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Introduction to Bayesian Analyses

MrBayes 3.1.2 should be already installed on the iMACs in the computer lab (in the MCB221 folder).

In case you work at home on a PC, go here and follow instructions to download and install MrBayes.

Exercise 1:
The goal of this exercise is to learn how to use MrBayes to reconstruct phylogenies.

1. Save testseq1c.nex into the MrBayes folder that also contains the MrBayes Program (Folder MrBayes3.1, probably your desktop). This is the dataset of vacuolar ATPase A subunit you used earlier, but in the NEXUS format that MrBayes reads (the nexus format is used by PAUP and many other programs - it allows to pass trees and commands to the different programs -- clustal and many other programs write nexus formated files, but usually, you need to go into the file with a texteditor and change things like the way gaps are treated, or the data type). You might need to rename the file after downloading. Start MrBayes through double clicking on the MrBayes icon. (do NOT use the one ending in .p).
   
   
2. At the MrBayes command prompt type "execute testseq1c.nex". This will load the data into the program.
   
   
3. Type the following commands one by one:
   
   prset aamodelpr=fixed(jones)
   mcmcp samplefreq=50 printfreq=50 nchains=2 startingtree=random
   mcmcp savebrlens=yes filename=testseq1c
   mcmc ngen=20000
   sump filename=testseq1c
   
   Rather than typing the commands one by one you could use a MrBayes block at the end of the input file:
   begin mrbayes;
       prset aamodelpr=fixed(jones);
       mcmcp samplefreq=50 printfreq=50 nchains=2 startingtree=random;
       mcmcp savebrlens=yes filename=testseq1c;
       mcmc ngen=20000;
       sump filename=testseq1c;
   end;
   
   " prset" sets the priors for the model used to calculate likelihoods. In this case we choose the substitution parameters from the JTT amino acid substitution model (Jones et al., 1992).
   " mcmcp " sets parameters for Markov Chain Monte Carlo: we set to sample every 50 generation, to print results to a screen every 50th generation, run 2 chains simultaneously, start with random tree, save branch lengths an d outfile name will be testseq1c.
   " mcmc " actually runs the chain, and we set it to run for 20000 generations.
   The program runs to analyses in parallel (each with 4 chains). The smaller the reported average standard deviation of split frequencies is, the more reliable the result (i.e., your run is close enough to infinitely long). When the value is below .015, or when your patience is exhausted, terminate the run, by typing no at the prompt.
   
   After the run is finished, the " sump " command will plot the logL vs. generation number, that allows to determine the necessary burnin (you want to discard those samples as "burnin" where the -logL is still rising steadily).
   
   [Rather than using the sump command, you also can import the parameter file into EXEL and plot the logL values as a chart in EXEL. See below.]
   
   During the start of the run, the likelihood rapidly increases by
   orders of magnitude. If the first samples are included in the plot, one
   really cannot see if the likelihood values fluctuate around a constant
   value. You can exclude the first couple of samples by specifying a burnin.
   sump burnin=20 excludes the first 20 samples.
   
   Type
   " sumt burnin=20 " or " sumt filename=testseq1c burnin=20 "
   , where you need to substitute '20' with the number you obtained in the previous step of the exercise (Note: that burnin values is the # of generations divided by 50, since we sample every 50th generation). This command creates a consensus tree, and shows posterior probabilities of the clades. You can take a look at the tree in Treeview by loading the testseq1.con file.
   
   Which branch in the tree is the longest?
   How long is it?
   What is the measure?
   Can you explain in a few words, why is it important to do a 'burnin' on our samplings?
   

MrBayes by example: Identification of sites under positive selection in a protein

Background:

Professor Walter M. Fitch and assistant research biologist Robin M. Bush of UCI's Department of Ecology and Evolutionary Biology, working with researchers at the Centers for Disease Control and Prevention, studied the evolution of a prevalent form of the influenza A virus during an 11-year period from 1986 to 1997. They discovered that viruses having mutations in certain parts of an important viral surface protein were more likely than other strains to spawn future influenza lineages. Human susceptibility to infection depends on immunity gained during past bouts of influenza; thus, new viral mutations are required for new epidemics to occur. Knowing which currently circulating mutant strains are more likely to have successful offspring potentially may help in vaccine strain selection. The researchers' findings appear in the Dec. 3 issue of Science magazine.

Fitch and his fellow researchers followed the evolutionary pattern of the influenza virus, one that involves a never-ending battle between the virus and its host. The human body fights the invading virus by making antibodies against it. The antibodies recognize the shape of proteins on the viral surface. Previous infections only prepare the body to fight viruses with recognizable shapes. Thus, only those viruses that have undergone mutations that change their shape can cause disease. Over time, new strains of the virus continually emerge, spread and produce offspring lineages that undergo further mutations. This process is called antigenic drift. "The cycle goes on and on-new antibodies, new mutants," Fitch said.

The research into the virus' genetic data focused on the evolution of the hemagglutinin gene-the gene that codes for the major influenza surface protein. Fitch and fellow researchers constructed "family trees" for viral strains from 11 consecutive flu seasons. Each branch on the tree represents a new mutant strain of the virus. They found that the viral strains undergoing the greatest number of amino acid changes in specified positions of the hemagglutinin gene were most closely related to future influenza lineages in nine of the 11 flu seasons tested.

By studying the family trees of various flu strains, Fitch said, researchers can attempt to predict the evolution of an influenza virus and thus potentially aid in the development of more effective influenza vaccines.

