# Difference between revisions of "Phylogenetics: BEAST Lab"

Paul Lewis (Talk | contribs) (→Setting up the Priors) |
Paul Lewis (Talk | contribs) (→Adding a calibration) |
||

(29 intermediate revisions by the same user not shown) | |||

Line 23: | Line 23: | ||

BEAST and BEAUti form a pair. BEAUti is a user-friendly, graphical Java application that can be used to create the data file that is then fed to BEAST, which is neither user-friendly nor graphical, but is nevertheless also written in Java. Thus, to do anything with BEAST, you will need a working Java runtime environment. You will actually use the cluster to run BEAST, but you will need to run BEAUti on your own laptop. If you have trouble getting Java running on your laptop, pair with another student until you have an XML file. At that point, you can use your own computer to interact with the cluster. | BEAST and BEAUti form a pair. BEAUti is a user-friendly, graphical Java application that can be used to create the data file that is then fed to BEAST, which is neither user-friendly nor graphical, but is nevertheless also written in Java. Thus, to do anything with BEAST, you will need a working Java runtime environment. You will actually use the cluster to run BEAST, but you will need to run BEAUti on your own laptop. If you have trouble getting Java running on your laptop, pair with another student until you have an XML file. At that point, you can use your own computer to interact with the cluster. | ||

− | == Analysis of simulated data == | + | == Analysis of strict-clock simulated data == |

Download the file [http://hydrodictyon.eeb.uconn.edu/people/plewis/courses/phylogenetics/labs/simyule.nex simyule.nex] to your hard drive and import it into BEAUTi using the ''File > Import alignment'' menu command. An entry called <tt>simyule</tt> should appear in the Partitions section. | Download the file [http://hydrodictyon.eeb.uconn.edu/people/plewis/courses/phylogenetics/labs/simyule.nex simyule.nex] to your hard drive and import it into BEAUTi using the ''File > Import alignment'' menu command. An entry called <tt>simyule</tt> should appear in the Partitions section. | ||

Line 42: | Line 42: | ||

| 0.279743 | | 0.279743 | ||

|- | |- | ||

+ | | log(Yule model probability density) | ||

+ | | 25.9954 | ||

|} | |} | ||

+ | |||

+ | The last line requires some explanation. Simulating a Yule tree requires choosing n-1 times (where n is the number of tips) and, at each step, deciding which of the current lineages will speciate after the chosen sojourn time. The probability density of a Yule tree thus involves the product of n-1 Exponential(lambda*k) densities and n-1 Discrete Uniform(k) probabilities, where k is the number of lineages at each step. The value reported in the table above is the log of this probability density evaluated using the times actually chosen for this particular tree. | ||

Sequence data (10000 sites) was simulated using this Yule tree. Here are some facts about the true substitution model: | Sequence data (10000 sites) was simulated using this Yule tree. Here are some facts about the true substitution model: | ||

Line 72: | Line 76: | ||

=== Setting up the Site Model === | === Setting up the Site Model === | ||

− | Click on the ''Site Model'' tab in BEAUTi and set ''Gamma Category Count'' to 4 | + | We will begin by estimating the parameters of the substitution model that we know was used to generate these data. |

+ | |||

+ | Click on the ''Site Model'' tab in BEAUTi and set ''Gamma Category Count'' to 4, the model to ''HKY'', and check ''estimate'' for ''Shape'' and ''Kappa''. The ''Frequencies'' drop-down list should be set to ''Estimated'', ''Proportion Invariant'' should remain fixed to 0.0, and ''Substitution Rate'' should be fixed at 1.0. | ||

=== Setting up the Clock Model === | === Setting up the Clock Model === | ||

− | Click on the ''Clock Model'' tab in BEAUTi | + | Click on the ''Clock Model'' tab in BEAUTi. We will leave everything here at the default values (''Strict Clock'' with ''Clock.rate'' fixed to 1). Again, we know the truth, and the truth was that all 10000 sites were generated under a strict clock, with expected number of substitutions equal to the Yule branch lengths (which is why we keep clock rate set at 1, which says that a branch length of 1 means 1 expected substitution per site). |

