Difference between revisions of "Phylogenetics: BayesTraits Lab"

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|<span style="font-size: x-large">[http://hydrodictyon.eeb.uconn.edu/eebedia/index.php/Phylogenetics:_Syllabus EEB 349: Phylogenetics]</span>
 
|<span style="font-size: x-large">[http://hydrodictyon.eeb.uconn.edu/eebedia/index.php/Phylogenetics:_Syllabus EEB 349: Phylogenetics]</span>
 
|-
 
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|In this lab you will learn how to use the program BayesTraits, written by Andrew Meade and Mark Pagel. BayesTraits can perform several analyses related to evaluating evolutionary correlation in discrete morphological traits. This program is meant to replace the older programs Discrete and Multistate. You will learn not only how to use the program on the Windows-based PCs in the computer lab, but also how to download and use it on the cluster (the cluster is better for long runs).
+
|In this lab you will learn how to use the program BayesTraits, written by Andrew Meade and Mark Pagel. BayesTraits can perform several analyses related to evaluating evolutionary correlation and ancestral state reconstruction in discrete morphological traits. This program is meant to replace the older programs Discrete and Multistate. In this lab, you will download and use BayesTraits entirely on your own laptop.
 
|}
 
|}
  
We will use BayesTraits interactively for awhile on the PCs in the computer room (Part 1), then we will set up a non-interactive run on the cluster in Part 2 so that you know how to do this.
+
== Download BayesTraits ==
 
+
== Part 1: Running BayesTraits on your own laptop ==
+
 
+
=== Download BayesTraits ===
+
  
 
Download BayesTraits from [http://www.evolution.reading.ac.uk/ Mark Pagel's web site], click on the "Software" link, then click on the "Description and Downloads" link under "BayesTraits". Download the version specific to your platform. BayesTraits will unpack itself to a folder containing the program itself along with several tree and data files (e.g. <tt>Primates.txt</tt> and <tt>Primates.trees</tt>). I will hereafter refer to the folder containing these files as simply the '''BayesTraits folder'''. Go back to Mark Pagel's web site and '''download the manual''' for BayesTraits. This is a PDF file and should open in your browser window.
 
Download BayesTraits from [http://www.evolution.reading.ac.uk/ Mark Pagel's web site], click on the "Software" link, then click on the "Description and Downloads" link under "BayesTraits". Download the version specific to your platform. BayesTraits will unpack itself to a folder containing the program itself along with several tree and data files (e.g. <tt>Primates.txt</tt> and <tt>Primates.trees</tt>). I will hereafter refer to the folder containing these files as simply the '''BayesTraits folder'''. Go back to Mark Pagel's web site and '''download the manual''' for BayesTraits. This is a PDF file and should open in your browser window.
  
=== Download the tree and data files ===
+
== Download the tree and data files ==
 
For this exercise, you will use data and trees used in the SIMMAP analyses presented in this paper (you should recognize the names of at least two of the authors of this paper):
 
For this exercise, you will use data and trees used in the SIMMAP analyses presented in this paper (you should recognize the names of at least two of the authors of this paper):
  
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:[http://hydrodictyon.eeb.uconn.edu/people/plewis/courses/phylogenetics/restricted/pelly.tre pelly.tre] This is the tree file. It contains 99 trees sampled from an MCMC analysis of DNA sequences.
 
:[http://hydrodictyon.eeb.uconn.edu/people/plewis/courses/phylogenetics/restricted/pelly.tre pelly.tre] This is the tree file. It contains 99 trees sampled from an MCMC analysis of DNA sequences.
  
 +
If you are using version 1 of BayesTraits, it will complain about basal polytomies in the trees. The following versions of the files provide a workaround (I deleted one taxon from both the data file and the tree file to eliminate the basal polytomy):
 +
:[http://hydrodictyon.eeb.uconn.edu/people/plewis/courses/phylogenetics/restricted/pellyrooted.txt pellyrooted.txt] This is the data file. It contains data for two traits (see below) for 154 taxa in the plant genus ''Pelargonium''.
 +
:[http://hydrodictyon.eeb.uconn.edu/people/plewis/courses/phylogenetics/restricted/pellyrooted.tre pellyrooted.tre] This is the tree file. It contains 99 trees sampled from an MCMC analysis of DNA sequences.
 
You should move these files to the aforementioned BayesTraits folder so that they can be easily found by the BayesTraits program.
 
You should move these files to the aforementioned BayesTraits folder so that they can be easily found by the BayesTraits program.
  
=== Assessing the strength of association between two binary characters ===
+
== Assessing the strength of association between two binary characters ==
  
 
The first thing we will do is see if the two characters (leaf dissection and leaf venation) in <tt>pelly.txt</tt> are evolutionarily correlated.  
 
The first thing we will do is see if the two characters (leaf dissection and leaf venation) in <tt>pelly.txt</tt> are evolutionarily correlated.  
  
