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Bayesian Inference of Species Trees from Multilocus Data using *BEAST, Alexei J Drummond, Walter Xie and Joseph Heled April 13, 2012

Provides joint inference of a species tree topology, divergence times, population sizes, and gene trees from multiple genes sampled from multiple individuals across a set of closely related species. It's an extension of BEAST to *BEAST (pronounced ”star beast”).

Publication: Joseph Heled and Alexei J. Drummond Bayesian Inference of Species Trees from Multilocus Data Mol. Biol. Evol. 2010 27: 570-580.

The protocol is taken from the tutorial.


You will need the following software at your disposal:

  • BEAST - this package contains the BEAST program, BEAUti, TreeAnnotator and other utility programs. This tutorial is written for BEAST v1.7.x, which is

available for download from http://beast.bio.ed.ac.uk/.

  • Tracer - this program is used to explore the output of BEAST (and other

Bayesian MCMC programs). It graphically and quantitively summarizes the distributions of continuous parameters and provides diagnostic information. At the time of writing, the current version is v1.5. It is available for download from http://beast.bio.ed.ac.uk/.

  • FigTree - this is an application for displaying and printing molecular phylogenies,in particular those obtained using BEAST. At the time of writing, the current

version is v1.3.1. It is available for download from http://tree.bio.ed.ac.uk/.

This tutorial will guide you through the analysis of three loci sampled from 26 individuals representing nine species of pocket gophers. This is a subset of previous published data [1]. The objective of this tutorial is to estimate the species tree that is most probable given the multi-individual multi-locus sequence data. The species tree has 9 taxa, whereas each gene tree has 26 taxa.

  • BEAST will co-estimate three gene trees embedded in a shared species tree (see Heled and Drummond, 2010 for details).

Step 1: Load data in NEXUS format

The first step will be to convert a NEXUS file with a DATA or CHARACTERS block into a BEAST XML input file. This is done using the program BEAUti (Bayesian Evolutionary Analysis Utility). This is a user-friendly program for setting the evolutionary model and options for the MCMC analysis. The second step is to actually run BEAST using the input file that contains the data, model and settings. The final step is to explore the output of BEAST in order to diagnose problems and to summarize the results.

BEAUti Run BEAUti and load a NEXUS format alignment, simply select the Import Data... option fromthe File menu.

Select three files called 26.nex, 29.nex, 47.nex by holding shift key. Each file contains an alignment of sequences of from an independent locus.

Once loaded, the three partitions are displayed in the main panel. Double click any alignment (partition) to show its detail.

Step2: Import or create traits

Import trait(s) from a mapping file to fire *BEAST To enable *BEAST in BEAST v1.7.x, simply click the check box labelled Use species tree ancestral reconstruction (*BEAST) Heled & Drummond 2010 on the top of Data Partitions panel. Then, a Create or Import Trait(s) dialog will pop up.

There are two options to be selected: 1. Import trait(s) from a mapping file; 2. Create a new trait and then guess trait value from taxa name species. Choose the first option and click OK to load the mapping file, named gopher mapping.txt. Once loaded, a message indicating the use of *BEAST will be displayed in the status at the bottom of the window, and a trait named species is created in the trait table in the Traits tab. Click it to show trait values.

A proper trait file is tab delimited. The first row is always traits followed by the keyword species in the second column and separated by tab. The rest of the rows map each individual taxon name to a species name: the taxon name in the first column and species name in the second column separated by tab. For example:

traits species
taxon1 speciesA
taxon2 speciesA
taxon3 speciesB

For multi-locus analyses, BEAST can link or unlink substitutions models across the loci by clicking buttons on the top of Data Partitions panel. The default of *BEAST is unlinking all models: substitution model, clock model, and tree models. Note that you should only unlink the tree model across data partitions that are actually genetically unlinked. For example, in most organisms all the mitochondrial genes are effectively linked due to a lack of recombination and they should be set up to use the same tree model in a *BEAST analysis.