=== Setting up the Priors === | === Setting up the Priors === | ||

− | Click on the ''Priors'' tab in BEAUTi and set up the priors as follows | + | Click on the ''Priors'' tab in BEAUTi and set up the priors as follows. |

==== Tree ==== | ==== Tree ==== | ||

− | Keep this set to ''Yule Model'' and be sure ''estimate'' is checked (but leave ''Conditional On Root'' unchecked) | + | Keep this set to ''Yule Model'' and be sure ''estimate'' is checked for ''Birth Diff Rate'' (but leave ''Conditional On Root'' unchecked) |

==== birthRate ==== | ==== birthRate ==== | ||

− | Set this to an Exponential distribution with mean 100 (do not check ''estimate'') | + | Set this to an Exponential distribution with mean 100 (do not check ''estimate''). An Exponential distribution with mean 100 has variance 100 squared (10000), so this prior should not argue very strongly with the likelihood about the value of the Yule per-lineage speciation rate. |

==== gammaShape ==== | ==== gammaShape ==== | ||

Line 98: | Line 104: | ||

Set this to an Exponential distribution with mean 100 (do not check ''estimate'') | Set this to an Exponential distribution with mean 100 (do not check ''estimate'') | ||

− | === | + | === Setting up MCMC === |

− | + | Click on the ''MCMC'' tab in BEAUTi and set the ''Chain Length'' to 300000, leave ''Store Every'' set to -1, and set ''Pre Burnin'' to 10000. | |

− | + | Do NOT check the box at the bottom labeled ''Sample From Prior'' | |

− | + | The chain length of 300,000 is way to short, but we can't afford to wait for the default 10,000,000 or we will not be able to finish this in lab. As you will see, 300K MCMC steps is long enough to get most estimates reasonably close to their true values. | |

− | ==== | + | === Saving the XML file === |

+ | |||

+ | You are now ready to save the XML file that BEAST will use. To do this, choose ''File > Save As'' from the main menu and save the file as ''simyule.xml'' in a directory of your choosing. Upload this file to your home directory on the cluster. | ||

+ | |||

+ | === Running BEAST on the cluster === | ||

+ | |||

+ | I am assuming that you are now logged into the cluster and have issued a <tt>qlogin</tt> command to acquire a free node. (You should also be able to see your ''simyule.xml'' file in your home directory when you type the <tt>ls</tt> command.) | ||

+ | |||

+ | The version of BEAST that was installed on the cluster was a little out of date, so I installed the latest version (2.4.0 at the time I wrote this) in the directory <tt>/common/phylogenetics</tt>. To further complicate things, this version of BEAST requires a more recent version of Java than we had available on the cluster, so in that same directory is a freshly downloaded Java Runtime Environment. To make all this work, we have to set an environmental variable so that the default version of Java is not used when we run BEAST. | ||

+ | |||

+ | export PATH="/common/phylogenetics/jre1.8.0_77/bin:$PATH" | ||

+ | |||

+ | This command puts the latest Java Runtime Environment's <tt>bin</tt> directory at the head of the <tt>PATH</tt>, where the <tt>PATH</tt> is a list of directories that the system will search when looking for a program (e.g. <tt>java</tt>). | ||

+ | |||

+ | You should now be able to start BEAST as follows: | ||

+ | |||

+ | java -jar /common/phylogenetics/beast.jar simyule.xml | ||

+ | |||

+ | === Using Tracer to examine the parameter estimates === | ||

+ | |||

+ | Once you are finished, bring the log file back to your local computer and open it in Tracer. Use the ''Estimates'' tab in Tracer to answer these questions. | ||

