relaxed phylogenetics and dating with confidence – primates
table of contents
- expected learning outcome
- exercise 1: rates and dates
- BEAUti
- loading the NEXUS file
- defining the calibration nodes
- setting the substitution model
- setting the clock model
- trees
- priors
- setting the MCMC options
- generating the BEAST XML file
- running BEAST
- analyzing the results
- questions
- obtaining an estimate of the phylogenetic tree
- Viewing the tree
- comparing your results to the prior
- BEAUti
expected learning outcomes
This activity will introduce the BEAST software for Bayesian evolutionary analysis, with a focus on estimating phylogenies and divergence times when you have calibration information from fossil evidence or other prior knowledge.
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 v1.6.x, which has support for multiple partitions.
- Tracer – this program is used to explore the output of BEAST (and other Bayesian MCMC programs). It graphically and quantitively summarizes the dis- tributions of continuous parameters and provides diagnostic information. At the time of writing, the current version is v1.5.
- 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.
The data files for this activity can be downloaded here: Divergence Dating (Primates) v1.3.zip
part 1: rates and dates
This exercise will guide you through the analysis of an alignment of sequences sampled from twelve primate species. The goal is to estimate the phylogeny as well as the rate of evolution on each lineage based on dates of divergence of their host species.
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 (this stands for 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
The program BEAUti is a user-friendly program for setting the model parameters for BEAST. Run BEAUti by double clicking on its icon or invoking it from the command-line.
Loading the NEXUS file
To load a NEXUS format alignment, simply select the Import Alignment… option from the File menu:
Select the file called primates.nex. This file contains an alignment of sequences of 12 species of primates. It looks like this (the lines have been truncated):
#NEXUS begin data; dimensions ntax=12 nchar=898; format datatype=dna interleave=no gap=-; matrix Tarsius_syrichta AAGTTTCATTGGAGCCACCACTCTTATAATTGCCCATGGCCTCACC Lemur_catta AAGCTTCATAGGAGCAACCATTCTAATAATCGCACATGGCCTTACA Homo_sapiens AAGCTTCACCGGCGCAGTCATTCTCATAATCGCCCACGGGCTTACA Pan AAGCTTCACCGGCGCAATTATCCTCATAATCGCCCACGGACTTACA Gorilla AAGCTTCACCGGCGCAGTTGTTCTTATAATTGCCCACGGACTTACA Pongo AAGCTTCACCGGCGCAACCACCCTCATGATTGCCCATGGACTCACA Hylobates AAGCTTTACAGGTGCAACCGTCCTCATAATCGCCCACGGACTAACC Macaca_fuscata AAGCTTTTCCGGCGCAACCATCCTTATGATCGCTCACGGACTCACC M_mulatta AAGCTTTTCTGGCGCAACCATCCTCATGATTGCTCACGGACTCACC M_fascicularis AAGCTTCTCCGGCGCAACCACCCTTATAATCGCCCACGGGCTCACC M_sylvanus AAGCTTCTCCGGTGCAACTATCCTTATAGTTGCCCATGGACTCACC Saimiri_sciureus AAGCTTCACCGGCGCAATGATCCTAATAATCGCTCACGGGTTTACT ; end; begin assumptions; charset firsthalf = 1-449; charset secondhalf = 450-898; end; end;
Once loaded, the two character partitions are displayed in the main panel:
Defining the calibration nodes
Select the Taxon Sets tab at the top of the main window. You will see the panel that allows you to create sets of taxa. Once you have created a taxa set you will be able to add calibration information for its most recent common ancestor (MRCA) later on. Press the small “plus” button at the bottom left of the panel. This will create a new taxon set.
Rename it by double-clicking on the entry that appears (it will initially be called untitled1). Call it ingroup (it will contain all taxa except the lemur, which will form the outgroup). In the next table along you will see the available taxa. Select all taxa and press the green arrow button. Move the lemur back into the excluded taxa set. Since we know that lemur is the outgroup, we will set select the checkbox in the Monophyletic? column. This will ensure that the ingroup is kept monophyletic during the course of the MCMC analysis.
Now repeat the whole procedure creating a set called Human-Chimp that contains only Homo sapiens and Pantaxa. Finally, create a taxon group that contains everything under the hominoid/cercopithecoid split (i.e. everything except Lemur, Saimiri and Tarsius). Call this taxon set something like HomiCerco. The screen should look like this:
Unlink partition models
At this point we will need to unlink the substitution model so that each parameter is estimated separately for the two partitions. To do this return to the Data Partitions panel, select both partitions in the table and click the “Unlink Subst Models” button:
And you can also change the partition model name in its respective panel (e.g. Clock Models panel), and make the final partitions as illustrated below:
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, amino acids, binary data, or general data. The settings that will appear after loading the Primates 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 respectively select substitution models for each partition listed on the left side. Make the same change: select Gamma under the Site Heterogeneity Modelmenu which will allow rate variation between sites in the associated alignment:
Setting the clock model
Second, we will click on the Clock Models tab at the top of the main window and change the molecular clock model to Relaxed Clock: Uncorrelated Log-normal so as to account for lineage-specific rate heterogeneity. Your model options should now look like this:
The Estimate check box is required to be checked because we wish to estimate the clock rate (and in doing so the divergence times). But this will be automatically checked, in this case, when we put a proper prior on tmrcain the Priors panel.