The research team is currently expanding its work to include all three groups of circulating influenza viruses, hoping that contrasting their evolutionary strategies may lend more insight into the evolution of influenza.

Along with Fitch and Bush, Catherine A. Bender, Kanta Subbarao and Nancy J. Cox of the Centers for Disease Control and Prevention participated in the study.

Exercise2:

The goal of this exercise is to detect sites in hemmagglutinin that are under positive selection.

Since the analysis takes a very long time to run (several days), here are the saved results of the MrBayes run: Fitch_HA.nex.p , Fitch_HA.nex .t .

The original data file is flu_data.paup . The dataset is obtained from an article by Yang et al, 2000 . The File used for MrBayes is here


The MrBayes block used to obtain results above is:

Selecting a nucmodel=codon with Omegavar=Ny98 specifies a model in which for every codon the ratio of the rate of non-synonymous to synonymous substitutions is considered. This ratio is called OMEGA. The Ny98 model considers three different omegas, one equal to 1 (no selection, this site is neutral); the second with omega < 1, these sites are under purifying selection; and the third with Omega >1, i.e. these sites are under positive or diversifying selection. (The problem of this model is that the there are only three distinct omegas estimated, and for each site the probability to fall into one of these three classes. If the omega>1 is estimated to be very large, because one site has a large omega, the other sites might not have a high probability to have the same omega, even though they might also be under positive selection. This leads to the site with largest omega to be identified with confidence, the others have more moderate probabilities to be under positive selection).

Note : Version 2.0 of Mr Bayes has a model that estimates omega for each site individually, the new version only allows the Ny98 model as described above..

1. First, you need to detect how many generations to burn in (meaning the number of samples you will have to discard). Import the file Fitch_HA.nex.p.txt into Excel ((link is above, open a new spreadsheet, select DATA, get external data, import text file -- select windows format, else defaults) and plot # of generations versus -LnL values. Determine after how many generations the graph becomes "stationary". The burnin value is that number of generations divided by 50 (since only every 50th generation was sampled; i.e. the burnin value roughly is equal to the number of rows - not quite because there is a header). To more accurately determine the burnin, you need to rescale the Y-axis (click at the Y-axis -- if you aim accurately, you'll get a box that allows rescaling). Selecting the values to plot becomes easier, if you delete the first row from the spreadsheet (then the first row acts as headers).
   The result (scatterplot of LogL versus generation) might look like this:
   
   
   
2. Load Fitch_HA.nex.p into Excel. (You need to load the data into 2 sheets, since Excel does not allow to load more than 256 columns per sheet. To load the data, create a new Excel spreadsheet. Go to Data->Get External Data->Import Text File , and load first 256 columns.
   
   Go to a separate sheet, and repeat "Get External Data" command to load the rest of the data, you need to block out (=select =make black) and exclude the first 256 columns). This file contains information for posterior probabilities for each site (columns) at each sampled generation (rows).
   
   
3. Calculate average posterior probability for each site of being under positive selection ( see example from Monday ). Do not forget to exclude first N rows as a burnin; you should have detected value of N in the first question of this exercise - to be clear on where the burnin ends, you might want to highlight the rows representing the burnin and select a different font color. (Use AVERAGE() function of Excel, enter the formula in a cell below the values for the individual trees, copy the formula to all columns)
   
   
4. Plot average posterior probability vs. site # . (select the row in which you calculated the averages, then click Graph, and select a bar graph). Write down the codon positions for a few sites with the highest posterior probability of being positively selected (the columns name pr+(1,2,3), pr+(4,5,6)....and so on. pr+(1,2,3) mean probability of codon #1 (nucleotide #1, #2 and #3) to be under positive selection)) (Examples are here and here , check all sheets - note: these were calculated from only 30 000 generations)
   
   
5. Create a histogram for the omega value <1 and the omega>1. To do this you need to use Analysis ToolPak of Excel ( Tools->Data Analyses ; if you do not see this item in the Tools menu, you need to activate the ToolPak. To do that go to Tools->Add-Ins... and check "Analysis ToolPak").
   The histogram data will be placed into a separate sheet. Again, do not forget to discard the burnin from consideration. Plot the calculated histogram data as a histogram. What is the shape of the distribution?
   The histogram fro omega <1 should look something like this:
   
   
6. Determine the 95% credibility interval for the omega<1 value. To do this you sort posterior probability column in ascending order (Select data you want to sort, and go to Data->Sort... ). Again, do not forget to discard the burnin ; the easiest might be to actually delete it.. After sorting, exclude 2.5% of the data on the top and on the bottom. The range of the remaining data gives you the 95% confidence interval. (The values for the 95% credibility interval should be approximately .31- .52 ; using a burnin of 55500 generations, 2.5% of the remainder is about 7.)
   
   
7. The structure of hemagglutinin has been crystallized and is publicly available through PDB. Download the PDB file here and examine it with SPDBV. Chain A of the PDB file corresponds to the sequences we did our analysis with (color the molecule according to chain). Below is a comparison of the one of the sequences we used for analyses with the sequence for which the structure was determined:
   
   
   
   Using this alignment as a help, map the sites which have the highest probability to belong to the class with omega>1. Where are these sites located in the protein? (Reminders: The position number in the nexus file corresponds to nucleotide sequence, the structure is based on the amino acid sequence - take the third codon position and divide by 3 to find the amino acid. You only want to be concerned with Chain A!)
   

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