+ | |||

+ | <div style="background-color:#ccccff"> | ||

+ | * What is the true tree height? {{title|0.28|answer}} Does the estimated 95% credible interval for tree height include the true value? {{title|yes, I got (0.2598, 0.281)|answer}} | ||

+ | * What is the true log Yule model probability density? {{title|25.834|answer}} Does the estimated 95% credible interval for Yule model include the true value? {{title|yes, I got (24.2759, 26.8244)|answer}} | ||

+ | * What is the true Yule model per-lineage speciation rate? {{title|10|answer}} Does the estimated 95% credible interval for birthRate include the true value? {{title|yes, I got (7.197,16.8877)|answer}} | ||

+ | * Were the true values of any substitution model parameters outside their respective 95% credible intervals? {{title|yes, true gamma shape was 0.5 but credible interval was (0.4164,0.4551)|answer}} | ||

+ | * If the answer to the last question was "yes", can you explain why the estimate is off by looking at the ESS column and/or the trace plot? {{title|In my case, ESS was only 7 and trace plot showed that this parameter was seldom sampled. Also, tail end of BEAST output shows that in only a fraction 0.0013 of MCMC steps was an attempt made to change this parameter|answer}} | ||

+ | </div> | ||

+ | |||

+ | === Using TreeAnnotator and FigTree to examine the tree and divergence time credible intervals === | ||

+ | |||

+ | On your local computer, start the TreeAnnotator program that was downloaded as part of BEAST2. Choose the file ''simyule.trees'' for ''Input Tree File'' and specify ''simyulemcc.tre'' as ''Output File'' and press the ''Run'' button. After TreeAnnotator finishes, open the file ''simyulemcc.tre'' in FigTree and do the following steps after the tree has loaded: | ||

+ | * In the ''Trees'' section on the left, check ''Order nodes'' (ordering should be increasing) | ||

+ | * Click ''Node Bars'' | ||

+ | * Uncheck ''Scale Bar'' | ||

+ | * Check ''Scale Axis'' and check ''Reverse axis'' after opening up the ''Scale Axis'' section | ||

+ | |||

+ | Now choose ''File > New'' from the main FigTree menu to create a new, blank window. Copy the tree description below and paste it into this window (this is the true tree for comparison): | ||

+ | |||

+ | ((((taxon7:0.07448,taxon3:0.07448):0.05612,(((((taxon8:0.04474,taxon18:0.04474):0.00447,((taxon10:0.00318,taxon11:0.00318):0.03218,taxon13:0.03536):0.01384):0.00412,(taxon14:0.00616,taxon1:0.00616):0.04717):0.03522,taxon16:0.08855):0.03100,((taxon17:0.04256,taxon20:0.04256):0.00894,(taxon4:0.01598,taxon15:0.01598):0.03552):0.06805):0.01104):0.02259,taxon19:0.15318):0.12656,((taxon6:0.02920,taxon12:0.02920):0.16953,((taxon9:0.05268,taxon2:0.05268):0.01422,taxon5:0.06690):0.13183):0.08101) | ||

+ | |||

+ | Set up this tree the same way you set up the estimated tree (except checking ''Node Bars'' will have no effect this time). | ||

+ | <div style="background-color:#ccccff"> | ||

+ | * Does the estimated tree have the correct topology? {{title|yes, and the times are quite accurate as well|answer}} | ||

+ | * Which divergences are associated with the most uncertainty? {{title|the oldest ones closest to the root have the largest 95% credible intervals|answer}} | ||

+ | </div> | ||

+ | |||

+ | == Analysis of relaxed-clock simulated data == | ||

+ | |||

+ | Let's do the exercise again with data that does not conform to a strict molecular clock. | ||

+ | |||

+ | Download the file [http://hydrodictyon.eeb.uconn.edu/people/plewis/courses/phylogenetics/labs/lognormal.nex lognormal.nex] to your hard drive and import it into BEAUTi using the ''File > Import alignment'' menu command. | ||