Trees
The Trees tab allows priors to be specified for each parameter in the model. The first thing to do is to specify that we wish to use the Yule model as the tree prior. This is a simple model of speciation that is generally more appropriate when considering sequences from different species. Select this from the Tree prior dropdown menu:
Priors
The Priors tab allows priors to be specified for each parameter in the model. The first thing to do is to specify that we wish to use the Yule model as the tree prior. This is a simple model of speciation that is generally more appropriate when considering sequences from different species. Select this from the Tree prior dropdown menu.
We now need to specify a prior distribution for some of the divergence times, based on our prior fossil knowledge. This is known as calibrating our tree. We will actually use two calibrations in this analysis. Click on the button in the table next to tmrca(human-chimp). A dialog box will appear allowing you to specify a prior for the MRCA of these three species. Select the Normal distribution:
We are going to assume a normal distribution centered at 6 million years with a standard deviation of 0.5 million years. This will give a central 95% range of about 5-7 My. This corresponds to the consensus estimate of the date of the most recent common ancestor of humans and chimps.
Following the same procedure, set a calibration of 24 +/- 0.5 million (stdev) for the hominoid-cercopithecoid split.
Although we created a taxon set for the ingroup (tmrca(ingroup) in the prior table), we are not going to put an informative prior on this. We can then estimate this divergence time based on the other calibrations.
And the clock model parameters will appear when the clock rate is estimated. The priors table should now look like this:
Setting the MCMC options
Ignore the Operators tab as this just contains technical settings effecting the efficiency of the MCMC program.
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. How long this should be depends on the size of the data set, the complexity of the model and the quality of 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 800,000 as this will run reasonably quickly on most modern computers (a few 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 program’s progress so can be set to any value (although if set too small, 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 200. 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 are using Windows then we suggest you add the suffix .txt to both of these (so, Primates.log.txt andPrimates.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 at the bottom of the window. Save the file with an appropriate name (we usually end the filename with .xml, i.e., Primates.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:
BEAST will then run until it has finished reporting information to the screen. The actual results files are saved to disk in the same location as your input file. The screen output will look something like this:
BEAST v1.6.1, 2002-2010
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
[email protected]
Institute of Evolutionary Biology
University of Edinburgh
[email protected]
David Geffen School of Medicine
University of California, Los Angeles
[email protected]
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, Erik Bloomquist, Joseph Heled, Sebastian Hoehna,
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: 1303338739767
Parsing XML file: primates.xml
File encoding: MacRoman
Read alignment: alignment
Sequences = 12
Sites = 898
Datatype = nucleotide
Site patterns 'firsthalf.patterns' created from positions 1-449 of alignment 'alignment'
pattern count = 227
Site patterns 'secondhalf.patterns' created from positions 450-898 of alignment 'alignment'
pattern count = 231
Using Yule prior on tree
Creating the tree model, 'treeModel'
initial tree topology = ((((((Gorilla,Tarsius_syrichta),Pan),M_sylvanus),(M_mulatta,Macaca_fuscata)),((((Homo_sapiens,Saimiri_sciureus),Pongo),M_fascicularis),Hylobates)),Lemur_catta)
tree height = 311.73866128365125
Using discretized relaxed clock model.
over sampling = 1
parametric model = logNormalDistributionModel
rate categories = 22
Creating state frequencies model: Initial frequencies = {0.25, 0.25, 0.25, 0.25}
Creating HKY substitution model. Initial kappa = 2.0
Creating site model.
4 category discrete gamma with initial shape = 0.5
Creating state frequencies model: Initial frequencies = {0.25, 0.25, 0.25, 0.25}
Creating HKY substitution model. Initial kappa = 2.0
Creating site model.
4 category discrete gamma with initial shape = 0.5
TreeLikelihood(treeModel) using native nucleotide likelihood core
Ignoring ambiguities in tree likelihood.
With 227 unique site patterns.
Branch rate model used: discretizedBranchRates
TreeLikelihood(treeModel) using native nucleotide likelihood core
Ignoring ambiguities in tree likelihood.
With 231 unique site patterns.
Branch rate model used: discretizedBranchRates
Creating swap operator for parameter branchRates.categories (weight=10.0)
Likelihood is using -1 threads.
