 There is a lot of other useful information in the output of showmodel but this table is the key to the partitioned model We can see that there are five partitions in the model and four active free parameters There are two stationary state frequency parameters one for the morphological data parameter 1 and one for the DNA data par
70. g to the F81 model or the JC model if the stationary state frequencies are forced to be equal using the prset command see below We want the GTR model Nst 6 instead of the F81 model so we type lset nst 6 MrBayes should acknowledge that it has changed the model settings MrBayes 3 1 Manual 5 26 2005 13 The Code setting is only relevant if the Nucmodel is set to Codon The Ploidy setting is also irrelevant for us However we need to change the Rates setting from the default Equal no rate variation across sites to Invgamma gamma shaped rate variation with a proportion of invariable sites Do this by typing 1set rates invgamma Again MrBayes will acknowledge that it has changed the settings We could have changed both 1set settings at once if we had typed 1set nst 6 rates invgamma in a single line We will leave the Ngammacat setting the number of discrete categories used to approximate the gamma distribution at the default of 4 In most cases four rate categories are sufficient It is possible to increase the accuracy of the likelihood calculations by increasing the number of rate categories However the time it will take to complete the analysis will increase in direct proportion to the number of rate categories you use and the effects on the results will be negligible in most cases Of the remaining settings it is only Covarion and Parsmodel that are relevant for single nucleotide models We will use neither the parsimony mode
71. h estimate may be obtained easily as the harmonic mean of the likelihood values of the MCMC samples Newton and Raftery 1994 MrBayes calculates this estimator when you summarize your samples with the command sump In the output from the sump command you will find the following table it might look a little different depending on how many simultaneous runs you have performed this table is for two runs Estimated marginal likelihoods for runs sampled in files replicase nex runl p replicase nex run2 p etc Use the harmonic mean for Bayes factor comparisons of models Run Arithmetic mean Harmonic mean 1 5883 41 5892 10 2 5883 82 5892 81 TOTAL 5883 60 5892 52 For instance assume we want to compare a GTR model with an HKY model Then simply run two separate analyses one under each model and estimate the logarithm of the marginal likelihoods for the two models using only samples from the stationary phase of the runs Then simply take the difference between the logarithms of the harmonic means and find the corresponding interpretation in the table of Kass and Raftery 1995 to use this table you actually have to calculate twice the difference in the logarithm of the model likelihoods The same approach can be used to compare any pair of models you are interested in For instance one model might have a group constrained to be monophyletic while the other is unconstrained or one model can have gamma shaped rate variation whil
72. he extremely low value of the average standard deviation at the end of the run there appears to be no need to continue the analysis beyond 10 000 generations so when MrBayes asks Continue with analysis yes no stop the analysis by typing no Although we recommend using a convergence diagnostic such as the standard deviation of split frequencies to determine run length we want to mention that there are simpler but less powerful methods of determining when to stop the analysis Arguably the simplest technique is to examine the log likelihood values or more exactly the log probability of the data given the parameter values of the cold chain that is the values printed to screen within square brackets In the beginning of the run the values typically increase rapidly the absolute values decrease since these are negative numbers This phase of the run is referred to as the burn in and the samples from this phase are typically discarded Once the likelihood of the cold chain stops to increase and starts to randomly fluctuate within a more or less stable range the run may have reached MrBayes 3 1 Manual 5 26 2005 22 stationarity that is it is producing a good sample from the posterior probability distribution At stationarity we also expect different independent runs to sample similar likelihood values Trends in likelihood values can be deceiving though you re more likely to detect problems with convergence by comparing
73. he shape parameter of the gamma distribution of rate variation Pinvarpr for the proportion of invariable sites Topologypr for the topology and Brlenspr for the branch lengths The default prior probability density is a flat Dirichlet all values are 1 0 for both Revmatpr and Statefreqpr This is appropriate if we want estimate these parameters from the data assuming no prior knowledge about their values It is possible to fix the rates and nucleotide frequencies but this is generally not recommended However it is occasionally necessary to fix the nucleotide frequencies to be equal for instance in specifying the JC and SYM models This would be achieved by typing prset statefreqpr fixed equal If we wanted to specify a prior that put more emphasis on equal nucleotide frequencies than the default flat Dirichlet prior we could for instance use prset statefreqpr Dirichlet 10 10 10 10 or for even more emphasis on equal frequencies prset statefreqpr Dirichlet 100 100 100 100 The sum of the numbers in the Dirichlet distribution determines how focused the distribution is and the balance between the numbers determines the expected proportion of each nucleotide in the order A C G and T Usually there is a connection between the parameters in the Dirichlet distribution and observations Thus you can think of a Dirichlet 150 100 90 140 distribution as one arising from observing 150 A s 100 C s 90 G s and 140 T s in some
74. hlet distribution with all distribution parameters set to 1 as the prior for both the stationary state frequencies and the substitution rates This is a reasonable uninformative prior that should work well for most analyses During the analysis both the stationary state frequencies and substitution rates are estimated If you want to fix the stationary state frequencies or substitution rates you can MrBayes 3 1 Manual 5 26 2005 32 do that by using the prset command For instance assume that we want to fix the stationary state frequencies to be equal converting the GTR model to the so called SYM model This is achieved by prset statefreqpr fixed 0 25 0 25 0 25 0 25 or more conveniently prset statefreqpr fixed equal The substitution rate matrix now becomes D236 a 0 25r 0 255 025 6 0 25rog 0 25ror Q 025r 025m 025m 025r 0 237 ODay and the stationary state frequencies are no longer estimated during the analysis Similarly it is possible to fix the substitution rates of the GTR model using prset revmatpr fixed Assume for instance that we want to fix the substitution rates to be rac 0 1 1 lAG 0 22 VAT 7 0 12 FCG 0 14 ET 0 35 GT 0 06 Then the correct statement would be prset revmatpr fixed 0 11 0 22 0 12 0 14 0 35 0 06 Note the order of the rates The substitution rates can be given either as percentages of the rate sum as here or they can be scaled to the rgr rate The former representat
75. hta Taxon 2 Lemur catta Taxon 3 gt Homo sapiens Taxon 4 gt Pan Taxon 5 Gorilla Taxon 6 gt Pongo Taxon 7 gt Hylobates Taxon 8 Macaca fuscata Taxon 9 M mulatta Taxon 10 gt M fascicularis Taxon 11 gt M sylvanus Taxon 12 Saimiri sciureus Setting output file names to primates nex lt run lt i gt p run lt i gt t gt Successfully read matrix Exiting data block Reached end of file 2 3 Specifying a Model All of the commands are entered at the MrBayes gt prompt At a minimum two commands 1set and prset are required to specify the evolutionary model that will be used in the analysis Usually it is also a good idea to check the model settings prior to the MrBayes 3 1 Manual 5 26 2005 12 analysis using the showmodel command In general 1set is used to define the structure of the model and prset is used to define the prior probability distributions on the parameters of the model In the following we will specify a GTR I _ model a General Time Reversible model with a proportion of invariable sites and a gamma shaped distribution of rates across sites for the evolution of the mitochondrial sequences and we will check all of the relevant priors If you are unfamiliar with stochastic models of molecular evolution we suggest that you consult a general text such as Felsenstein 2004 In general a good start is to type help lset Ignore the help information for now and concen
76. iagonal elements are either so or s10 and R3 is the chosen model for the evolution in the on state The covarion like model can be described as a general case of the proportion of invariable sites model Huelsenbeck 2002 As the switching rates go to zero the proportion of these rates represented by the switch to the off state s79 becomes identical to the proportion of invariable sites When the switching rates are zero there is no exchange between the on and off states and the characters in the off state remain off throughout the tree in other words they are invariable sites Note that the covarion like model implemented in MrBayes differs from the original covarion model in that sites switch completely independently of each other between the on and off states To invoke the covarion like model simply use 1set covarion yes and then choose the desired nucleotide or amino acid model using the MrBayes 3 1 Manual 5 26 2005 47 other 1set and the prset options The covarion like model can be combined with the gamma model of rate variation across sites 4 8 Topology and Branch Length Models The topology and branch length models in MrBayes are set using the prset topologypr options which deal with the tree topology prior and the prset brlenspr options which deal with the branch lengths 4 8 1 Unconstrained and Constrained Topology There are two choices for the prior probability distribution on topology uniform or constrained By