==== Trait 1: Leaf dissection ====
+
=== Trait 1: Leaf dissection ===
 
The '''leaf dissection''' trait comprises two states (I've merged some states in the original data matrix to produce just 2 states): 0 means leaves are ''entire'' (''unlobed'' or ''shallowly lobed'' in the original study), and 1 means leaves are ''dissected'' (''lobed'', ''deeply lobed'', or ''dissected'' in the original study).  
 
The '''leaf dissection''' trait comprises two states (I've merged some states in the original data matrix to produce just 2 states): 0 means leaves are ''entire'' (''unlobed'' or ''shallowly lobed'' in the original study), and 1 means leaves are ''dissected'' (''lobed'', ''deeply lobed'', or ''dissected'' in the original study).  
  
==== Trait 2: Leaf venation ====
+
=== Trait 2: Leaf venation ===
 
The '''leaf venation''' trait comprises two states: 0 means leaves are ''pinnately veined'' (one main vein runs down the long axis of the leaf blade), and 1 means leaves are ''palmately veined'' (several major veins meet at the base of the leaf).  
 
The '''leaf venation''' trait comprises two states: 0 means leaves are ''pinnately veined'' (one main vein runs down the long axis of the leaf blade), and 1 means leaves are ''palmately veined'' (several major veins meet at the base of the leaf).  
  
 
To test whether these two traits are correlated, we will estimate the marginal likelihood under two models. The independence model assumes that the two traits are uncorrelated. The dependence model allows the two traits to be correlated in their evolution. The model with the higher marginal likelihood will be the preferred model. You will recall that we discussed both of these models in lecture, and also discussed the harmonic mean method that BayesTraits uses to evaluate models. You may wish to pull up those lectures to help answer the questions that you will encounter momentarily, as well as the BayesTraits manual, which is in the form of a pdf file included with the program.
 
To test whether these two traits are correlated, we will estimate the marginal likelihood under two models. The independence model assumes that the two traits are uncorrelated. The dependence model allows the two traits to be correlated in their evolution. The model with the higher marginal likelihood will be the preferred model. You will recall that we discussed both of these models in lecture, and also discussed the harmonic mean method that BayesTraits uses to evaluate models. You may wish to pull up those lectures to help answer the questions that you will encounter momentarily, as well as the BayesTraits manual, which is in the form of a pdf file included with the program.
  
==== Maximum Likelihood: Independence model ====
+
=== Maximum Likelihood: Independence model ===
  
 
'''If you are using Windows''', start BayesTraits by opening a console window , navigate to the BayesTraits directory, and type the following to start the program:
 
'''If you are using Windows''', start BayesTraits by opening a console window , navigate to the BayesTraits directory, and type the following to start the program:
Line 103: Line 102:
 
</div>
 
</div>
  
==== Maximum Likelihood: Dependence model ====
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=== Maximum Likelihood: Dependence model ===
  
 
Run BayesTraits again, this time typing 3 on the first screen to choose the dependence model and again typing 1 on the second screen to select maximum likelihood. You should see this output showing the options selected:
 
Run BayesTraits again, this time typing 3 on the first screen to choose the dependence model and again typing 1 on the second screen to select maximum likelihood. You should see this output showing the options selected:
Line 152: Line 151:
 
</div>
 
</div>
  
==== Bayesian MCMC: Dependence model ====
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=== Bayesian MCMC: Dependence model ===
  
 
Run BayesTraits again, typing 3 on the first screen to choose the dependence model and this time typing 2 on the second screen to select MCMC. You should see this output showing the options selected:
 
Run BayesTraits again, typing 3 on the first screen to choose the dependence model and this time typing 2 on the second screen to select MCMC. You should see this output showing the options selected:
Line 235: Line 234:
 
This should produce counts of model strings. (If it doesn't, check to make sure your output file is named <tt>rjmcmc-dependent.txt</tt> because btsummary.py tries to open a file by that name.)  Answer the following questions using the counts provided by btsummary.py.
 
This should produce counts of model strings. (If it doesn't, check to make sure your output file is named <tt>rjmcmc-dependent.txt</tt> because btsummary.py tries to open a file by that name.)  Answer the following questions using the counts provided by btsummary.py.
 
<div style="background-color:#ccccff">
 
<div style="background-color:#ccccff">
* ''xxxx'' {{title|xxxx|answer}}
+
* ''Which model string is most common?'' {{title|I got 0 0 Z 0 0 0 0 0 with count 333|answer}}
* ''xxxx'' {{title|xxxx|answer}}
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* ''What does this model imply?'' {{title|all rates are the same except q21, which is forced to have rate zero. q21 equals 0 implies that entire,palmate leaves never change to entire,pinnate|answer}}
* ''xxxx'' {{title|xxxx|answer}}
+
 