+ | |||

+ | The tree and substitution model used to simulate the data in ''lognormal.nex'' were identical to the tree and model used to simulate the data in ''simyule.nex''. What's different is that the branch lengths of the tree were modified before the sequences were simulated. There are 38 edges in the tree, so I drew 38 relative rates from a Lognormal(-0.0196104, 0.198042) distribution and multiplied each edge length by one of these rates. | ||

+ | |||

+ | <div style="background-color:#ccccff"> | ||

+ | * What was the mean relative rate given that they were independently sampled from a Lognormal distribution with mu = -0.0196104 and sigma = 0.198042? {{title|1.0|answer}} (hint: see [https://en.wikipedia.org/wiki/Log-normal_distribution formula for mean on the Lognormal distribution Wikipedia page]) | ||

+ | * What was the true standard deviation of relative rates? {{title|0.2|answer}} | ||

+ | </div> | ||

+ | |||

+ | If you want to see the effect of multiplying edge lengths by relative rates, copy the tree description below and paste it into a FigTree window: | ||

+ | ((((taxon7:0.0719125,taxon3:0.0508014):0.0536504,(((((taxon8:0.0373785,taxon18:0.0443175):0.00624889,((taxon10:0.00242665,taxon11:0.00243614):0.035207,taxon13:0.0342883):0.0125615):0.00328008,(taxon14:0.00630138,taxon1:0.0063153):0.0404656):0.0456252,taxon16:0.0600948):0.0318929,((taxon17:0.0370861,taxon20:0.0462936):0.00773252,(taxon4:0.0126342,taxon15:0.0163993):0.0270225):0.102974):0.0133684):0.0183383,taxon19:0.140667):0.117726,((taxon6:0.0255848,taxon12:0.0313106):0.134908,((taxon9:0.068912,taxon2:0.0489807):0.0116809,taxon5:0.0687154):0.101499):0.0705456) | ||

+ | |||

+ | === Setting up the Clock Model === | ||

+ | |||

+ | After importing the ''lognormal.nex'' data into BEAUTi, set up the ''Site Model'' as before and then click on the ''Clock Model'' tab. This time choose ''Relaxed Clock Log Normal'' but keep ''Clock.rate'' fixed to 1. | ||

+ | |||

+ | === Setting up the Priors === | ||

− | + | Set up the priors as before, but you will note that a new parameter has been added: ucldStdev. Set the prior for this parameter to the same Exponential(100) prior distribution we have used for all the other parameters. | |

=== Setting up MCMC === | === Setting up MCMC === | ||

− | + | Let's do more sampling than before. In the MCMC tab, set ''Chain Length'' to 1 million and ''Pre Burnin'' to 100,000. Save the file as ''lognormal.xml'', copy it to the cluster, and run it as you did for ''simyule.xml''. | |

− | + | <div style="background-color:#ccccff"> | |

+ | * What was the estimated variance (and credible interval) of relative rates? {{title|estimate of rate.variance is 0.04852, (0.0189, 0.0859)|answer}} | ||

+ | * What was the true variance of relative rates? {{title|0.04, which is 0.2 squared|answer}} | ||

+ | </div> | ||

− | === | + | === Adding a calibration === |

− | + | The analyses we performed above all provide relative divergence times under either a strict or relaxed clock, but normally the purpose of a divergence time analysis is to obtain absolute divergence times (in thousands or millions of years) using fossils to calibrate the molecular clock. | |

− | + | [[File:LognormalModelTree.png|thumb|right|Model tree used to simulate data under lognormal relaxed clock]]On the right is the tree used to simulate the ''lognormal.nex'' data. Let's pretend that we have a 100 million year old fossil that we know is in the clade of 5 taxa at the bottom of the tree (comprising taxa 2, 5, 6, 9, and 12). Call this Clade A just to have a label for it. This means that the clade arose started diversifying some time before the age of the fossil. We will assume that the fossil and its date imply that the age of the most recent common ancestor of Clade A occurred, with 95% probability, between 100 and 130 million years ago. | |