77. ian approach there is only a moderate computational penalty associated with estimating parameters rather than fixing them prior to analysis The Bayesian approach is typically also good at handling multi parameter models Therefore we recommend that you take the general type of model suggested by your model selection method and then estimate all of the parameters in that model in MrBayes If the suggested model is not implemented in MrBayes use the next more complex model available in the program If for some reason you feel that you really need to fix model parameters in MrBayes to specific values you can do that using prset parameter prior name fixed value or comma separated values gt For instance if you want to fix the shape parameter of the gamma model to 0 12 useprset shapepr fixed 0 05 How many data partitions can I have in MrBayes MrBayes 3 allows 150 partitions If you need more partitions simply change the variable MAX NUM DIVS in the source file mb h and recompile the program Does MrBayes run faster on a dual processor machine No The Windows and Mac versions of MrBayes 3 1 are not multithreaded so they will not take advantage of more than one processor on a single machine However you should be able to run two copies of MrBayes without noticeable decrease in performance on a dual processor machine provided you have enough RAM for both analyses How much memory is required MrBayes 3 1 Manual 5 26 2005
78. ion 3 of this manual as well as the discussion of partition models in section 4 Iset revmat Whether this parameters is estimated or fixed to a particular value in version 3 is controlled by setting the prior with prset revmatpr By default all parameters are estimated There is no revmat option in the 1 set command of version 3 of MrBayes Iset seqerror The model of sequencing error is no longer implemented in MrBayes 3 The model typically results in small corrections in partition support values but it conflicts with important algorithmic short cuts implemented in version 3 MrBayes 3 1 Manual 5 26 2005 59 Iset shape Whether this parameters is estimated or fixed to a particular value in version 3 is controlled by setting the prior with prset shapepr By default all parameters are estimated There is no shape option in the 1set command of version 3 of MrBayes Iset sitepartition The partition of sites is now set using set partition Iset tratio Whether this parameters is estimated or fixed to a particular value in version 3 is controlled by setting the prior with prset tratiopr By default all parameters are estimated There is no t ratio option in the 1set command of version 3 of MrBayes prset basefreqpr Now set using prset statefreqgpr prset brlenpr Now set using prset brlenspr The options are now more complicated as well since the prior includes information both about the general type of the branch lengths clock non c
79. ion is the Dirichlet parameterization used internally by MrBayes By default MrBayes reports substitution rates in the Dirichlet format but you can request conversion of sampled rates to the scaled format using the report command if you prefer this representation One disadvantage with the scaled format is that the posterior distribution tends to be strongly skewed such that the arithmetic mean of the sampled values is considerably higher than the mode and the median Therefore consider using the median instead of the mean when reporting a posterior distribution sampled in the scaled format Before using the GTR model for some of your data we recommend that you make sure there are at least a few possible substitutions of each type For instance if there is not a single GT substitution in your data it will be difficult to estimate the GT substitution rate In such cases you should consider either the HKY model nst 2 or the F81 model nst 1 instead of the GTR model The HKY model Hasegawa Kishino and Yano 1985 has different rates for transitions 7 and transversions r Ach Tl Trl T hy xz TF ty TTE T AFi Tcr d Trl T Vy Tchi Tl The HKY model is often parameterized in terms of the ratio between the transition and transversion rates K r r and this is the default format used by MrBayes when reporting samples from the posterior distribution Internally however MrBayes uses the Dirichlet parameterization i
80. irichlet 3 Parameter Shape Prior Uniform 0 05 50 00 4 Parameter Pinvar Prior Uniform 0 00 1 00 5 Parameter Topology Prior All topologies equally probable a priori 6 Parameter Brlens Prior Branch lengths are Unconstrained Exponential 10 0 Note that we have six types of parameters in our model All of these parameters will be estimated during the analysis see section 5 for information on how to fix parameter values 2 6 Setting up the Analysis The analysis is started by issuing the mcmc command However before doing this we recommend that you review the run settings by typing help mcmc The help mcmc command will produce the following table at the bottom of the output Parameter Options Current Setting Seed lt number gt 1115403472 Swapseed lt number gt 1115403472 Ngen lt number gt 1000000 Nruns lt number gt 2 Nchains lt number gt 4 Temp lt number gt 0 200000 Reweight lt number gt lt number gt 0 00 v 0 00 Swapfreq number 1 Nswaps number 1 Samplefreq number 100 Printfreq number 100 Printall Yes No Yes Printmax number 8 cmcdiagn Yes No Yes Diagnfreq number 1000 inpartfreq number 0 10 Allchains Yes No o Allcomps Yes No o Relburnin Yes No Yes Burnin number 0 Burninfrac lt number gt 0 25 Stoprule Yes No o Stopval number 0 01 MrBayes 3 1 Manual 5 26 2005 17 Filename lt name gt primates nex lt p t gt Startingtree Ran
81. itialized c o mb o mb c gcc DUNIX VERSION 03 Wall Wno uninitialized c o mcmc o mcmc c gcc DUNIX VERSION 03 Wall Wno uninitialized c o bayes o bayes c gcc DUNIX VERSION 03 Wall Wno uninitialized c o command o command c gcc DUNIX VERSION 03 Wall Wno uninitialized c o mbmath o mbmath c gcc DUNIX VERSION 03 Wall Wno uninitialized c o model o model c gcc DUNIX VERSION 03 Wall Wno uninitialized c o plot o plot c gcc DUNIX VERSION 03 Wall Wno uninitialized c o sump o sump c gcc DUNIX VERSION 03 Wall Wno uninitialized c o sumt o sumt c gcc DUNIX VERSION 03 Wall Wno uninitialized lm mb o bayes o command o mbmath o mcmc o model o plot o sump o sumt o o mb ronquistg5 mrbayes gt The compilation usually stops for several minutes at the mcmc c file this is perfectly normal This is the largest source file and optimization of the code takes quite a while We assume as the default C compiler gcc which is installed on most systems If you do not have gcc installed on your machine or you want to produce the MPI version or some other special version of the program you have to change the compiler information in the Makefile as described in section 7 of this manual The executable serial version of the MrBayes 3 1 Manual 5 26 2005 6 program is called mb To execute the program simply type mb in the directory where you compiled the program The prefix is needed to tell Unix that you want
82. ization has some advantages in the Bayesian context in particular it allows convenient formulation of priors If you want to scale the rates relative to the G T rate just divide all rate proportions by the G T rate proportion The last column in the table contains a convergence diagnostic the Potential Scale Reduction Factor PSRF If we have a good sample from the posterior probability distribution these values should be close to 1 0 If you have a small number of samples there may be some spread in these values indicating that you may need to sample the analysis more often or run it longer In our case we can probably easily obtain more accurate estimates of some parameters by running the analysis slightly longer 2 10 Summarizing Samples of Trees and Branch Lengths Trees and branch lengths are printed to the t files These files are Nexus formatted tree files with a structure like this NEXUS ID 5848203808 begin trees translate 1 Lemur_catta Homo sapiens Pan Gorilla Pongo Hylobates acaca fuscata mulatta 9 M fascicularis 10 M sylvanus 11 Saimiri sciureus 12 Tarsius syrichta tree rep 1 2 0 100000 8 0 100000 7 0 000748 0 197415 0 100000 5 0 100000 6 0 100 000 0 100000 0 100000 9 0 100000 10 0 100000 3 0 100000 0 100000 0 100000 0 100000 12 0 100000 0 100000 11 0 100000 0 100000 4 0 100000 1 0 100000 AANA 01 4 CO h2 tree rep 10000 6 0 126475
83. l depends heavily on the uniform reinsertion of x so changing may have limited effect Extending TBR An internal branch a is chosen at random The length of a is changed using a multiplier with tuning paremeter The node x is moved with one of the adjacent branches in subtree A one node at a time each time the probability of moving one more branch is p the extension probability The node y is moved similarly in subtree B Bolder proposals increase p More modest proposals decrease p Changing A has little effect on the boldness of the proposal