</div>
 
</div>
  
 +
Notice that many (but not all) model strings have Z for q21. One way to estimate the marginal posterior probability of the hypothesis that q21=0 is to sum the counts for all model strings that have Z in that third position corresponding to q21. It is easy to modify btsummary.py to do this for us: open btsummary.py and locate the line containing the regular expression search that pulls out all the model strings from the BayesTrait output file:
 +
model_list = re.findall("'[Z0-9] [Z0-9] [Z0-9] [Z0-9] [Z0-9] [Z0-9] [Z0-9] [Z0-9]", stuff, re.M | re.S)
 +
The re.findall function performs a regular expression search of the text stored in the variable stuff looking for strings that have a series of 8 space-separated characters, each of which is either the character Z or a digit between 0 and 9 (inclusive). Copy this line, then comment out one copy by starting the line with the hash (#) character. Now modify the other copy by forcing the regular expression search to look only for model strings having a Z in the third position:
 +
#model_list = re.findall("'[Z0-9] [Z0-9] [Z0-9] [Z0-9] [Z0-9] [Z0-9] [Z0-9] [Z0-9]", stuff, re.M | re.S)
 +
model_list = re.findall("'[Z0-9] [Z0-9] [Z] [Z0-9] [Z0-9] [Z0-9] [Z0-9] [Z0-9]", stuff, re.M | re.S)
 +
Rerun btsummary.py, and now the total matches should equal the number of model strings sampled in which q21=0.
 
<div style="background-color:#ccccff">
 
<div style="background-color:#ccccff">
* On p. 11, where does Pagel get his rule of thumb that says "...if this [constrained] model is two or more log-likelihood units worse than the unconstrained model, then the two rate coefficients differ."? (hint: what would the likelihood ratio test statistic be in this case, how many degrees of freedom are there, and what would the [http://www.fourmilab.ch/rpkp/experiments/analysis/chiCalc.html significance probability] be in this case?)
+
* ''So what is the estimated marginal posterior probability that q21=0?'' {{title|I got 0.935|answer}}
* In the section ''Reconstruct an ancestral state'' under ''Using maximum likelihood'': Given that we are using an unrooted tree, would you agree or disagree with the statement "The attraction of MRCA’s is that one exists in each tree"?
+
* ''Why is the term marginal appropriate here (as in marginal posterior probability)?'' {{title|We are estimating the sum of all joint posteriors in which q21 equals 0|answer}}
* After conducting a reversible-jump analysis, the results are stored in the file <tt>MatingSystem.txt.log.txt</tt>. One of the columns is labeled "model" and has values that are either <tt>'00</tt> or <tt>'0Z</tt>. If you wanted to know the marginal posterior probability of the model <tt>00</tt> (corresponding to <math>q_{01}=q_{10}</math>), how would you go about figuring this out from the output provided?
+
* At the very end of the section ''Reconstruct an ancestral state'' under ''Using Markov chain Monte Carlo'': the manual says "Note: Harmonic means can be unstable so this analysis should be repeated maybe 5 times and with very long runs (10s or 100s of million of iterations) to be sure of the result." Assuming you get a very stable harmonic mean value over 5 runs, as recommended. Does this mean that you will accurately assess the Bayes factor?
+
 
</div>
 
</div>
  
==== Tutorial Notes ====
+
== Estimating ancestral states ==
  
'''1.''' Remember throughout the tutorial to use <tt>Primates.first.tree</tt> instead of <tt>Primates.trees</tt>! Note that your output will only correspond to that of tree number 1 in the sample output from the BayesTraits manual.  
+
[[File:Xerophytevenation.png|right]] The Jones et al. 2009 study estimated ancestral states using SIMMAP. In particular, they found that the most recent common ancestor (MRCA) of the xerophytic (dry-adapted) clade of pelargoniums almost certainly had pinnate venation (see red circle in figure on right). Let's see what BayesTraits says.
  
'''2.''' BayesTraits must be run from the command line, which means you must open a command window to run the program. Simply double-clicking the <tt>BayesTraits</tt> executable file will cause it to run, but not for long! The problem is that when you double-click the program, you have no way to tell it what tree and data file to use, so it simply quits immediately. Open a Terminal window (Mac) or console window (Windows) in the directory where the <tt>BayesTraits</tt> executable is located. You can then start the program as follows:
+
Start BayesTraits in the usual way, specifying 1 (Multistate) on the first screen and 2 (MCMC) on the second. After the options are output, type the following commands in, one line at a time, finishing with the run command:
BayesTraits Primates.first.tree MatingSystem.txt
+
  pa exp 30
Note however that later the tutorial switches  to using the data fle <tt>Primates.txt</tt>, so at that point you should replace <tt>MatingSystem.txt</tt> with <tt>Primates.txt</tt> on the command line.
+
  addmrca xero alternans104 rapaceum130
 
+
'''3.''' BayesTraits stops after it executes the run command, so you will need to restart it numerous times during the tutorial.
+
 
+
'''4.''' The output that you see scrolling by on the screen (especially during the MCMC analyses) is saved automatically in the file <tt>MatingSystem.txt.log.txt</tt>. This file is overwritten each time you run BayesTraits, so rename it before running BayesTraits again if you want to save it.
+
 
+
'''5.''' The default number of MCMC iterations is 5,050,000. This will take some time to run. For our purposes, it is ok to reduce this number. For example, to tell BayesTraits to only run for 550,000 iterations, type in the following command before you type run:
+
it 550000
+
 
+
'''6.''' There is a listing of all commands recognized by BayesTraits at the end of the manual.
+
 