Creating the MCMC chain:
chainLength=800000
autoOptimize=true
autoOptimize delayed for 8000 steps
# BEAST v1.6.1, Build r3651
# Generated Thu Apr 21 16:27:15 NZST 2011 [seed=1303338739767]
state Posterior Prior Likelihood rootHeight ucld.mean
0 -115044.0238 -105244.7369 -9799.2869 311.739 3.3E-2 -
10000 -6019.0942 -48.1460 -5970.9482 31.2013 1.13161E-2 -
20000 -5932.1777 -53.7968 -5878.3809 58.3426 7.80428E-3 0.11 hours/million states
30000 -5864.1836 -55.6386 -5808.5450 54.7400 9.7303E-3 0.09 hours/million states
40000 -5845.2874 -58.9120 -5786.3753 82.1531 6.86446E-3 0.08 hours/million states
50000 -5798.2689 -60.2217 -5738.0472 87.4058 7.84354E-3 0.08 hours/million states
60000 -5779.7566 -57.1298 -5722.6268 49.1015 1.17545E-2 0.07 hours/million states
70000 -5787.4056 -60.5876 -5726.8180 81.5675 1.03161E-2 0.07 hours/million states
80000 -5785.8794 -58.9768 -5726.9027 70.4040 9.80333E-3 0.07 hours/million states
90000 -5778.6354 -59.2618 -5719.3737 77.9236 1.0054E-2 0.07 hours/million states
100000 -5780.4106 -60.2610 -5720.1496 78.7802 8.80928E-3 0.07 hours/million states
... ...
790000 -5772.8359 -59.0540 -5713.7819 77.1089 9.1281E-3 0.06 hours/million states
800000 -5774.2917 -57.2419 -5717.0498 61.2605 9.77329E-3 0.06 hours/million states
Operator analysis
Operator Tuning Count Time Time/Op Pr(accept) Performance suggestion
scale(firsthalf.kappa) 0.536 701 232 0.33 0.2596 good
firsthalf.frequencies 0.059 677 206 0.3 0.2851 good
scale(firsthalf.alpha) 0.598 719 220 0.31 0.3255 good
scale(secondhalf.kappa) 0.555 685 222 0.32 0.3109 good
secondhalf.frequencies 0.058 661 216 0.33 0.3238 good
scale(secondhalf.alpha) 0.598 680 210 0.31 0.3015 good
scale(ucld.mean) 0.697 21192 7410 0.35 0.2786 good
scale(ucld.stdev) 0.274 21350 7342 0.34 0.3526 good
subtreeSlide(treeModel) 4.405 105795 18763 0.18 0.337 good
Narrow Exchange(treeModel) 106685 19150 0.18 0.0004 very low
Wide Exchange(treeModel) 21301 2071 0.1 0.0 very low
wilsonBalding(treeModel) 21229 3431 0.16 0.0 very low
scale(treeModel.rootHeight) 0.853 21224 1334 0.06 0.218 good
uniform(nodeHeights(treeModel)) 213114 43645 0.2 0.222 good
scale(yule.birthRate) 0.268 21594 697 0.03 0.2761 good
up:ucld.mean down:nodeHeights(treeModel) 0.596 21448 7551 0.35 0.2417 slightly high Try setting scaleFactor to about 0.586
swapOperator(branchRates.categories) 70928 16433 0.23 0.6553 high No suggestions
randomWalkInteger(branchRates.categories) 70818 13509 0.19 0.9432 very high Try increasing windowSize to about 2.0
uniformInteger(branchRates.categories) 71199 14008 0.2 0.7518 high
3.028016666666667 minutes
analyzing the results
Run 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 Primates.log.txt. 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 left brings up analyses for this trace on the right hand side depending on the 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.
Select meanRate to look at the rate of evolution averaged over the whole tree. 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 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.
questions
- What is the rate of molecular evolution in Primates (include the HPD interval)?
- What sources of error does this estimate include?
The coefficientOfVariation statistic gives a summary of how much the rate of evolution varies from lineage to lineage (expressed as a proportion of the mean rate).
- Does the rate of evolution differ substantially amongst different lineages in the tree?
Selecting the treeModel.rootHeight parameter gives the marginal posterior distribution of the age of the root of entire tree.
- How old is the root of the tree (give the mean and the HPD range)?
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 MRCAs we specified in BEAUti. The two parameters that we used to calibrate the tree (tmrca(HomiCerco) and tmrca(human-chimp)) will have posterior distributions very similar to the prior distributions that we specified.
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 overlaid:
obtaining an estimate of the phylogenetic tree
BEAST also produces a sample of plausible trees along with its sample of parameter estimates. These need to be summarized using the program TreeAnnotator. This will take the set of trees and find the best supported one. It will then annotate this summary tree with the mean ages of all the nodes and the HPD ranges. It will also calculate the posterior clade probability for each node. Run the TreeAnnotator program and set it up to look like this:
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, you specified a chain length of 800,000 steps sampling every 200 steps. Thus the trees file will contain 4000 trees and so to specify a 1% burnin use the value 40.
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 Primates.trees) and select a file for the output (here we called it Primates_MCC.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 thePrimates_MCC.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 color the branches by the rate. You should end up with something like this:
- Which branch has the fastest rate of evolution and what is the estimated rate?
- Which branch has the slowest rate of evolution and what is the estimated rate?
- Are these two rate estimates significantly different? How would you answer this question?
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.