84. l nor the covariotide model for our data so we will leave these settings at their default values If you type help lset now to verify that the model is correctly set the table should look like this Model settings for partition 1 Parameter Current Setting Nucmodel Nst Code Ploidy Rates Ngammacat Nbetacat Omegavar Covarion Coding Parsmodel 4by4 Doublet Codon 1 2 6 Universal Vertmt Mycoplasma Yeast Ciliates Metmt Haploid Diploid Equal Gamma Propinv Invgamma Adgamma number number Equal Ny98 M3 o Yes All Variable Noabsencesites opresencesites o Yes Universal Diploid Invgamma 4 5 Equal 2 4 Setting the Priors We now need to set the priors for our model There are six types of parameters in the model the topology the branch lengths the four stationary frequencies of the nucleotides the six different nucleotide substitution rates the proportion of invariable sites and the shape parameter of the gamma distribution of rate variation The default priors in MrBayes work well for most analyses and we will not change any of them here so if you are impatient you can skip this step and continue with Checking the Model However it is good practice to go through all the priors and make sure you understand the default settings and the available options Start reviewing this information by typing help prset to obtain a list of the default settings for the parameters in your model The t
85. lock and the specific shape of the prior for example uniform or exponential prset siteratepr Now set using prset ratepr The options are fixed or variable Dirichlet The parameters of the Dirichlet can be set to reflect various types of prior information concerning the site rates prset qmatpr Now set using prset revmatprandprset aarevmatpr for nucleotide and amino acid substitution rates respectively set This command only controlled the autoclose option in MrBayes 2 In version 3 it controls a number of different things including the currently selected partition shownodes This command is no longer included in MrBayes 3 Use showt ree to display the user tree 7 Advanced Topics 7 1 Compiling MrBayes Compiling the MrBayes executable from the source code can be done on several different compilers targeting all the common operating systems Macintosh Windows and Unix The easiest way to build MrBayes is to use the included Makefile with a make tool One can also compile MrBayes with the Metroworks Codewarrior and Microsoft Visual Studio suites 7 1 1 Compiling with GNU Make In the header of the Makefile you can define a number of variables ARCHITECTURE This variable defines the architecture you are targeting Setting this variable is mandatory For example for a Unix environment you would use ARCHITECTURE unix Other options are windows and mac MrBayes 3 1 Manual 5 26 2005 60 MPI Set this variable to y
86. mands will output a lot of information and write fairly long lines so you may want to change the size of the MrBayes window to make it easier to read the output On Macintosh and Unix machines you should be able to increase the window size simply by dragging the margins On a Windows machine you cannot increase the size of the window beyond the preset value by simply dragging the margins but on MrBayes 3 1 Manual 5 26 2005 7 Windows XP 2000 and NT you can change both the size of the screen buffer and the console window by right clicking on the blue title bar of the MrBayes window and then selecting Properties in the menu that appears Make sure the Layout tab is selected in the window that appears and then set the Screen Buffer Size and Window Size to the desired values 1 5 Getting Help At the MrBayes gt prompt type help to see a list of the commands available in MrBayes Most commands allow you to set values options for different parameters If you type help lt command gt where lt command gt is any of the listed commands you will see the help information for that command as well as a description of the available options For most commands you will also see a list of the current settings at the end Try for instance help lsetorhelp memc The 1set settings table looks like this Default model settings Parameter Options Current Setting Nucmodel 4by4 Doublet Codon 4by4 Nst 1 2 6 1 Code Universal Vertmt Myco
87. metimes distinguishes between ordered and unordered characters In ordered characters evolution between some states is assumed to go through intermediate states MrBayes implements a stochastic model for such characters For a three state character assumed to be ordered by convention in the sequence 0 1 2 the instantaneous rate matrix is 0 1 2 0 1 0 2 Hl eed Apt ar 8 Note that the instantaneous rate of going between the two end states is 0 that is a transition from 0 to 2 or from 2 to 0 has to go through state 1 By default MrBayes treats all standard characters as unordered To change this use the ct ype command For MrBayes 3 1 Manual 5 26 2005 4 instance if you want to treat characters 3 and 4 as ordered you need to include the statement ctype ordered 3 4 in your MrBayes block or enter it using the command line if you prefer The number of states of each standard character is determined by MrBayes simply by looking at the state codes in your matrix Thus a three state model will be used for a three state character and a six state model for a six state character MrBayes does not check that all state codess are used it simply finds the largest state code in the matrix for each character Thus make sure that you use the state codes 0 1 and 2 for a three state character and state codes 0 1 2 3 4 and 5 for a six state character Because state labels are arbitrary in the standard model we cannot estim
88. mined by the 0 theta parameter it is also affected by the ploidy of the data haploid or diploid The prior for the theta parameter is set using prset thetapr The ploidy level is set using 1set ploidy The simple clock model is invoked by prset brlenspr clock uniform There is only one additional parameter in the simple clock model namely the total tree height The prior for this parameter is set by prset treeheightpr The default prior is an exponential distribution with parameter 1 0 Exponential 1 0 MrBayes 3 1 Manual 5 26 2005 49 4 8 4 Relaxed Clock Trees Relaxed clock models and functions for dating are not implemented in MrBayes 3 1 According to current plans they will be available in version 3 2 4 9 Partitioned Models MrBayes provides great flexibility in setting up partitioned models By default the characters are divided into partitions based on the data type If there is only one data type in the matrix then all characters will be in a single partition The default partitioning scheme is called default For information on how to set up a file with mixed data types see the example file cynmix nex and the tutorial in section 3 of this manual You can easily set up partitioning schemes that divide the characters up further than the default partition does using the partition command The most convenient way of partitioning data is to define character sets first using the charset command For instance assume that you h
89. n 1 Jones 2 Dayhoff 3 Mtrev 4 Mtmam 5 Wag 6 Rtrev 7 Cprev 8 Vt 9 Blosum When you use the sump command you will get a table with the names of the amino acid models and their posterior probabilities 4 2 3 Variable Rate Models There are two variable rate models implemented in MrBayes for amino acid data The Equalin model is a glorified F81 model in that it allows the stationary state frequencies of all amino acids to be different but assumes the same substitution rate Thus the instantaneous rate matrix for this model is MrBayes 3 1 Manual 5 26 2005 38 A R IN ID C Q IV A Hp Ay Tp Ro Ry e Ty R 3 Hy Tp Ae Ag e My N 7 Tp Rp Ao Ag My Q q D 7 Ar Ay Me Mo My C 9 He Ry Mp Tg e My Q 7 He By Ay Me T Ty V T4 Agr Ry Ap Xo Ag mw and it has 19 free parameters 20 stationary state frequencies minus one because the frequencies sum to 1 that will be estimated from data The other variable rate model is the glorified GTR model which allows all stationary state frequencies and substitution rates to vary Thus the instantaneous rate matrix for this model is A R IN D C Q IV A Val Tyan Tpi Acre Tofo WyFay R zr Ty lryn Tp rop UWelpo Moro Myry N rao Welpn Tp yp Mc yc Towo Mynwy Q q D fp Arro JUyYWp m Tc pc Topog Myfpy C c Ja Tyfye Tprpe Torco Uyloy Q Taso Mr ro JUy wo ppo cleo es UyVoy V z
90. n of protein molecules Pages 21 132 in Mammalian Protein Metabolism H Munro ed Academic Press New York Kass R E and A E Raftery 1995 Bayes factors Journal of the American Statistical Association 90 773 795 MrBayes 3 1 Manual 5 26 2005 65 Kimura M 1980 A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences Journal of Molecular Evolution 16 111 120 Larget B and D Simon 1999 Markov chain Monte Carlo algorithms for the Bayesian analysis of phylogenetic trees Mol Biol Evol 16 750 759 Lewis P O 2001a Phylogenetic systematics turns over a new leaf Trends in Ecology and Evolution 16 30 37 Lewis P O 2001b A likelihood approach to estimating phylogeny from discrete morphological character data Systematic Biology 50 913 925 Li S 1996 Phylogenetic tree construction using Markov chain Monte carlo Ph D dissertation Ohio State University Columbus Mau B 1996 Bayesian phylogenetic inference via Markov chain Monte carlo methods Ph D dissertation University of Wisconsin Madison Mau B and M Newton 1997 Phylogenetic inference for binary data on dendrograms using Markov chain Monte Carlo Journal of Computational and Graphical Statistics 6 122 131 Mau B M Newton and B Larget 1999 Bayesian phylogenetic inference via Markov chain Monte carlo methods Biometrics 55 1 12 Metropolis N A W Rosenbluth M N Rosen