+
== Part 2: Running BayesTraits on the cluster ==
+
 
+
We will now switch to using the (older, Mac-based) cluster to run BayesTraits. BayesTraits is not installed on the cluster, so this provides a good opportunity to show you how to download and unpack software into your home directory and run programs not already installed for you.
+
 
+
BayesTraits is different than most of the programs used on the cluster in that it is interactive: it expects you to type some commands after it starts. This is difficult when you use <tt>qsub</tt> to submit a job to the cluster since you are not there to supply these commands once it starts. This part of the lab shows you how to get around this difficulty when using programs like BayesTraits.
+
 
+
=== Downloading and unpacking BayesTraits ===
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First, connect to <tt>bbcxsrv1.biotech.uconn.edu</tt> to get a command prompt (using either <tt>putty.exe</tt> on Windows or the <tt>ssh</tt> command in your Mac Terminal application). The full URL to the OS X PPC version of BayesTraits is
+
http://www.evolution.reading.ac.uk/Files/BayesTraits-OSX-PPC-V1.0.tar.gz
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If you had a browser open, and you typed in this URL, your browser would save the file <tt>BayesTraits-OSX-PPC-V1.0.tar.gz</tt> on your hard drive. But you are not using a browser on the cluster, you are logged in using secure shell.
+
 
+
You could download the file to your PC, then upload it to the cluster using FileZilla (Windows) or Fugu (Mac), but let's instead use the curl command:
+
  curl http://www.evolution.reading.ac.uk/Files/BayesTraitsV2-Beta-Linux64.tar.gz > BayesTraitsV2-Beta-Linux64.tar.gz
+
This tells curl to access the specified URL (curl will stand in for a web browser) and the <tt>-o</tt> option says to save the resulting file as <tt>BayesTraits-OSX-PPC-V1.0.tar.gz</tt>.
+
 
+
Once you have the file in your home directory (use the <tt>ls</tt> command to check), you will need to unpack it using the <tt>tar</tt> command:
+
  tar zxvf BayesTraits-OSX-PPC-V1.0.tar.gz
+
The file extension <tt>.tar.gz</tt> is very common for software targeting Linux and Mac OS X systems. This extension has a very specific meaning: the <tt>.tar</tt> part means that the file is actually an archive comprising several files saved one after the other (<tt>tar</tt> stands for "tape archive", even though no one uses magnetic tapes anymore). The <tt>.gz</tt> part means that the archive has been compressed using the <tt>gzip</tt> program. The command line switches for tar (<tt>zxvf</tt>) are decoded as follows:
+
* <tt>z</tt> means un'''Z'''ip the archive first
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* <tt>x</tt> means e'''X'''tract the component files
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* <tt>v</tt> means be '''V'''erbose and tell me what's going on as you work
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* <tt>f</tt> simply means that the name of the '''F'''ile to extract follows immediately afterwards
+
Once the <tt>tar</tt> command has completed, you should have a directory named BayesTraits. Use the <tt>cd</tt> command to move into that directory, then use the <tt>ls</tt> command to see what's there. You should see the same 5 files as before.
+
 
+
=== Running BayesTraits ===
+
We will do a very simple analysis just so you will know how to run BayesTraits in batch mode. Because analyses on the cluster are submitted via the <tt>qsub</tt> command, and thus no one will be present to answer those questions BayesTraits asks when it runs, we'll supply the answers in a file (arbitrarily named <tt>commands.txt</tt>) and feed that file to BayesTraits when it is invoked.
+
 
+
==== Create the commands.txt file ====
+
 
+
Create a file inside the BayesTraits directory using the <tt>pico</tt> editor named <tt>commands.txt</tt>, and save the following in the file:
+
  # choose the model (1 = multistate, 2 = independence, 3 = dependence)
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  3
+
# choose the method (1 = ML, 2 = MCMC)
+
2
+
ratedev 10
+
rjhp exp 0 30
+
 
  run
 
  run
The lines starting with a pound sign (or hash) are comments and are optional. Otherwise, this file just presents to BayesTraits exactly what you would type if you were running the program interactively.
+
The addmrca command tells BayesTraits to add columns of numbers to the output that display the probabilities of each state for each character in the most recent common ancestor of the taxa listed (2 taxa are sufficient to define the MRCA, but more taxa may be included). The column headers for the last four columns of output should be
 
+
xero - S(0) - P(0) <-- character 0 (dissection), probability of state 0 (unlobed)
==== Create the qsub script ====
+
  xero - S(0) - P(1) <-- character 0 (dissection), probability of state 1 (dissected)
As you know by now, you use the <tt>qsub</tt> command to submit a job to the cluster. The advantage of using the <tt>qsub</tt> command is that it will start your job on a processor that is currently idle (assuming there are idle processors available in the cluster). Not using <tt>qsub</tt> results in your job being started on the ''head'' node of the cluster. The head node is the processor that everyone uses to interact with the cluster, and if you start a run there, it has a fair chance of simply being killed as soon as the system administrator (Jeff Lary) notices it because it makes the head node appear very sluggish to other users!
+
  xero - S(1) - P(0) <-- character 1 (venation), probability of state 0 (pinnate)
 