Alternatively: Create a species trait from taxa names The advantage of using the Traits panel is that we can extract species names from the taxa names if they already contain that information. Let’s go to Data Partitions panel and unselect the check box labelled Use species tree ancestral reconstruction (*BEAST) Heled & Drummond 2010. As we can see in the status bar on the bottom, the analysis has been reverted to a standard BEAST analysis. To enable *BEAST again, click the Use species tree ancestral reconstruction (*BEAST) Heled & Drummond 2010 on the top of Data Partitions panel, and then choose the second option in Create or Import Trait(s) dialog this time. Click OK to continue, and then we will get to Traits panel and click on the Guess trait values at the top to pop out Guess Trait Value for Taxa dialog. Choose second in the drop list of Defined by its order, and input as separator. Click OK, and *BEAST is applied again.

Step 4: Setting the substitution model

The next thing to do is to click on the Site Models tab at the top of the main window. This will reveal the evolutionary model settings for BEAST. Exactly which options appear depend on whether the data are nucleotides, or amino acids, or binary data, or general data. The settings that will appear after loading the data set will be the default values so we need to make some changes. Most of the models should be familiar to you. For this analysis, we will select each substitution model listed on the left side in turn to make the following change: select Empirical for the Base frequencies. Remember to do this for all site models.


�Setting the clock model Second, click on the Clock Models tab at the top of the main window. In this analysis, we use the Strict Clock molecular clock model as default. Your model options should now look like this:


�The Estimate check box is unchecked for the first clock model and checked for the rest clock models, because we wish to estimate the mutation rate of each subsequent locus relative to the first locus whose rate is fixed to 1.0. Trees The Trees panel allows priors to be specified for each parameter in the model, which can be defined on the top of the panel. *BEAST has a different tree prior panel where users can only configure the species tree prior not gene tree priors (which are automatically specified by the multispecies coalescent). Currently, we have two species tree priors: Yule Process and Birth-Death Process; and three population size models: Piecewise linear and constant root, Piecewise linear, and Piecewise constant. In this analysis, we use the default options. The bottom right panel is used to configure the corresponding starting trees. The Ploidy Type menu determines the type of sequence (mitochondrial, nuclear, X, Y). This matters since different modes of inheritance give rise to different effective population sizes. The Starting Tree menu provides three options, where the user-specified starting tree has to be loaded from the data file (e.g. NEXUS file) in advance. In this analysis, we simply use a random starting tree.


�Priors and Operators The Priors panel allows priors to be specified for each parameter in the model. The Operators panel is used to configure technical settings that affect the efficiency of the MCMC program (see Notes for details). We leave these two panels unchanged in this analysis. Setting the MCMC options The next tab, MCMC, provides more general settings to control the length of the MCMC and the file names. Firstly we have the Length of chain. This is the number of steps the MCMC will make in the chain before finishing. The appropriate length of the chain depends on the size of the data set, the complexity of the model and the accuracy of the answer required. The default value of 10,000,000 is entirely arbitrary and should be adjusted according to the size of your data set. For this data set let’s initially set the chain length to 5,000,000 as this will run reasonably quickly on most modern computers (less than 20 minutes). The next options specify how often the parameter values in the Markov chain should be displayed on the screen and recorded in the log file. The screen output is simply for monitoring the programs progress so can be set to any value (although if set too small, 10

�the sheer quantity of information being displayed on the screen will actually slow the program down). For the log file, the value should be set relative to the total length of the chain. Sampling too often will result in very large files with little extra benefit in terms of the precision of the analysis. Sample too infrequently and the log file will not contain much information about the distributions of the parameters. You probably want to aim to store no more than 10,000 samples so this should be set to no less than chain length / 10,000. For this exercise we will set the screen log to 10000 and the file log to 1000. The final two options give the file names of the log files for the sampled parameters and the trees. These will be set to a default based on the name of the imported NEXUS file. If you would like to save the operator analysis into a file, you need to check Create operator analysis file which will generate a file with the suffix .ops.

• If you are using windows then we suggest you add the suffix .txt to both of these (so, gopher.log.txt and gopher.trees.txt) so that Windows recognizes these as text files. Generating the BEAST XML file We are now ready to create the BEAST XML file. To do this, either select the Generate BEAST File... option from the File menu or click the similarly labelled button 11

�at the bottom of the window. Check the default priors setting and click Continue. Save the file with an appropriate name (we usually end the filename with .xml, i.e., gopher.xml). We are now ready to run the file through BEAST.