91. n uninformative prior than the uniform distribution We advise against using a uniform prior on branch lengths because of the large prior probability it puts on long branches and their close to random substitution probabilities To change the prior on unconstrained branch lengths you use prset brlenspr For instance assume you wanted to use an exponential prior with parameter 1 instead of the default prior This prior is set by typing prset brlenspr unconstrained exponential 1 4 8 3 Strict Clock Trees MrBayes implements three strict clock models the simple uniform model the birth death model and the coalescence model The birth death model and coalescence models both have additional parameters describing the tree generating process whereas the simple model does not In the birth death model see Yang and Rannala 1997 for a Bayesian implementation trees are generated according to a birth death model with a speciation and an extinction rate The model as implemented in MrBayes can also be associated with a sampling probability of terminal lineages The priors for these three parameters are set using the Speciationpr extinctionpr and sampleprob parameters of the prset command In the coalescence model the tree generating process is looked at from the opposite perspective backward in time Instead of lineages branching this model sees them as coalescing into fewer and fewer ancestral lineages This process occurs at a rate deter
92. n which the transition and transversion rates are expressed as percentages of the unscaled rate sum If you prefer you can have MrBayes report the MrBayes 3 1 Manual 5 26 2005 33 sampled values using the Dirichlet format instead of the ratio format by using the command report tratio dirichlet The caveats described above for the GT scaled substitution rates also apply to the transition transversion rate ratio In the p files the ratio will be referred to as kappa and the transition and transversion rate proportions will be referred to as ti and tv The setting of the report tratio option will determine whether you will see a single kappa column or the two ti and tv columns As with the GTR model you can fix both the stationary state frequencies and the transition transversion rate ratio of the HKY model If you fix the stationary state frequencies to be equal you will get the K2P model Kimura 1980 Finally MrBayes implements the F81 model Felsenstein 1981 which assumes that all substitution rates are equal but stationary state frequencies are not that is Ue Jg Tr My Tc Hg If the stationary state frequencies are fixed to be equal using prset statefreqpr fixed equal you will get the simplest of all nucleotide substitution models the JC model Jukes and Cantor 1969 A large number of other subsets of the GTR model are often used in Maximum Likelihood inference Why do we not allow more substitution model t
93. ontains standard morphology characters in columns 1 166 and DNA characters in the remaining columns The mixed datatype is an extension to the Nexus standard This extension was originated by MrBayes 3 and may not be compatible with other phylogenetics programs Second the matrix is interleaved It is often convenient to specify mixed data in interleaved format with each block consisting of a natural subset of the matrix such as the morphological data or one of the gene regions Third the Nexus file contains a MrBayes block at the end after the data block The MrBayes block begins with begin mrbayes and ends with the end statement The block contains various instructions to the MrBayes program for the purposes of the tutorial comment out these instructions by adding an opening square bracket before the begin statement begin mrbayes and a closing square bracket after the end statement end MrBayes will skip everything within square brackets nested square brackets MrBayes 3 1 Manual 5 26 2005 28 are allowed so this will ensure that the entire existing MrBayes block is ignored when the data file is processed 3 2 Dividing the Data into Partitions By default MrBayes partitions the data according to data type There are only two data types in the matrix so this model will include only a morphology standard and a DNA partition To divide the DNA partition into gene regions it is convenient to first specify character
94. oposing new values for those parameters The proposal probabilities can be changed with the props command but be warned that inappropriate changes of proposal probabilities may destroy any hopes of achieving convergence After the initial log likelihoods MrBayes will print the state of the chains every 100th generation like this Chain results 1 7812 831 7523 685 7485 569 7700 309 7832 045 7618 595 7776 608 7836 826 100 6771 532 6857 529 6766 678 6682 527 6506 277 6944 449 6784 126 6991 307 0 01 39 200 6321 464 6179 561 6338 168 6272 242 6339 400 6715 840 6265 329 6599 698 0 01 38 300 6201 285 6084 899 6139 200 6049 061 6073 056 6359 134 6106 834 6515 348 0 01 37 400 6015 429 5924 177 6074 274 5967 236 6002 941 6215 415 5980 096 6036 624 0 01 12 500 5963 069 5851 415 6019 301 5948 768 5925 423 6072 446 5925 549 5963 427 0 01 16 600 5931 545 5802 472 5997 276 5927 204 5899 590 6035 097 5904 327 5896 520 0 01 18 700 5852 405 5782 934 5966 224 5880 975 5890 220 6008 142 5876 956 5838 392 0 01 19 800 5844 426 5754 416 5963 531 5860 182 5883 474 5902 784 5790 765 5789 326 0 01 20 900 5814 885 5741 101 5926 666 5855 916 5870 8
95. or this purpose For instance if there are only two genes in your data set the first with 960 sites you would specify the break between them with the statement databreaks 960 Note that you specify the break by giving the last sequence site before the break The databreaks command is only needed when you invoke a single autocorrelated gamma model for a multigene dataset The databreaks command cannot be used to partition a data set 4 6 3 Proportion of Invariable Sites A completely different approach to rate variation is to allow a proportion of sites to be invariable This model is invoked using lset rates propinv The proportion of invariable sites is referred to as pinvar it can vary from 0 no invariable sites to 1 all sites are invariable The default prior is a uniform distribution on the interval 0 1 change it using prset pinvarpr The proportion of invariable sites model can be combined with the gamma model using lset rates invgamma Although this model is slightly better than the simple gamma model for many data sets it sometimes results in a bimodal or ridge like posterior probability distribution In particular it is not uncommon to see two peaks in the posterior one with a low proportion of invariable sites and significant rate variation in the gamma distribution low alpha value and the other with a high proportion of invariable sites and moderate amounts of rate variation in the gamma distribution moderately high alpha v
96. orge You can access the CVS repository from the MrBayes home page at SourceForge www mrbayes sourceforge net SourceForge gives detailed instructions for anonymous access to the CVS repository on their documentation pages If you are interested in contributing code with bug fixes the best way is to send a diff with respect to the most recent file versions in the CVS repository to Paul van der Mark paulvdm csit fsu edu and we will include your fixes in the main development branch as soon as possible If you would like to add functionality to MrBayes or improve some of the algorithms please contact Paul for directions before you start any extensive work on your project to make sure your additions will be compatible with other ongoing development activities You should also consider whether you want to work with version 3 or version 4 of the program We are currently shifting our focus to the development of MrBayes 4 Unlike version 3 which is written in C this version will be written in C and our goal is to provide a cleaner faster and more extensively documented implementation of Bayesian MCMC phylogenetic analysis This means among other things that the code will be better organized and all important sections will be documented using Doxygen www doxygen org for easy access to other developers You are welcome to examine this project as it develops by downloading the source code doxygen documentation or programming style directives
97. parate Nexus file that you process after you have read in your data MrBayes will keep the data set in memory until you read in a new data block so you can have your different MrBayes blocks pertaining to the same data file distributed over as many separate Nexus files as you like We recommend that before you run your analysis you check the current model settings using the showmodel command This command will list all the active parameters and how they are linked across partitions as well as the priors associated with each parameter Finally we want to give you a warning Even though MrBayes allows you to easily set up extremely complex and parameter rich models and the Bayesian MCMC approach is good at handling such models think carefully about the parameters you introduce in your model There should be at least some reasonable chance of estimating the parameters based on your data For instance a common mistake is to use a separate GTR model for a partition with so few substitutions that there is not a single observation for several rate categories Making sure there are at least some observations allowing you to estimate each parameter is good practice Over parameterized models often result in problems with convergence in addition to the excessive variance seen in the parameter estimates 4 10 Ancestral State Reconstruction MrBayes allows you to infer ancestral states at ancestral nodes using the full hierarchical Bayesian approach in