+
  xero - S(1) - P(1) <-- character 1 (venation), probability of state 1 (palmate)
The <tt>qsub</tt> command accepts the name of a script file that carries out your wishes, so we must first create this script (use pico to create and save the following in your home directory as a file named '''btgo''', for example):
+
<div style="background-color:#ccccff">
  #$ -o junk.txt -j y
+
* ''Which state is most common at the xerophyte MRCA node for leaf venation?'' {{title|pinnate venation; xero - S(1) - P(0) is normally above 0.9|answer}}
  #$ -m bea
+
* ''Which state is most common at the xerophyte MRCA node for leaf dissection?'' {{title|dissected; xero - S(0) - P(1) is normally above 0.9|answer}}
  #$ -M your.name@uconn.edu
+
</div>
cd $HOME/BayesTraits
+
./BayesTraits Primates.trees Primates.txt < commands.txt
+
You have experienced these scripts before. The '''first few lines''' begin with the sequence of characters #$, which alerts <tt>qsub</tt> that a <tt>qsub</tt> command is coming. The first command is the <tt>-o junk.txt -j y</tt> part, which tells <tt>qsub</tt> that you want the output of the run saved in a file named <tt>junk.txt</tt> and you would like any error message appended to this same file (the <tt>-j y</tt> part is indeed cryptic, but stands for "join [standard error to output] yes"). '''Be sure to delete or rename any file named <tt>junk.txt</tt> that already exists.'''
+
 
+
The '''second line''' says to send an email notification '''b'''efore, at the '''e'''nd of, and in case of '''a'''bort.
+
 
+
The '''third line''' tells the Sun Grid Engine where to send the email notifications. You should of course '''change this to your own UConn email address''' Email addressed outside UConn will be ignored.
+
 
+
The '''fourth line''' says to cd into the BayesTraits directory (this means that the BayesTraits folder will now be the working directory, and any output files created by the program will be saved there).
+
 
+
The '''fifth line''' actually starts the program. Since we are running this on the cluster and are not so limited by time, we'll use the full <tt>Primates.trees</tt> file (containing 500 trees). Note the very important <tt>commands.txt</tt> part, which feeds the answers to all questions to the BayesTraits executable. Also, note the period-slash (./) before the name of the program. This says that the program can be found in the current directory (the current directory is signified by a dot; one of the crazy things about unix is that the current directory is not searched by default when looking for files!).
+
  
==== Submit the script ====
+
That concluded the introduction to BayesTraits. A glance through the manual will convince you that there is much more to this program than we have time to cover in a single lab period, but you should know enough now to explore the rest on your own if you need these features.  
Now submit the job as follows:
+
  qsub btgo
+
As before, you can periodically check to see if it is still running using the '''qstat''' command. You can use pico to look at the <tt>junk.txt</tt> file in your home directory, or look in the <tt>BayesTraits</tt> directory and examine the files created there as the program runs. A useful command is tail:
+
  cd $HOME/BayesTraits
+
  tail Primates.txt.log.txt
+
  
This shows you only the last few lines of the file listed. To show the last 100 lines, you can use the -n switch:
 
  tail -n 100 Primates.txt.log.txt
 
 
 
[[Category: Phylogenetics]]
 
[[Category: Phylogenetics]]

Revision as of 13:56, 10 April 2014

Adiantum.png EEB 349: Phylogenetics
In this lab you will learn how to use the program BayesTraits, written by Andrew Meade and Mark Pagel. BayesTraits can perform several analyses related to evaluating evolutionary correlation and ancestral state reconstruction in discrete morphological traits. This program is meant to replace the older programs Discrete and Multistate. In this lab, you will download and use BayesTraits entirely on your own laptop.

Download BayesTraits

Download BayesTraits from Mark Pagel's web site, click on the "Software" link, then click on the "Description and Downloads" link under "BayesTraits". Download the version specific to your platform. BayesTraits will unpack itself to a folder containing the program itself along with several tree and data files (e.g. Primates.txt and Primates.trees). I will hereafter refer to the folder containing these files as simply the BayesTraits folder. Go back to Mark Pagel's web site and download the manual for BayesTraits. This is a PDF file and should open in your browser window.

Download the tree and data files

For this exercise, you will use data and trees used in the SIMMAP analyses presented in this paper (you should recognize the names of at least two of the authors of this paper):

Jones C.S., Bakker F.T., Schlichting C.D., Nicotra A.B. 2009. Leaf shape evolution in the South African genus Pelargonium L'Her. (Geraniaceae). Evolution. 63:479–497.

The data and trees were not made available in the online supplementary materials for this paper, but I have obtained permission to use them for this laboratory exercise. The links below are password-protected, so ask us for the username and password before clicking on the links:

pelly.txt This is the data file. It contains data for two traits (see below) for 154 taxa in the plant genus Pelargonium.
pelly.tre This is the tree file. It contains 99 trees sampled from an MCMC analysis of DNA sequences.