Running BEAST Now run BEAST and when it asks for an input file, provide your newly created XML file as input by click Choose File ..., and then click Run.

BEAST will then run until it has finished reporting information to the screen. The actual results files are saved to the disk in the same location as your input file. The output to the screen will look something like this:

BEAST v1.7.1, 2002-2012 Bayesian Evolutionary Analysis Sampling Trees Designed and developed by Alexei J. Drummond, Andrew Rambaut and Marc A. Suchard


�Department of Computer Science University of Auckland alexei@cs.auckland.ac.nz Institute of Evolutionary Biology University of Edinburgh a.rambaut@ed.ac.uk David Geffen School of Medicine University of California, Los Angeles msuchard@ucla.edu Downloads, Help & Resources: http://beast.bio.ed.ac.uk Source code distributed under the GNU Lesser General Public License: http://code.google.com/p/beast-mcmc BEAST developers: Alex Alekseyenko, Trevor Bedford, Erik Bloomquist, Joseph Heled, Sebastian Hoehna, Denise Kuehnert, Philippe Lemey, Wai Lok Sibon Li, Gerton Lunter, Sidney Markowitz, Vladimir Minin, Michael Defoin Platel, Oliver Pybus, Chieh-Hsi Wu, Walter Xie Thanks to: Roald Forsberg, Beth Shapiro and Korbinian Strimmer

Random number seed: 1334282107812

Parsing XML file: gopher.xml File encoding: MacRoman Read alignment: alignment1 Sequences = 26 Sites = 614 Datatype = nucleotide Read alignment: alignment2 Sequences = 26 Sites = 601 Datatype = nucleotide Read alignment: alignment3 Sequences = 26 Sites = 819 Datatype = nucleotide Site patterns ’26.patterns’ created from positions 1-614 of alignment ’alignment1’ pattern count = 144 Site patterns ’29.patterns’ created from positions 1-601 of alignment ’alignment2’ pattern count = 71 Site patterns ’47.patterns’ created from positions 1-819 of alignment ’alignment3’ pattern count = 153 Creating the tree model, ’26.treeModel’ initial tree topology = ((((((((((Thomomys_bottae_bottae,Thomomys_monticola_b),Orthogeomys_heterodus),(Thomomys_talpoides_y tree height = 0.017 Creating the tree model, ’29.treeModel’ initial tree topology = (((((((((Thomomys_bottae_albatus,Thomomys_bottae_xerophilus),Thomomys_bottae_saxatilis),Thomomys_mo tree height = 0.016 Creating the tree model, ’47.treeModel’ initial tree topology = (((((((((Thomomys_bottae_cactophilus,Thomomys_bottae_saxatilis),(Thomomys_bottae_mewa,Thomomys_town tree height = 0.017 Using strict molecular clock model. Using strict molecular clock model. Using strict molecular clock model. Creating state frequencies model ’26.frequencies’: Using empirical frequencies from data = {0.40772, 0.20916, 0.19046, 0.1926


�Creating HKY substitution model. Initial kappa = 2.0 Creating site model. Creating state frequencies model ’29.frequencies’: Using empirical frequencies from data = {0.24545, 0.21384, 0.23701, 0.3037 Creating HKY substitution model. Initial kappa = 2.0 Creating site model. Creating state frequencies model ’47.frequencies’: Using empirical frequencies from data = {0.2017, 0.21368, 0.21208, 0.37254 Creating HKY substitution model. Initial kappa = 2.0 Creating site model. Loading native NucleotideLikelihoodCore successfully TreeLikelihood(26.treeModel) using native nucleotide likelihood core Ignoring ambiguities in tree likelihood. With 144 unique site patterns. Branch rate model used: strictClockBranchRates TreeLikelihood(29.treeModel) using native nucleotide likelihood core Ignoring ambiguities in tree likelihood. With 71 unique site patterns. Branch rate model used: strictClockBranchRates TreeLikelihood(47.treeModel) using native nucleotide likelihood core Ignoring ambiguities in tree likelihood. With 153 unique site patterns. Branch rate model used: strictClockBranchRates Using Yule prior on tree Likelihood is using -1 threads. Creating the MCMC chain: chainLength=5000000 autoOptimize=true autoOptimize delayed for 50000 steps