98. plasma Yeast Ciliates Metmt Universal Ploidy Haploid Diploid Diploid Rates Equal Gamma Propinv Invgamma Adgamma Equal Ngammacat number 4 Nbetacat number 5 Omegavar Equal Ny98 M3 Equal Covarion o Yes o Coding All Variable Noabsencesites opresencesites All Parsmodel o Yes o Note that MrBayes 3 supports abbreviation of commands and options so in many cases it is sufficient to type the first few letters of a command or option instead of the full name A complete list of commands and options is given in the command reference which can be downloaded from the program web site www mrbayes net You can also produce an ASCII text version of the command reference at any time by giving the command manual to MrBayes Further help is available in a set of hyperlinked html pages produced by Jeff Bates and available on the MrBayes web site Finally you can get in touch with other MrBayes users and developers through the mrbayes users email list subscription information at www mrbayes net 1 6 Reporting and Fixing Bugs If you find a bug in MrBayes we are very grateful if you tell us about it using the bug reporting functions of SourceForge as explained on the MrBayes web site www mrbayes net When you submit a bug make sure that you upload a data file with the data set and sequence of commands that produced the error If the bug occurs during a MCMC analysis after issuing the memc command you can help us greatly by m
99. program is optimized for speed and not for minimizing memory requirements This manual explains how to use the program After this section which introduces the program we will first walk you through a simple analysis section 2 of the manual which will get you started and a more complex analysis that uses more of the program s capabilities section 3 We then briefly describe the models implemented in the program section 4 answer some frequently asked questions section 5 and discuss the differences between versions 2 and 3 of the program section 6 Finally we give more detailed instructions on how to compile the program and how to run the parallel versions of it section 7 Section 7 also contains brief information for developers interested in tweaking MrBayes code or contributing to the MrBayes project The manual ends with a series of diagrams giving a graphical overview of all the models and proposal mechanisms implemented in the program Appendix For more detailed information about commands and options in MrBayes see the command reference that can either be downloaded from the program web site or generated from the program itself see section 1 4 Getting Help below All the information in the command reference is also available on line when using the program The manual assumes that you are familiar with the basic concepts of Bayesian phylogenetics If you are new to the subject we recommend the recent reviews by Holder and Lewi
100. ptimization flags might yield numerically incorrect code For example one can set mfpmath sse 386 but this flag leads to incorrect results when used in combination with march pentium4 fomit frame pointer saves some function overhead 03 instead of 02 turns on even more optimization flags However it does not always produce faster code than 02 Mac G4 and G5 Some compiler flags for gcc for OS X fast This flag is specific for the gcc version delivered by Apple It turns on a set of compiler flags which tries to optimize for maximum performance This is the recommended setting if you have a G5 processor and this version of gcc 02 or O3 mcpu X with X one of G4 or G5 MrBayes 3 1 Manual 5 26 2005 61 Setting mcpu or fast on the Mac results in gcc enabling a number of different flags Read the gcc manual carefully if you want to experiment with other flags 7 1 2 Compiling with Code Warrior or Visual Studio We provide MrBayes project files for both Metrowerks Code Warrior and Microsoft Visual Studio in the source code package All the relevant flags are set in these files so you should be able to compile the code without any further modifications 7 2 Compiling and Running the Parallel Version of MrBayes Metropolis coupling or heating is well suited for parallelization MrBayes 3 takes advantage of this and uses MPI to distribute heated and cold chains among available processors Altekar et al 2004 There ar
101. r Welpy Tyfyy o pYpy Rcley Wofoy and the model has 19 free stationary state frequency parameters and 189 free substitution rate parameters The Bayesian MCMC approach is good at handling uncertainty in multi parameter models so the GTR model may be used successfully with moderate size data sets but the model is so parameter rich that you need a fairly sizable data set to be able to estimate all parameters with reasonable precision The GTR model can be used to express a user derived fixed rate model other than those already implemented in MrBayes Simply use the prset command to fix the stationary state frequencies and substitution rates of the GTR model to the desired values You need to set two options prset aarevmatpr fixed lt 190 comma separated values andprset statefreqpr fixed lt 20 comma separated values gt Once the values are fixed prior to analysis the MCMC procedure will not change them and they will remain the same throughout the analysis MrBayes 3 1 Manual 5 26 2005 39 4 3 Restriction Site Binary Model MrBayes implements a simple F81 like model for restriction sites and other binary data The instantaneous rate matrix for this model is simply 0 1 Q q 0 m om Any asymmetry in the rate of 0 to 1 and 1 to 0 transitions is expressed in terms of the stationary state frequencies Thus if the stationary frequencies are sto 0 25 and zr 0 75 then the rate of 0 to 1 transitions is 3 times as high a
102. rBayes 3 1 Manual 5 26 2005 44 In the worst case a small symmetric tree the extra computational complexity incurred by invoking the auto correlated gamma model instead of the gamma model is comparable to a doubling of the number of taxa in the analysis In more typical cases moderate to large data sets the additional computational cost is negligible and equivalent to adding a single taxon As with the gamma model the autocorrelated gamma distribution is approximated with a number of discrete rate categories determined by 1set ngammacat As described by Yang 1995 protein coding sequences tend to have a three position offset in their autocorrelation That is the first codon position sites tend to have rates that are correlated with the adjacent first position sites second position site rates are correlated with adjacent second position rates etc You can take this effect into account by partitioning your sites into the three codon positions and then applying a separate autocorrelated gamma model to each of the categories You might want to invoke an autocorrelated gamma model with the same correlation coefficient for a dataset consisting of several concatenated genes If so it is necessary to inform MrBayes about the break points between different genes Otherwise the rates at the first site of each gene except the first one will be erroneously compared to the rates at the last site in the preceding gene The command databreaks is provided f
103. rc Tacco Tarer 0 Weclac 0 AG Trig Tac eg JE ihe 0 0 a 0 Q q AT 7f ce acter 0 0 e Upp Var CA rc 0 0 0 Mel ie s 0 CC 0 fd 0 0 eaae es 0 TT 0 0 0 H itir 0 0 T Instead of using the GTR model we could of course have used the HKY or F81 model resulting in obvious modifications of the rmn values Use 1set nst to change among those options for instance use set nst 6 to choose the GTR model The default model is the F81 model lset nst 1 Before the doublet model can be used it is necessary to specify all the nucleotide pairs in the alignment This is done using the pairs command most conveniently in a MrBayes block in a data file For instance pairs 1 10 2 9 would pair nucleotide 1 with 10 MrBayes 3 1 Manual 5 26 2005 35 and 2 with 9 See the kim nex data file for an example of an analysis using the doublet model 4 1 3 Codon Models The codon models implemented in MrBayes are based on the first formulations of such models Goldman and Yang 1994 Muse and Gaut 1994 The approach is similar to that used in the doublet model A codon can change to another only through steps of one nucleotide change at a time These steps are modeled using a standard four by four nucleotide model There is one additional complication though some nucleotide changes are synonymous while others lead to changes in amino acids and thus may be subject to selection a factor modifying the substitution rate Assume that i and j are
104. rsions of the tutorial You will first find a Quick Start version for impatient users who want to get an analysis started immediately The rest of the section contains a much more detailed description of the same analysis 2 1 Quick Start Version There are four steps to a typical Bayesian phylogenetic analysis using MrBayes Read the Nexus data file Set the evolutionary model Run the analysis Summarize the samples poser In more detail each of these steps is performed as described in the following paragraphs 1 At the MrBayes gt prompt type execute primates nex This will bring the data into the program The data file primates nex must be in the same directory as the MrBayes program If you run into problems refer to section 2 2 for possible solutions If you are running your own data file beware that it may contain some MrBayes commands that can change the behavior of the program delete those commands or put them in square brackets to follow this tutorial MrBayes 3 1 Manual 5 26 2005 9 2 At the MrBayes gt prompt type lset nst 6 rates invgamma This sets the evolutionary model to the GTR model with gamma distributed rate variation across sites and a proportion of invariable sites If your data are not DNA or RNA if you want to invoke a different model or if you want to use non default priors refer to the rest of this manual particularly sections 3 to 5 and the Appendix 3 1 At the MrBayes gt prompt type meme ngen