+ | |||

+ | Start by setting up BEAUTi as you did for the ''lognormal.nex'' data. If you still have BEAUTi open, then it is already set up and ready to go. | ||

+ | |||

+ | Click on the + symbol at the bottom of the ''Priors'' panel. That will allow you to define a calibration prior. Use the buttons provided to include taxa 2, 5, 6, 9, and 12 in a taxon set labeled ''Clade A''. Choose an Exponential prior with ''Mean'' 10 and ''Offset'' 100. Note that the diagram on the right shows that the 95% Quantile is 130; this means that 95% of the distribution is between 100 and 130. We will need to remember that we've specified the distribution in terms of millions of years (i.e. we entered 100 for the offset, not 100,000,000, which is what we would have needed to enter had we wanted times to be in years rather than millions of years. | ||

+ | |||

+ | When the run is finished, create a consensus tree in TreeAnnotator and take a look at it. You should be a bit surprised at the result. We will discuss this toward the end of the lab today after you have a chance to formulate an explanation of the behavior you see here! | ||

+ | |||

+ | == Further study == | ||

+ | |||

+ | For tutorials involving analysis of real data, you may wish to explore [http://phyloworks.org/workshops/divtime.html Tracy Heath's Fossilzed Birth-Death Tutorial] or the Divergence Dating tutorial on the [http://beast2.org/tutorials/ BEAST2 web site]. | ||

[[Category: Phylogenetics]] | [[Category: Phylogenetics]] |

## Latest revision as of 12:29, 14 April 2016

EEB 5349: Phylogenetics | |

In this lab you will learn how to use the program BEAST, and its companion BEAUTi, written by Alexei Drummond, Andrew Rambaut, Marc Suchard, Remco Bouckaert, and numerous other contributors. BEAST specializes in estimating divergence times under uncorrelated relaxed clock models, estimating species trees using a model that accounts for the independent coalescent history of each gene tree, and Bayesian skyline analyses that estimate population growth or decline through time. While BEAST itself is written in C and Java and has no user interface, the companion program BEAUTi has a nice graphical user interface that allows you to create an XML data file that is consulted by BEAST when it runs. |

In this lab, you will use BEAST to estimate divergence times. Rather than analyze a real data set, you will simulated a data set in which you know the true values of all parameters, and then see how to obtain estimates of those parameters in BEAST.

## Contents

- 1 Login to the UConn Bioinformatics cluster
- 2 Download BEAUTi and BEAST
- 3 Analysis of strict-clock simulated data
- 3.1 Setting up the Site Model
- 3.2 Setting up the Clock Model
- 3.3 Setting up the Priors
- 3.4 Setting up MCMC
- 3.5 Saving the XML file
- 3.6 Running BEAST on the cluster
- 3.7 Using Tracer to examine the parameter estimates
- 3.8 Using TreeAnnotator and FigTree to examine the tree and divergence time credible intervals

- 4 Analysis of relaxed-clock simulated data
- 5 Further study

## Login to the UConn Bioinformatics cluster

Once you login, type

qlogin

to obtain a session on a currently unused node.

## Download BEAUTi and BEAST

While we will be using BEAST on the cluster, you will need to download the software locally in order to get BEAUTi, which cannot be easily run remotely on the cluster because of its interactive GUI (Graphical User Interface).

Download the version of BEAST 2.4.0 from the BEAST web site. You will also need FigTree and Tracer (but you should already have those).

BEAST and BEAUti form a pair. BEAUti is a user-friendly, graphical Java application that can be used to create the data file that is then fed to BEAST, which is neither user-friendly nor graphical, but is nevertheless also written in Java. Thus, to do anything with BEAST, you will need a working Java runtime environment. You will actually use the cluster to run BEAST, but you will need to run BEAUti on your own laptop. If you have trouble getting Java running on your laptop, pair with another student until you have an XML file. At that point, you can use your own computer to interact with the cluster.