If you are using version 1 of BayesTraits, it will complain about basal polytomies in the trees. The following versions of the files provide a workaround (I deleted one taxon from both the data file and the tree file to eliminate the basal polytomy):

pellyrooted.txt This is the data file. It contains data for two traits (see below) for 154 taxa in the plant genus Pelargonium.
pellyrooted.tre This is the tree file. It contains 99 trees sampled from an MCMC analysis of DNA sequences.

You should move these files to the aforementioned BayesTraits folder so that they can be easily found by the BayesTraits program.

Assessing the strength of association between two binary characters

The first thing we will do is see if the two characters (leaf dissection and leaf venation) in pelly.txt are evolutionarily correlated.

Trait 1: Leaf dissection

The leaf dissection trait comprises two states (I've merged some states in the original data matrix to produce just 2 states): 0 means leaves are entire (unlobed or shallowly lobed in the original study), and 1 means leaves are dissected (lobed, deeply lobed, or dissected in the original study).

Trait 2: Leaf venation

The leaf venation trait comprises two states: 0 means leaves are pinnately veined (one main vein runs down the long axis of the leaf blade), and 1 means leaves are palmately veined (several major veins meet at the base of the leaf).

To test whether these two traits are correlated, we will estimate the marginal likelihood under two models. The independence model assumes that the two traits are uncorrelated. The dependence model allows the two traits to be correlated in their evolution. The model with the higher marginal likelihood will be the preferred model. You will recall that we discussed both of these models in lecture, and also discussed the harmonic mean method that BayesTraits uses to evaluate models. You may wish to pull up those lectures to help answer the questions that you will encounter momentarily, as well as the BayesTraits manual, which is in the form of a pdf file included with the program.

Maximum Likelihood: Independence model

If you are using Windows, start BayesTraits by opening a console window , navigate to the BayesTraits directory, and type the following to start the program:

BayesTraits pelly.tre pelly.txt

If you are using a Mac, start BayesTraits by opening a terminal window, navigate to the BayesTraits directory, and type the following to start the program:

./BayesTraits pelly.tre pelly.txt

You should see this selection appear:

Please Select the model of evolution to use.
1)	MultiState
2)	Discrete: Independent
3)	Discrete: Dependant
4)	Continuous: Random Walk (Model A)
5)	Continuous: Directional (Model B)
6)	Continuous: Regression
7)	Independent contrast

Press the 2 key to select the Independent model. Now you should see these choices appear:

Please Select the analysis method to use.
1)	Maximum Likelihood.
2)	MCMC

Press the 1 key to select maximum likelihood. Now you should see some output showing the choices you explicitly (or implicitly) made:

Options:
Model:                           Discete Independant
Tree File Name:                  pelly.tre
Data File Name:                  pelly.txt
Log File Name:                   pelly.txt.log.txt
Summary:                         False
Seed                             3162959925
Analsis Type:                    Maximum Likelihood
ML attempt per tree:             10
Precision:                       64 bits
Cores:                           1
No of Rates:                     4
Base frequency (PI's)            None
Character Symbols:               00,01,10,11
Using a covarion model:          False
Restrictions:
    alpha1                       None
    beta1                        None 
    alpha2                       None
    beta2                        None 
Tree Information
     Trees:                      99
     Taxa:                       154
     Sites:                      1
     States:                     4

Now type run to perform the analysis, which will consist of estimating the parameters of the independent model on each of the 99 trees contained in the pelly.tre file.

Tree No	Lh	alpha1	beta1	alpha2	beta2	Root - P(0,0)	Root - P(0,1)	Root - P(1,0)	Root - P(1,1)
1	-157.362972	53.767527	34.523176	35.319157	20.707416	0.249998	0.250002	0.249998	0.250002
2	-158.179984	53.313539	34.182683	36.038859	20.997536	0.249999	0.250001	0.249999	0.250001
.
.
.
98	-156.647307	52.357626	36.749282	27.270771	13.086248	0.250244	0.249756	0.250244	0.249756 
99	-156.532925	52.321467	36.641688	27.402067	13.200124	0.250234	0.249767	0.250233	0.249766

You will notice that BayesTraits created a new file: pelly.txt.log.txt. Rename this file ml-independant.txt so that it will not be overwritten the next time you run BayesTraits.

Try to answer these questions using the output you have generated (ask us if anything doesn't make sense):

  • Which occurs at a faster rate: pinnate to palmate, or palmate to pinnate? answer
  • Which occurs at a faster rate: entire to dissected, or dissected to entire? answer
  • What do you think Root - P(1,1) means (i.e. the last column of numbers)? answer

Maximum Likelihood: Dependence model

Run BayesTraits again, this time typing 3 on the first screen to choose the dependence model and again typing 1 on the second screen to select maximum likelihood. You should see this output showing the options selected:

Options:
Model:                           Discete Dependent
Tree File Name:                  pelly.tre
Data File Name:                  pelly.txt
Log File Name:                   pelly.txt.log.txt
Summary:                         False
Seed                             3601265953
Analsis Type:                    Maximum Likelihood
ML attempt per tree:             10
Precision:                       64 bits
Cores:                           1
No of Rates:                     8
Base frequency (PI's)            None
Character Symbols:               00,01,10,11
Using a covarion model:          False
Restrictions:
    q12                          None
    q13                          None
    q21                          None
    q24                          None
    q31                          None
    q34                          None
    q42                          None
    q43                          None
Tree Information
     Trees:                      99
     Taxa:                       154
     Sites:                      1
     States:                     4