105. s 2003 Lewis 2001 and Huelsenbeck et al 2001 2002 It is also worthwhile to study the early papers introducing Bayesian phylogenetic methods Li 1996 Mau 1996 Rannala and Yang 1996 Mau and Newton 1997 Rannala and Yang 1997 Larget and Simon 1999 Mau Newton and Larget 1999 Newton Mau and Larget 1999 The basic MCMC techniques are described in Metropolis et al 1953 and Hastings 1970 The Metropolis coupled MCMC used by MrBayes was introduced by Geyer 1991 1 1 Conventions Used in this Manual What you see on the screen and what is in the input file isin plain typewriter font What you type isinbold typewriter font 1 2 Acquiring and Installing MrBayes MrBayes 3 is distributed without charge by download from the MrBayes web site http mrbayes net If someone has given you a copy of MrBayes 3 we strongly suggest that you download the most recent version from this site The site also gives information MrBayes 3 1 Manual 5 26 2005 5 about the MrBayes users email list and describes how you can report bugs or contribute to the project MrBayes 3 is a plain vanilla program that uses a command line interface and therefore behaves virtually the same on all platforms Macintosh Windows and Unix There is a separate download package for each platform The Macintosh package contains two versions of the program the standard serial version named MrBayes3 1 program icon one copy of Reverend Bayes s portrait and
106. s gamma The trickiest part is to allow the overall rate to be different across partitions This is achieved using the ratepr parameter of the prset command By default ratepr is set to fixed meaning that all partitions have the same overall rate By changing this to variable the rates are allowed to vary under a flat Dirichlet prior see the help info for prset if you want to modify this prior To allow all our partitions to evolve under different rates type prset applyto all ratepr variable The model is now essentially complete but there is one final thing to consider Typically morphological data matrices do not include all types of characters Specifically morphological data matrices do not usually include any constant invariable characters Sometimes autapomorphies are not included either and the matrix is restricted to parsimony informative characters For MrBayes to calculate the probability of the data correctly we need to inform it of this ascertainment coding bias By default MrBayes assumes that standard data sets include all variable characters but no constant characters If necessary one can change this setting using lset coding We will leave the coding setting at the default though Now showmodel1 should produce this table Active parameters Partition s Parameters 12 33 4 5 Revmat 1 2 3 4 Statefreq 5 6 v 9 39 Shape 10 11 12 13 14 Pinvar 15 16 17 18 Ratemultiplier 19 19 19 19 19 Topology 20 20 20 2
107. s the rate of transitions in the other direction Jt a 3 A problem with some binary data sets notably restriction sites is that there is an ascertainment coding bias such that certain characters will always be missing from the observed data It is impossible for instance to detect restriction sites that are absent in all of the studied taxa MrBayes corrects for this bias by calculating likelihoods conditional on the unobservable characters being absent Felsenstein 1992 The ascertainment coding bias is selected using 1set coding There are five options 1 there is no bias all types of characters could in principle be observed lset coding all 2 characters that are absent state 0 in all taxa cannot be observed lset coding noabsencesites 3 characters that are present state 1 in all taxa cannot be observed lset coding nopresencesites 4 characters that are constant either state 0 or 1 in all taxa cannot be observed lset coding variable and 5 only characters that are parsimony informative have been scored 1set coding informative For restriction sites it is typically true that all absence sites cannot be observed so the correct coding bias option is noabsencesites The binary model is useful for a number of character types other than restriction sites For instance the model can be used for gap characters The presence and absence of gaps must be coded consistently for all characters let us assume here
108. set of sequences If that set of sequences were independent of your set of MrBayes 3 1 Manual 5 26 2005 15 sequences but clearly relevant to the analysis of your sequences it might be reasonable to use those numbers as a prior in your analysis In our analysis we will be cautious and leave the prior on state frequencies at its default setting If you have changed the setting according to the suggestions above you need to change it back by typing prset statefreqpr Dirichlet 1 1 1 1 orprs st Dir 1 1 1 1 if you want to save some typing Similarly we will leave the prior on the substitution rates at the default flat Dirichlet 1 1 1 1 1 1 distribution The Shapepr parameter determines the prior for the a shape parameter of the gamma distribution of rate variation We will leave it at its default setting a uniform distribution spanning a wide range of a values The prior for the proportion of invariable sites is set with Pinvarpr The default setting is a uniform distribution between 0 and 1 an appropriate setting if we don t want to assume any prior knowledge about the proportion of invariable sites For topology the default Uniform setting for the Topologypr parameter puts equal probability on all distinct fully resolved topologies The alternative is to constrain some nodes in the tree to always be present but we will not attempt that in this analysis The Brlenspr parameter can either be set to unconstrained or clock constrained
109. should look something like this posh Soa a2Se 22 Bees S22 esses oS ee as oe es eee eee se See bees ese t 5716 56 1 1 2 1 12 1 1 2 1 2 1 1 1 2 1 22 2 ak 1 2 2 2 2 Ze i2u 2 1 E lt 2 22 271 d TL X 12 1 2 T FL 2 2 Zu IU 1211 ak 11 1 2 T 2 2 21 L 12 112 2 ji 2 Y 1 2 qp 2 2 2 21 2 25 22 1 1 1 2 2 2 1 2 1 2 2 1 21 11 2 1 2 T 2 4 5733 79 2500 10000 If you see an obvious trend in your plot either increasing or decreasing you probably need to run the analysis longer to get an adequate sample from the posterior probability distribution At the bottom of the sump output there is a table summarizing the samples of the parameter values Model parameter summaries over the runs sampled in files primates nex runl p and primates nex run2 p Summaries are based on a total of 1502 samples from 2 runs Each run produced 1001 samples of which 751 samples were included 95 Cred Interval Parameter Mean Variance Lower Upper Median PSRF TL 2 885314 0 071446 2 408000 3 464000 2 861000 1 004 rv A lt gt C 0 045110 0 000070 0 031406 0 061424 0 044756 0 999 r A G 0 477554 0 002421 0 387141 0 569168 0 473521 1 040 r A T 0 03854 0 000060 0 024204 0 053787 0 038402 0 999 r C G 0 033765 0 000195 0 010836 0 064049 0 032475 1 033 r C T 0 386144 0 001735 0 311504 0 459011 0 386897 1 012 r G T 0 018885 0 000133 0 001217 0
110. split frequencies than by looking at likelihood trends When you stop the analysis MrBayes will print several types of information useful in optimizing the analysis This is primarily of interest if you have difficulties in obtaining convergence Since we apparently have a good sample from the posterior distribution already we will ignore this information for now We will return to the subject of optimizing the MCMC analysis in section 5 of the manual 2 9 Summarizing Samples of Substitution Model Parameters During the run samples of the substitution model parameters have been written to the p files every samplefreq generation These files are tab delimited text files that look something like this ID 5848203808 Gen LnL TL r A C veo PLG pi T alpha pinvar 1 7559 137 2 044 0 166667 0 250000 0 250000 0 500000 0 000000 10 6585 519 2 181 20 090180 0 169513 0 247418 0 569271 0 036162 9990 5728 935 2 527 20 051106 0 076213 0 262107 0 932771 0 194004 10000 5722 857 2 642 0 051106 0 078383 0 246791 0 721217 0 185486 The first number in square brackets is a randomly generated ID number that lets you identify the analysis from which the samples come The next line contains the column headers and is followed by the sampled values From left to right the columns contain 1 the generation number Gen 2 the log likelihood of the cold chain Ln L 3 the total tree length the sum of all branch lengths TL 4
111. state frequencies of the binary model must be fixed to be equal such that the estimation of model parameters becomes independent of the labeling of character states An alternative is to consider the standard model which provides more sophisticated ways of dealing with arbitrary state labels When is the correction for ascertainment bias important This is strongly dependent on the size of the tree the sum of the branch lengths on the tree The larger the tree the less important the correction for ascertainment bias becomes In our experience when there are more than 20 30 taxa even the most severe bias only informative characters observed is associated with an insignificant correction of the likelihood values 4 4 Standard Discrete Morphology Model The model used by MrBayes for standard discrete data is based on the ideas originally presented by Lewis 2001 Essentially the model is analogous to a JC model except that it has a variable number of states from 2 to 10 For instance a three state standard character would be evolving according to the instantaneous rate matrix 0 1 2 Ol ee 3E 3 ijr fee d d Sk wz Q Because all rates are the same we can maintain the essential property of standard characters namely that state labels are arbitrary Thus the standard model assures that you will get the same results regardless of the way in which you label the states In morphology based parsimony analyses one so