## Analysis of strict-clock simulated data

Download the file simyule.nex to your hard drive and import it into BEAUTi using the *File > Import alignment* menu command. An entry called `simyule` should appear in the Partitions section.

The tree from which these data were simulated was itself simulated using the Yule model. Here are some facts about the true tree:

Number of leaves (species) | 20 |

Per-lineage speciation rate | 10 |

Tree length (sum of all edge times) | 1.77537 |

Tree height (length of path from root to any tip) | 0.279743 |

log(Yule model probability density) | 25.9954 |

The last line requires some explanation. Simulating a Yule tree requires choosing n-1 times (where n is the number of tips) and, at each step, deciding which of the current lineages will speciate after the chosen sojourn time. The probability density of a Yule tree thus involves the product of n-1 Exponential(lambda*k) densities and n-1 Discrete Uniform(k) probabilities, where k is the number of lineages at each step. The value reported in the table above is the log of this probability density evaluated using the times actually chosen for this particular tree.

Sequence data (10000 sites) was simulated using this Yule tree. Here are some facts about the true substitution model:

Model | HKY85 |

Gamma rate heterogeneity shape | 0.5 |

Equilibrium frequency for A | 0.3 |

Equilibrium frequency for C | 0.2 |

Equilibrium frequency for G | 0.2 |

Equilibrium frequency for T | 0.3 |

Kappa (trs./trv. rate ratio) | 4.0 |

### Setting up the Site Model

We will begin by estimating the parameters of the substitution model that we know was used to generate these data.

Click on the *Site Model* tab in BEAUTi and set *Gamma Category Count* to 4, the model to *HKY*, and check *estimate* for *Shape* and *Kappa*. The *Frequencies* drop-down list should be set to *Estimated*, *Proportion Invariant* should remain fixed to 0.0, and *Substitution Rate* should be fixed at 1.0.

### Setting up the Clock Model

Click on the *Clock Model* tab in BEAUTi. We will leave everything here at the default values (*Strict Clock* with *Clock.rate* fixed to 1). Again, we know the truth, and the truth was that all 10000 sites were generated under a strict clock, with expected number of substitutions equal to the Yule branch lengths (which is why we keep clock rate set at 1, which says that a branch length of 1 means 1 expected substitution per site).

### Setting up the Priors

Click on the *Priors* tab in BEAUTi and set up the priors as follows.

#### Tree

Keep this set to *Yule Model* and be sure *estimate* is checked for *Birth Diff Rate* (but leave *Conditional On Root* unchecked)

#### birthRate

Set this to an Exponential distribution with mean 100 (do not check *estimate*). An Exponential distribution with mean 100 has variance 100 squared (10000), so this prior should not argue very strongly with the likelihood about the value of the Yule per-lineage speciation rate.

#### gammaShape

Set this to an Exponential distribution with mean 100 (do not check *estimate*)

#### kappa

Set this to an Exponential distribution with mean 100 (do not check *estimate*)

### Setting up MCMC

Click on the *MCMC* tab in BEAUTi and set the *Chain Length* to 300000, leave *Store Every* set to -1, and set *Pre Burnin* to 10000.

Do NOT check the box at the bottom labeled *Sample From Prior*

The chain length of 300,000 is way to short, but we can't afford to wait for the default 10,000,000 or we will not be able to finish this in lab. As you will see, 300K MCMC steps is long enough to get most estimates reasonably close to their true values.

### Saving the XML file

You are now ready to save the XML file that BEAST will use. To do this, choose *File > Save As* from the main menu and save the file as *simyule.xml* in a directory of your choosing. Upload this file to your home directory on the cluster.