Here is an example of the output produced after you type run to start the analysis:

Tree No	Lh	q12	q13	q21	q24	q31	q34	q42	q43	Root - P(0,0)	Root - P(0,1)	Root - P(1,0)	Root - P(1,1)
1	-151.930254	66.451053	37.783888	0.000000	62.220033	23.997490	23.299393	46.110432	36.632979	0.24999	0.249981	0.250026	0.250000
2	-152.925691	67.152271	38.611193	0.000000	60.925185	24.514488	23.937433	45.313366	37.199310	0.24999	0.249983	0.250023	0.250001
.
.
.
98	-150.816306	36.534843	27.359325	0.000000	66.563262	19.823546	24.944519	63.940577	31.074092	0.250048	0.249750	0.250304	0.249898
99	-150.712705	37.316351	27.260833	0.000000	64.364694	20.107653	25.004246	60.945163	31.658536	0.250030	0.249779	0.250272	0.249919

Before doing anything else, rename the file pelly.txt.log.txt to ml-dependant.txt so that it will not be overwritten the next time you run BayesTraits.

Try to answer these questions using the output you have generated:

  • What type of joint evolutionary transitions seem to often have very low rates (look for an abundance of zeros in a column)? answer
  • What type of joint evolutionary transitions seem to often have very high rates (look for columns with rates in the hundreds)? answer

Bayesian MCMC: Dependence model

Run BayesTraits again, typing 3 on the first screen to choose the dependence model and this time typing 2 on the second screen to select MCMC. You should see this output showing the options selected:

Options:
Model:                           Discete Dependent
Tree File Name:                  pelly.tre
Data File Name:                  pelly.txt
Log File Name:                   pelly.txt.log.txt
Summary:                         False
Seed                             3792635164
Precision:                       64 bits
Cores:                           1
Analysis Type:                   MCMC
Sample Period:                   1000
Iterations:                      1010000
Burn in:                         10000
MCMC ML Start:                   False
Schedule File:                   pelly.txt.log.txt.Schedule.txt
Rate Dev:                        AutoTune
No of Rates:                     8
Base frequency (PI's)            None
Character Symbols:               00,01,10,11
Using a covarion model:          False
Restrictions:
   q12                          None
   q13                          None
   q21                          None
   q24                          None
   q31                          None
   q34                          None
   q42                          None
   q43                          None 
Prior Information:
   Prior Categories:            100
   q12                          uniform 0.00 100.00
   q13                          uniform 0.00 100.00
   q21                          uniform 0.00 100.00
   q24                          uniform 0.00 100.00
   q31                          uniform 0.00 100.00
   q34                          uniform 0.00 100.00
   q42                          uniform 0.00 100.00
   q43                          uniform 0.00 100.00
Tree Information
    Trees:                      99
    Taxa:                       154
    Sites:                      1
    States:                     4

Before typing run type the following command, which tells BayesTraits to change all priors from the default Uniform(0,100) to an Exponential distribution with mean 30:

pa exp 30

Here is an example of the output produced after you type run to start the analysis:

Iteration	Lh	Harmonic Mean	Tree No	q12	q13	q21	q24	q31	q34	q42	q43	Root - P(0,0)	Root - P(0,1)	Root - P(1,0)	Root - P(1,1)
11000	-155.195365	-155.195365	78	14.423234	34.800270	8.845985	45.927148	12.622435	50.476188	52.844895	32.149168	0.250068	0.249969	0.249994	0.249968
12000	-154.161705	-154.806538	82	64.601017	12.382781	9.259134	51.796365	12.002095	23.744903	30.316089	21.865930	0.249936	0.249957	0.250095	0.250012 .
.
.
1009000	-154.343996	-158.180036	30	33.555198	50.086092	11.294490	38.518607	24.461032	47.295157	43.477964	21.726938	0.250057	0.249939	0.250045	0.249959
1010000	-154.195259	-158.179054	87	29.584898	35.410909	2.003582	61.981073	16.976124	14.895266	49.111354	14.419644	0.251115	0.247854	0.252551	0.248480

Before doing anything else, rename the file pelly.txt.log.txt to mcmc-dependant.txt so that it will not be overwritten the next time you run BayesTraits.

A couple of new columns have shown up in the output from the Bayesian analysis that were absent from the ML analysis output. The Harmonic Mean column provides a running estimate of the marginal likelihood. The fact that it is a running estimate means that the estimate is updated using each new sample so that the best estimate of the marginal likelihood from the entire run is provided on the last line of the output.

You will also notice that a column named 'Tree No is present that shows which of the 99 trees in the supplied pelly.tre> treefile was chosen at random to be used for that particular sample point. BayesTraits is trying to mimic sampling trees from the posterior distribution here; it cannot actually sample trees from the posterior because we have given it only data for two morphological characters, which would not provide nearly enough information to estimate the phylogeny for 154 taxa.