112. tead of starting it from a randomly chosen tree First define a good tree with or without branch lengths using the command usertree Then start the chains from this tree using MrBayes 3 1 Manual 5 26 2005 54 mcmcp startingtree user A disadvantage with starting the analysis from a good tree is that it is more difficult to detect problems with convergence using independent runs A compromise is to start each chain from a slightly perturbed version of a good tree MrBayes can introduce random perturbations of a starting tree this is requested using mcmcp nperts integer value How do I run MrBayes in parallel See section 7 of this manual The likelihood values first increase and then drop What is the problem Several users have observed that likelihood values can sometimes increase in the early phase of a run and then decrease to a stable value one user referred to the phenomenon as burn out Actually this type of behavior can be seen with certain types of data sets and models and is part of the normal burn in However it does indicate a problem with the model Typically the problem is due to over parameterization a poor prior or a combination of these factors In MrBayes the starting value for most parameters is an arbitrarily chosen value that is likely to be close to the maximum likelihood estimate MLE of the parameter The MLE value typically also corresponds to the mode peak in the posterior probability distribu
113. tegrating out uncertainty concerning topology and other model parameters The basic approach is described by Huelsenbeck and Bollback 2001 as well as in a recent review Ronquist 2004 You first need to constrain the node you want MrBayes 3 1 Manual 5 26 2005 51 to infer ancestral states for using a constraint definition and the topologypr constraints command as described above for constrained topology models Then ancestral state reconstruction is requested using report ancstates yes The probability of each state will be printed to the p file s under the heading p state code character number For instance the probability of an A at site 215 in a nucleotide data set would be found under the heading p A 215 If you constrain several nodes in your data set the node number will be given as well If you had constrained two nodes the probabilities of the above character would be distinguished as p A 21581 and p A 21502 However if you are interested in inferring ancestral states at two or more different nodes we recommend running separate analyses each constraining a single node The reason is that when you focus on one node you probably want to integrate over uncertainty in the rest of the tree including the potential uncertainty concerning the presence of the other node s Often there is interest in mapping only one or a few characters onto trees inferred using largely other types of data For instance a b
114. tgroup selected correctly By default MrBayes uses the first taxon in the data matrix as the outgroup You can change this by using the outgroup command For instance if you want taxon number 7 called My taxon to be the outgroup either use outgroup 7 or outgroup My taxon MrBayes 3 1 only allows a single taxon as the outgroup Before the constraints take effect you have to invoke them by using prset topologypr constraints lt comma separated list of constraints For instance to enforce the constraint my constraint defined above useprset topologypr constraints my constraint MrBayes 3 1 Manual 5 26 2005 48 4 8 2 Non clock Standard Trees If you do not want to enforce a molecular clock you choose an unconstrained branch length prior Actually you do not have to do anything because unconstrained branch lengths are the default You can associate unconstrained branch lengths with either a uniform prior from 0 to some arbitrary value or an exponential prior The default is an exponential distribution with parameter 10 Exponential 10 it has an expectation of 0 1 1 10 but in principle it allows branch lengths to vary from 0 to infinity The exponential distribution apparently puts a lot more probability on short branches than on long branches However because transition substitution probabilities change rapidly at small branch lengths but only very slowly at long branch lengths the exponential prior is actually closer to a
115. that absence of a gap is coded as 0 and presence as 1 Since the detection of gaps is typically contingent on observing some sequence length variation neither all absence nor all presence characters can be observed Thus the correct ascertainment bias for gap characters is variable The parameters 7r and zt would represent the rate at which insertions and deletions occur respectively assuming that state 0 denotes absence of a gap The binary model can also be used for ecological morphological or other binary characters of arbitrary origin However if the binary model is applied to more than one character then there is an implicit assumption that the state labels are not arbitrary for those characters That is the 0 state in one character must somehow be comparable to the 0 state in the others For instance 0 could mean absence or presence of a particular type of feature such as a wing vein a restriction site or a gap in a DNA sequence It is not appropriate to apply the default binary model to a set of characters where the state labels MrBayes 3 1 Manual 5 26 2005 40 are arbitrary as is true of most morphological characters Thus we can possibly estimate the rate of loss versus gain of wing veins over a set of consistently coded wing venation characters but we cannot compare the rate of loss of antennal articles to the rate at which a yellow patch evolves into a green patch If state labels are truly arbitrary then the stationary
116. thod is to focus on the common doublets A T and C G in particular MrBayes uses a more complex model originally formulated by Schoniger and von Haeseler 1994 where all doublets are taken into account The central idea in this model is that one common doublet is converted into another through a two step process In the first step one of the nucleotides is substituted with another according to a standard four by four model of nucleotide change In the second step the matching nucleotide is changed according to the same standard four by four model Thus in this model there is no momentary change from one doublet to another doublet this always occurs through an intermediate rare doublet Assume that we are using a GTR model for the single nucleotide substitutions that i and j are two different doublets that dj is the minimum number of nucleotides that must be changed when going between i and j and that mn is the pair of nucleotides that change when going between i and j when dj 1 Then the elements qj of the instantaneous rate matrix Q of the doublet model can be expressed as follows 0 if d gt 1 ToU an if dy for the case when i differs from j the diagonal elements i j are determined as usual to balance the rows in the instantaneous rate matrix to sum to zero This gives the instantaneous rate matrix only 7 rows and columns out of 16 shown AA AC AG AT CA CC TT AA E Tacho Macae Marar calac 0 e 0 AC 7
117. tion In most cases you expect the bulk of the probability mass in the posterior probability distribution to be in the region close to the MLE However it is possible that there is a region in parameter space with only moderate height lower likelihood values but considerably larger probability mass than the MLE region It is like comparing the mass of a tower to the mass of a huge office complex Even if the tower is considerably higher its mass is going to be only a fraction of the mass of the office complex A typical situation in which this can occur is if you 1 use a uniform prior on branch lengths which puts considerable prior probability on long branches 2 have data that are relatively uninformative about branch lengths and 3 have a model such as the gamma model with a low but not insignificant probability associated with long branches for weak data In such cases the MLE region at short branch lengths can have considerably smaller probability mass than the less likely but much larger region at longer branch lengths Unless you feed MrBayes with your own starting tree the run will start with all branch lengths set to 0 1 This is close to the MLE region and in the early phase of the run you will see the likelihood values climb as the topology is improved by branch rearrangements while the branch lengths remain small Eventually however the long branch length region will attract the chain through its high probability mass and yo