### Running BEAST on the cluster

I am assuming that you are now logged into the cluster and have issued a `qlogin` command to acquire a free node. (You should also be able to see your *simyule.xml* file in your home directory when you type the `ls` command.)

The version of BEAST that was installed on the cluster was a little out of date, so I installed the latest version (2.4.0 at the time I wrote this) in the directory `/common/phylogenetics`. To further complicate things, this version of BEAST requires a more recent version of Java than we had available on the cluster, so in that same directory is a freshly downloaded Java Runtime Environment. To make all this work, we have to set an environmental variable so that the default version of Java is not used when we run BEAST.

export PATH="/common/phylogenetics/jre1.8.0_77/bin:$PATH"

This command puts the latest Java Runtime Environment's `bin` directory at the head of the `PATH`, where the `PATH` is a list of directories that the system will search when looking for a program (e.g. `java`).

You should now be able to start BEAST as follows:

java -jar /common/phylogenetics/beast.jar simyule.xml

### Using Tracer to examine the parameter estimates

Once you are finished, bring the log file back to your local computer and open it in Tracer. Use the *Estimates* tab in Tracer to answer these questions.

- What is the true tree height? answer Does the estimated 95% credible interval for tree height include the true value? answer
- What is the true log Yule model probability density? answer Does the estimated 95% credible interval for Yule model include the true value? answer
- What is the true Yule model per-lineage speciation rate? answer Does the estimated 95% credible interval for birthRate include the true value? answer
- Were the true values of any substitution model parameters outside their respective 95% credible intervals? answer
- If the answer to the last question was "yes", can you explain why the estimate is off by looking at the ESS column and/or the trace plot? answer

### Using TreeAnnotator and FigTree to examine the tree and divergence time credible intervals

On your local computer, start the TreeAnnotator program that was downloaded as part of BEAST2. Choose the file *simyule.trees* for *Input Tree File* and specify *simyulemcc.tre* as *Output File* and press the *Run* button. After TreeAnnotator finishes, open the file *simyulemcc.tre* in FigTree and do the following steps after the tree has loaded:

- In the
*Trees*section on the left, check*Order nodes*(ordering should be increasing) - Click
*Node Bars* - Uncheck
*Scale Bar* - Check
*Scale Axis*and check*Reverse axis*after opening up the*Scale Axis*section

Now choose *File > New* from the main FigTree menu to create a new, blank window. Copy the tree description below and paste it into this window (this is the true tree for comparison):

((((taxon7:0.07448,taxon3:0.07448):0.05612,(((((taxon8:0.04474,taxon18:0.04474):0.00447,((taxon10:0.00318,taxon11:0.00318):0.03218,taxon13:0.03536):0.01384):0.00412,(taxon14:0.00616,taxon1:0.00616):0.04717):0.03522,taxon16:0.08855):0.03100,((taxon17:0.04256,taxon20:0.04256):0.00894,(taxon4:0.01598,taxon15:0.01598):0.03552):0.06805):0.01104):0.02259,taxon19:0.15318):0.12656,((taxon6:0.02920,taxon12:0.02920):0.16953,((taxon9:0.05268,taxon2:0.05268):0.01422,taxon5:0.06690):0.13183):0.08101)

Set up this tree the same way you set up the estimated tree (except checking *Node Bars* will have no effect this time).

- Does the estimated tree have the correct topology? answer
- Which divergences are associated with the most uncertainty? answer

## Analysis of relaxed-clock simulated data

Let's do the exercise again with data that does not conform to a strict molecular clock.

Download the file lognormal.nex to your hard drive and import it into BEAUTi using the *File > Import alignment* menu command.

The tree and substitution model used to simulate the data in *lognormal.nex* were identical to the tree and model used to simulate the data in *simyule.nex*. What's different is that the branch lengths of the tree were modified before the sequences were simulated. There are 38 edges in the tree, so I drew 38 relative rates from a Lognormal(-0.0196104, 0.198042) distribution and multiplied each edge length by one of these rates.