  1. BEAST v1.7.1, r4860
  2. Generated Fri Apr 13 16:02:42 NZST 2012 [seed=1334282107812]

state Posterior Prior Likelihood PopMean 26.rootHeight 29.rootHeight 47.rootHeight 26.clock.rate 29.clock.rate 47.clock.rate 0 -8271.7599 -408.9912 -7862.7688 1.0000 1.7E-2 1.6E-2 1.7E-2 1.00000 1.00000 1.0000 50000 -4402.6081 -110.7170 -4291.8911 0.0093 2.85227E-2 2.66503E-2 1.70572E-2 1.00000 0.83166 1. 100000 -4282.8572 5.5473 -4288.4044 0.0009 2.49661E-2 3.13122E-2 1.68536E-2 1.00000 0.80206 1 150000 -4321.6989 -32.7608 -4288.9382 0.0025 3.17837E-2 2.81154E-2 1.88322E-2 1.00000 0.83429 1 200000 -4301.2881 -12.5667 -4288.7214 0.0013 2.32344E-2 4.17748E-2 1.82301E-2 1.00000 0.65006 1 250000 -4312.7097 -9.6236 -4303.0861 0.0020 3.12738E-2 2.28171E-2 1.84486E-2 1.00000 0.82719 1 300000 -4278.9322 35.3165 -4314.2487 0.0008 2.27743E-2 2.26837E-2 1.82648E-2 1.00000 1.19420 1 ... ... 4900000 -4276.9360 4950000 -4238.0976 5000000 -4304.9506

17.6994 49.0728 -17.2098

-4294.6354 -4287.1704 -4287.7408

0.0018 0.0008 0.0017

2.23113E-2 2.45626E-2 2.47898E-2

1.66667E-2 1.28858E-2 3.78072E-2

1.36587E-2 1.29766E-2 2.25424E-2

Operator analysis Operator Tuning Count Time Time/Op scale(26.kappa) 0.36 1106 122 0.11 scale(29.kappa) 0.383 1097 91 0.08 scale(47.kappa) 0.438 1143 131 0.11 scale(29.clock.rate) 0.485 33005 2668 0.08 scale(47.clock.rate) 0.568 33415 3546 0.11 up:29.clock.rate 47.clock.rate species.yule.birthRate down:speciesTree species.popMean subtreeSlide(26.treeModel) 0.003 165916 7583 0.05 Narrow Exchange(26.treeModel) 165585 6047 0.04 Wide Exchange(26.treeModel) 33216 988 0.03 wilsonBalding(26.treeModel) 33151 1648 0.05 scale(26.treeModel.rootHeight) 0.511 33209 1527 0.05 uniform(nodeHeights(26.treeModel)) 331028 17469 0.05 subtreeSlide(29.treeModel) 0.003 166248 7404 0.04 Narrow Exchange(29.treeModel) 165728 5610 0.03 Wide Exchange(29.treeModel) 33262 887 0.03 wilsonBalding(29.treeModel) 33206 1468 0.04 scale(29.treeModel.rootHeight) 0.447 33466 1530 0.05 uniform(nodeHeights(29.treeModel)) 330344 16735 0.05


1.00000 1.00000 1.00000

0.91509 1.24784 0.74967

Pr(accept) 0.3698 0.381 0.3596 0.2684 0.2804 speciesTree.splitPopSize nodeHeights(2 0.2326 0.2971 0.0263 0.0379 0.2864 0.5605 0.2201 0.3173 0.0428 0.0473 0.2679 0.5782

�subtreeSlide(47.treeModel) Narrow Exchange(47.treeModel) Wide Exchange(47.treeModel) wilsonBalding(47.treeModel) scale(47.treeModel.rootHeight) uniform(nodeHeights(47.treeModel)) up:down:nodeHeights(26.treeModel) up:29.clock.rate down:nodeHeights(29.treeModel) up:47.clock.rate down:nodeHeights(47.treeModel) scale(species.popMean) scale(species.yule.birthRate) scale(speciesTree.splitPopSize) nodeReHeight(sptree,species)