Try to answer these questions using the output you have generated:

  • What is the estimated log marginal likelihood for this analysis? answer
  • Based on the Bayesian Model Selection lecture, do you expect this to be an accurate estimate of the true log marginal likelihood? If not, is it an over- or and under-estimate? answer

Run BayesTraits again, this time specifying the Independent model, and again using MCMC and pa exp 30. Rename the output file from pelly.txt.log.txt to mcmc-independant.txt.

  • What is the estimated log marginal likelihood for this analysis? answer
  • Which is the better model according to these estimates of marginal likelihood? answer

Run BayesTraits again, specifying Dependent model, MCMC and, this time, specify the reversible-jump approach using the command rj exp 30. Type run to start, then when it finishes rename the output file rjmcmc-dependent.txt.

The reversible-jump approach carries out an MCMC analysis in which the number of model parameters (the dimension of the model) potentially changes from one iteration to the next. The full model allows each of the 8 rate parameters to be estimated separately, while other models restrict the values of some rate parameters to equal the values of other rate parameters. The output contains a column titled Model string that summarizes the model in a string of 8 symbols corresponding to the 8 rate parameters q12, q13, q21, q24, q31, q34, q42, and q43. For example, the model string "'1 0 Z 0 1 1 0 2" sets q21 to zero (Z), q13=q24=q42 (parameter group 0), q12=q31=q34 (parameter group 1), and q43 has its own non-zero value distinct from parameter groups 0 and 1.

You could copy the "spreadsheet" part of the output file into Excel and sort by the model string column, but let's instead use Python to summarize the output file. Download the file btsummary.py file and run it as follows:

python btsummary.py

This should produce counts of model strings. (If it doesn't, check to make sure your output file is named rjmcmc-dependent.txt because btsummary.py tries to open a file by that name.) Answer the following questions using the counts provided by btsummary.py.

  • Which model string is most common? answer
  • What does this model imply? answer

Notice that many (but not all) model strings have Z for q21. One way to estimate the marginal posterior probability of the hypothesis that q21=0 is to sum the counts for all model strings that have Z in that third position corresponding to q21. It is easy to modify btsummary.py to do this for us: open btsummary.py and locate the line containing the regular expression search that pulls out all the model strings from the BayesTrait output file:

model_list = re.findall("'[Z0-9] [Z0-9] [Z0-9] [Z0-9] [Z0-9] [Z0-9] [Z0-9] [Z0-9]", stuff, re.M | re.S)

The re.findall function performs a regular expression search of the text stored in the variable stuff looking for strings that have a series of 8 space-separated characters, each of which is either the character Z or a digit between 0 and 9 (inclusive). Copy this line, then comment out one copy by starting the line with the hash (#) character. Now modify the other copy by forcing the regular expression search to look only for model strings having a Z in the third position:

#model_list = re.findall("'[Z0-9] [Z0-9] [Z0-9] [Z0-9] [Z0-9] [Z0-9] [Z0-9] [Z0-9]", stuff, re.M | re.S)
model_list = re.findall("'[Z0-9] [Z0-9] [Z] [Z0-9] [Z0-9] [Z0-9] [Z0-9] [Z0-9]", stuff, re.M | re.S)

Rerun btsummary.py, and now the total matches should equal the number of model strings sampled in which q21=0.

  • So what is the estimated marginal posterior probability that q21=0? answer
  • Why is the term marginal appropriate here (as in marginal posterior probability)? answer

Estimating ancestral states

Xerophytevenation.png
The Jones et al. 2009 study estimated ancestral states using SIMMAP. In particular, they found that the most recent common ancestor (MRCA) of the xerophytic (dry-adapted) clade of pelargoniums almost certainly had pinnate venation (see red circle in figure on right). Let's see what BayesTraits says.

Start BayesTraits in the usual way, specifying 1 (Multistate) on the first screen and 2 (MCMC) on the second. After the options are output, type the following commands in, one line at a time, finishing with the run command:

pa exp 30
addmrca xero alternans104 rapaceum130
run

The addmrca command tells BayesTraits to add columns of numbers to the output that display the probabilities of each state for each character in the most recent common ancestor of the taxa listed (2 taxa are sufficient to define the MRCA, but more taxa may be included). The column headers for the last four columns of output should be

xero - S(0) - P(0) <-- character 0 (dissection), probability of state 0 (unlobed)
xero - S(0) - P(1) <-- character 0 (dissection), probability of state 1 (dissected)
xero - S(1) - P(0) <-- character 1 (venation), probability of state 0 (pinnate)
xero - S(1) - P(1) <-- character 1 (venation), probability of state 1 (palmate)
  • Which state is most common at the xerophyte MRCA node for leaf venation? answer
  • Which state is most common at the xerophyte MRCA node for leaf dissection? answer

That concluded the introduction to BayesTraits. A glance through the manual will convince you that there is much more to this program than we have time to cover in a single lab period, but you should know enough now to explore the rest on your own if you need these features.