- What was the mean relative rate given that they were independently sampled from a Lognormal distribution with mu = -0.0196104 and sigma = 0.198042? answer (hint: see formula for mean on the Lognormal distribution Wikipedia page)
- What was the true standard deviation of relative rates? answer

If you want to see the effect of multiplying edge lengths by relative rates, copy the tree description below and paste it into a FigTree window:

((((taxon7:0.0719125,taxon3:0.0508014):0.0536504,(((((taxon8:0.0373785,taxon18:0.0443175):0.00624889,((taxon10:0.00242665,taxon11:0.00243614):0.035207,taxon13:0.0342883):0.0125615):0.00328008,(taxon14:0.00630138,taxon1:0.0063153):0.0404656):0.0456252,taxon16:0.0600948):0.0318929,((taxon17:0.0370861,taxon20:0.0462936):0.00773252,(taxon4:0.0126342,taxon15:0.0163993):0.0270225):0.102974):0.0133684):0.0183383,taxon19:0.140667):0.117726,((taxon6:0.0255848,taxon12:0.0313106):0.134908,((taxon9:0.068912,taxon2:0.0489807):0.0116809,taxon5:0.0687154):0.101499):0.0705456)

### Setting up the Clock Model

After importing the *lognormal.nex* data into BEAUTi, set up the *Site Model* as before and then click on the *Clock Model* tab. This time choose *Relaxed Clock Log Normal* but keep *Clock.rate* fixed to 1.

### Setting up the Priors

Set up the priors as before, but you will note that a new parameter has been added: ucldStdev. Set the prior for this parameter to the same Exponential(100) prior distribution we have used for all the other parameters.

### Setting up MCMC

Let's do more sampling than before. In the MCMC tab, set *Chain Length* to 1 million and *Pre Burnin* to 100,000. Save the file as *lognormal.xml*, copy it to the cluster, and run it as you did for *simyule.xml*.

- What was the estimated variance (and credible interval) of relative rates? answer
- What was the true variance of relative rates? answer

### Adding a calibration

The analyses we performed above all provide relative divergence times under either a strict or relaxed clock, but normally the purpose of a divergence time analysis is to obtain absolute divergence times (in thousands or millions of years) using fossils to calibrate the molecular clock.

On the right is the tree used to simulate the*lognormal.nex*data. Let's pretend that we have a 100 million year old fossil that we know is in the clade of 5 taxa at the bottom of the tree (comprising taxa 2, 5, 6, 9, and 12). Call this Clade A just to have a label for it. This means that the clade arose started diversifying some time before the age of the fossil. We will assume that the fossil and its date imply that the age of the most recent common ancestor of Clade A occurred, with 95% probability, between 100 and 130 million years ago.

Start by setting up BEAUTi as you did for the *lognormal.nex* data. If you still have BEAUTi open, then it is already set up and ready to go.

Click on the + symbol at the bottom of the *Priors* panel. That will allow you to define a calibration prior. Use the buttons provided to include taxa 2, 5, 6, 9, and 12 in a taxon set labeled *Clade A*. Choose an Exponential prior with *Mean* 10 and *Offset* 100. Note that the diagram on the right shows that the 95% Quantile is 130; this means that 95% of the distribution is between 100 and 130. We will need to remember that we've specified the distribution in terms of millions of years (i.e. we entered 100 for the offset, not 100,000,000, which is what we would have needed to enter had we wanted times to be in years rather than millions of years.

When the run is finished, create a consensus tree in TreeAnnotator and take a look at it. You should be a bit surprised at the result. We will discuss this toward the end of the lab today after you have a chance to formulate an explanation of the behavior you see here!

## Further study

For tutorials involving analysis of real data, you may wish to explore Tracy Heath's Fossilzed Birth-Death Tutorial or the Divergence Dating tutorial on the BEAST2 web site.