Integrative Biology 200B University of California, Berkeley "Ecology and Evolution" Spring 2009 Lab 14: Tree Comparisons Today we are going to look at ways of comparing trees that may have a different topology. First we’re going to mathematically compare a bunch of trees with the same taxa but different topology using Mesquite and then generate several types of consensus trees. Next we’re going to generate a consensus tree from trees that have overlapping but not identical taxa using Matrix Representation with Parsimony. Last we’re going to use Type I Brook’s Parsimony to generate a tree of geographic areas from cladograms of taxa living in those areas. Tree Distances First we’re going to use Mesquite to generate a number of different tree distance measures on a bunch of trees with the same taxa, like we talked about in class. The MrBayes Cephalopod Tprbs file contains the first 13 trees from the tprobs file of a cephalopod dataset. This has the highest 50% of trees that I found during stationarity. It also has the estimated posterior probabilities of those trees. Open the MrBayes Cephalopod Tprbs file in Mesquite. Open the tree window and page through the different trees. Do you see the differences in topology? Which trees look most similar? To compare these trees to themselves we have to open a second tree window with the same set of trees. I know that seams crazy, but that's just the way it is. Go to Taxa&Trees> New Tree Window, then select Use Trees from Separate NEXUS file, and choose the MrBayes Cephalopod Tprbs file again. You should now have two tree windows with the same set of trees. From Tree Window 2 (make sure that you are in Tree Window 2) select Analysis > Values for Current Tree, and then choose Compare with other trees. This is the third option from the bottom. Compare these to Current tree. We'll start with Shared partitions. Now a box will appear saying that it wants to use the tree in tree window 2 as the current tree for comparison. We don't want that. This would make the comparison between the tree and itself, so select No. We want to compare it to the trees in Tree window 1. A box will appear showing the number of partitions that the trees in our two tree windows share. A branch can be viewed as a partition, because it separates the taxa into two groups. So if branches in both trees separate the taxa into the same two groups, then that partition is shared. These are the same as shared clades on an unrooted tree. Thus more similar trees will disagree on fewer partitions and so have more shared partitions. These trees have 12 internal branches, so if two trees are identical, then they will have 12 shared partitions. Use the swishy arrow at the top of the tree window tab to separate these trees out into different windows, so that you can see both trees at once. Page through the different trees in both windows, so that you can look at every possible pair of trees. Are the trees with higher posterior probabilities more like the tree with the highest posteriorprobability? (Remember these trees are listed in the order from the highest posterior probability to the lowest.) Is the tree with the highest posterior probability more similar to the other trees than they are in general to each other? Why would this be? What trees have the biggest differences? Pull down the little arrow in the box showing the number of shared partitions and select Tree-Tree value > Patristic Distance correlation. The patristic distance between two taxa is the sum of the branch lengths between them. This value is the correlation coefficient of the patristic distances between the two different trees. Thus more similar trees should have a higher correlation, with 1 being the maximum for identical trees. How do the trees compare under this measure of difference? Do the two metrics agree on the relative distance between trees? Which metric is more informative? Question 1. What two trees are the most different under the Patristic distance correlation? Are these two trees also among the most different for the shared partitions? If you are interested in comparing a large number of trees, I would recommend that you look into the TSV package for Mesquite. It has dome useful ways of visualizing different trees. Consensus Trees Now we’re going to generate several different consensus trees from that same set of trees using Mesquite. I want to emphasize that this is not the appropriate way to generate a consensus tree from MrBayes. It is much better to use the sumt command in MrBayes, because that will consider the trees based on their estimated posterior probabilities and will also calculate branch lengths. However, there are many other situations when you would want to use this method, such as if you generate several most parsimonious trees. I’m just using this tree file, because it is convenient. Pull down Taxa&Trees >New Tree Window and select Consensus Tree. Use Stored Trees. First let’s generate a Strict Consensus. Select it then hit OK. This will output a tree that only contains the nodes that are present in all your input trees. If you want to save the consensus trees or any tree for that matter, you have to store the trees first by using Tree>Store Tree and then save the file. There is no need to do that right now, but it may be important for you in the future. Now let’s generate a Majority Rule tree with a cut off at 50%. This will output a tree with all the nodes that appear in more than 50% of the tree. It will also tell you in what percentage of those trees the nodes occurred. Does this have the same topology as the strict consensus? Which tree is better resolved? Why? Are the two trees compatible? You can generate Majority Rule trees with cut offs greater than 50%, so that more clades are eliminated. The cut off point is always kind of arbitrary, but can not be less than 50%. If it were less than 50%, then you couldn’t be sure that all the clades are compatible. How high would the cut off have to be to guarantee that you are going to get the same tree as strict consensus?Matrix Representation with Parsimony (MRP) So it’s easy to generate consensus trees if they all have exactly the same taxa, but what do you do if all the trees have different taxa? For example how would you put together a bunch of trees from different studies with overlapping but not identical taxa? Well, it is a matter of
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