118. to save trees with branch lengths to the t file Since this is what we want we leave this setting as is If you are running a large analysis many taxa and are not interested in branch lengths you can save a considerable amount of disk space by not saving branch lengths MrBayes 3 1 Manual 5 26 2005 19 The Startingtree parameter can be used to feed the chain s with a user specified starting tree The default behavior is to start each chain with a different random tree this is recommended for general use 2 7 Running the Analysis Finally we are ready to start the analysis Type meme MrBayes will first print information about the model and then list the proposal mechanisms that will be used in sampling from the posterior distribution In our case the proposals are the following The MCMC sampler will use the following moves With prob Chain will change 4 17 param 1 revmat with Dirichlet proposal 4 17 param state frequencies with Dirichlet proposal 4 17 param gamma shape with multiplier 4 17 param prop invariants with beta proposal 20 83 param topology and branch lengths with LOCAL 62 50 param topology and branch lengths with extending TBR Oo 0 IN Note that MrBayes will spend most of its effort changing topology and branch lengths In our experience topology and branch lengths are the most difficult parameters to integrate over and we therefore let MrBayes spend a large proportion of its time pr
119. trate on the table at the bottom of the output which specifies the current settings It should look like this Model settings for partition 1 Parameter Options Current Setting Nucmodel 4by4 Doublet Codon 4by4 Nst 1 2 6 1 Code Universal Vertmt Mycoplasma Yeast Ciliates Metmt Universal Ploidy Haploid Diploid Diploid Rates Equal Gamma Propinv Invgamma Adgamma Equal Ngammacat number 4 Nbetacat number 5 Omegavar Equal Ny98 M3 Equal Covarion o Yes o Coding All Variable Noabsencesites opresencesites All Parsmodel o Yes o First note that the table is headed by Model settings for partition 1 By default MrBayes divides the data into one partition for each type of data you have in your DATA block If you have only one type of data all data will be in a single partition by default How to change the partitioning of the data will be explained in section 3 of the manual The Nucmodel setting allows you to specify the general type of DNA model The Doublet option is for the analysis of paired stem regions of ribosomal DNA and the Codon option is for analyzing the DNA sequence in terms of its codons We will analyze the data using a standard nucleotide substitution model in which case the default 4by4 option is appropriate so we will leave Nucmode 1 at its default setting The general structure of the substitution model is determined by the Nst setting By default all substitutions have the same rate Nst 1 correspondin
120. u will see the branch lengths increase and the likelihood values decrease to a stable region There are basically two ways of fixing the burn out problem One is to change your priors so that they put more probability in the MLE region An obvious step is to change a uniform prior on branch lengths to an exponential prior as explained above in the MrBayes 3 1 Manual 5 26 2005 55 section on branch length priors an exponential prior is more uninformative than the uniform prior anyway The other possibility is to simplify your model For instance assume equal rates over sites instead of a gamma model or choose a substitution model with fewer free parameters How can I test models using Bayes factors The Bayesian approach provides a convenient way of comparing models through the calculation of Bayes factors which can be interpreted as indicators of the strength of the evidence in favor of the best of two models The Bayes factor values are typically interpreted according to recommendations developed by Kass and Raftery 1995 Unlike a hierarchical likelihood ratio test the models compared with Bayes factors need not be hierarchically nested A Bayes factor is calculated simply as the ratio of the marginal likelihoods of the two models being compared The logarithm of the Bayes factor is the difference in the logarithms of the marginal model likelihoods The marginal likelihood of a model is difficult to estimate accurately but a roug
121. uencies and omega 1 omega 2 and omega 3 for the w values The probability of a codon being positively selected is labeled by the site numbers in the original alignment Thus pr 16 17 18 is the probability of the codon corresponding to the original nucleotide alignment sites 16 17 and 18 being in a positively selected omega category 4 2 Amino acid Models MrBayes implements a large number of amino acid models They fall in two distinct categories the fixed rate models and the variable rate models The former have both the stationary state frequencies and the substitution rates fixed whereas one or both of these are estimated in the latter MrBayes 3 1 Manual 5 26 2005 37 4 2 1 Fixed Rate Models The Poisson model Bishop and Friday 1987 is the simplest of the fixed rate models It assumes equal stationary state frequencies and equal substitution rates thus it is analogous to the JC model for nucleotide characters The rest of the fixed rate models have unequal but fixed stationary state frequencies and substitution rates reflecting estimates of protein evolution based on some large training set of proteins These models include the Dayhoff model Dayhoff Schwartz and Orcutt 1978 the Mtrev model Adachi and Hasegawa 1996 the Mtmam model Cao et al 1998 Yang Nielsen and Hasegawa 1998 the WAG model Wheland and Goldman 2001 the Rtrev model Dimmic et al 2002 the Cprev model Adachi et al 2000 the Vt model
122. uncertainty the same way as uncertainty so it does not matter whether you use parentheses or curly brackets If you have other symbols in your matrix than the ones supported by MrBayes you need to replace them before processing the data block in MrBayes You also need to remove the Equate and Symbols statements in the Format line if they are included Unlike the Nexus standard MrBayes supports data blocks that contain mixed data types as described in section 3 of this manual To put the data into MrBayes type execute filename atthe MrBayes gt prompt where filename is the name of the input file To process our example file type execute primates nexorsimplyexe primates nex to save some typing Note that the input file must be located in the same folder directory as the MrBayes application or else you will have to give the path to the file and the name of the input file should not have blank spaces If everything proceeds normally MrBayes will acknowledge that it has read the data in the DATA block of the Nexus file by outputting the following information Executing file primates nex DOS line termination Longest line length 915 Parsing file Expecting NEXUS formatted file Reading data block Allocated matrix Matrix has 12 taxa and 898 characters Data is Dna Data matrix is not interleaved Gaps coded as Setting default partition does not divide up characters Taxon 1 Tarsius syric
123. waps states with the heated chains If the cold chain gets stuck in one of the columns then the heated chains are not successfully contributing states to the cold chain and the Metropolis coupling is inefficient The analysis may then have to be run longer or the temperature difference between chains may have to be lowered The star column separates the two different runs The last column gives the time left to completion of the specified number of generations This analysis approximately takes 1 second per 100 generations Because different moves are used in each generation the exact time varies somewhat for each set of 100 generations and the predicted time to completion will be unstable in the beginning of the run After a while the predictions will become more accurate and the time will decrease predictably 2 8 When to Stop the Analysis At the end of the run MrBayes asks whether or not you want to continue with the analysis Before answering that question examine the average standard deviation of split frequencies As the two runs converge onto the stationary distribution we expect the average standard deviation of split frequencies to approach zero reflecting the fact that the two tree samples become increasingly similar In our case the average standard deviation is about 0 07 after 1 000 generations and then drops to less than 0 000001 towards the end of the run Your values can differ slightly because of stochastic effects Given t
124. ypes in MrBayes One of the most important advantages of the Bayesian approach is that it allows you to integrate out uncertainty concerning the model parameters you have little information about Thus Bayesian inference is relatively robust to slight over parameterization of your model In addition the MCMC sampling procedure is typically efficient in dealing with complex multi parametric models For these reasons it is less important in the Bayesian context to find the simplest possible model that can reasonably represent your data If you use a model testing procedure and it suggests a four by four nucleotide model not implemented in MrBayes then you should obtain good results using the next more complex model available in the program 4 1 2 The Doublet Model The doublet model of MrBayes is intended for stem regions of ribosomal sequences where nucleotides pair with each other to form doublets The nucleotide pairing results in strong correlation of substitutions across sites when there is a substitution at one site it is typically accompanied by a compensatory substitution at the paired site If the correlation between paired sites is not accounted for parametric statistical methods will overestimate the confidence we should have in the best tree s Incidentally the same is true for parsimony and the non parametric bootstrap MrBayes 3 1 Manual 5 26 2005 34 There are various ways to model the evolution of nucleotide doublets One me

Download Pdf Manuals

Related Search

Related Contents

MANUAL dE SERVICIO TÉCNICO  LG PCS150R User's Manual  Samsung MW880BLA Manual de Usuario  Liste des titres - Ville de Sainte    取扱説明書    Akai ARF360D  warning avertissement  UML-Based Design Process  

Copyright © All rights reserved. Failed to retrieve file