0.61 0.782 0.766 0.713 0.495 0.24 0.171

165265 165918 33011 33105 33012 332093 32762 33152 32871 54949 33178 1037737 1036242

7854 6217 998 1795 1317 17991 3383 2502 3484 1784 1132 40459 39954

0.05 0.04 0.03 0.05 0.04 0.05 0.1 0.08 0.11 0.03 0.03 0.04 0.04

0.2449 0.2445 0.0141 0.0186 0.2409 0.5415 0.1912 0.1841 0.1732 0.2719 0.3156 0.2572 0.295

6.349283333333333 minutes

Analyzing the results Run the program called Tracer to analyze the output of BEAST. When the main window has opened, choose Import Trace File... from the File menu and select the file that BEAST has created called gopher.log. You should now see a window like the following:

Remember that MCMC is a stochastic algorithm so the actual numbers will not be exactly the same. On the left hand side is a list of the different quantities that BEAST has logged. There are traces for the posterior (this is the log of the product of the tree likelihood and the prior probabilities), and the continuous parameters. Selecting a trace on the 15

�left brings up analyses for this trace on the right hand side depending on tab that is selected. When first opened, the ‘posterior’ trace is selected and various statistics of this trace are shown under the Estimates tab. In the top right of the window is a table of calculated statistics for the selected trace. Tracer will plot a (marginal posterior) distribution for the selected parameter and also give you statistics such as the mean and median. The 95% HPD lower or upper stands for highest posterior density interval and represents the most compact interval on the selected parameter that contains 95% of the posterior probability. It can be thought of as a Bayesian analog to a confidence interval. Select the treeModel.rootHeight parameter and the next three (hold shift whilst selecting). This will show a display of the age of the root and the three gene trees. If you switch the tab at the top of the window to Marginal Density then you will get a plot of the marginal posterior densities of each of these date estimates overlayed:

Obtaining an estimate of the phylogenetic tree BEAST also produces a sample of plausible trees. These need to be summarized using the program TreeAnnotator (see Notes for details). This will take the set of trees and identify a single tree that best represents the posterior distribution. It will then annotate this selected tree topology with the mean ages of all the nodes as well as the 95% HPD interval of divergence times for each clade in the selected tree. It will also calculate the posterior clade probability for each node. Run the TreeAnnotator program and set it up to look like this: 16

�The burnin is the number of trees to remove from the start of the sample. Unlike Tracer which specifies the number of steps as a burnin, in TreeAnnotator you need to specify the actual number of trees. For this run, we use the default setting. The Posterior probability limit option specifies a limit such that if a node is found at less than this frequency in the sample of trees (i.e., has a posterior probability less than this limit), it will not be annotated. The default of 0.5 means that only nodes seen in the majority of trees will be annotated. Set this to zero to annotate all nodes. For Target tree type you can either choose a specific tree from a file or ask TreeAnnotator to find a tree in your sample. The default option, Maximum clade credibility tree, finds the tree with the highest product of the posterior probability of all its nodes. Choose Mean heights for node heights. This sets the heights (ages) of each node in the tree to the mean height across the entire sample of trees for that clade. For the input file, select the trees file that BEAST created (by default this will be called gopher.species.trees) and select a file for the output (here we called it gopher.species.tree). Now press Run and wait for the program to finish.

Viewing the Tree Finally, we can look at the tree in another program called FigTree. Run this program, and open the gopher.species.tree file by using the Open command in the File menu. The tree should appear. You can now try selecting some of the options in the control panel on the left. Try selecting Node Bars to get node age error bars. Also turn on Branch Labels and select posterior to get it to display the posterior probability for each node. Under Appearance you can also tell FigTree to colour the branches by the length. You should end up with something like this:

Comparing your results to the prior Using BEAUti, set up the same analysis but under the MCMC options, select the Sample from prior only option. This will allow you to visualize the full prior distribution in the absence of your sequence data. Summarize the trees from the full prior distribution and compare the summary to the posterior summary tree.

References [1] N.M. Belfiore, L. Liu, and C. Moritz, Multilocus phylogenetics of a rapid radiation in the genus Thomomys (Rodentia: Geomyidae), Systematic Biology 57 (2008), no. 2, 294