Integrative Biology 200B University of California, Berkeley "Ecology and Evolution" Spring 2009 Lab 3b: Correlated Changes in Discrete Characters Today we are going to look at several different statistical methods for determining if an apparent correlation between two discrete characters on a phylogeny is significant. All of these methods are available in Mesquite. These analyses can be done with other programs and there are other types of analyses that seek to answer the same question, but for now we’ll stick with the programs that we will use on a regular basis. The essential question at hand here is weather a character is more likely to change into a particular state in lineages that are in a particular state for another character, but they all take different approaches. Pagel’s test looks at changes across the whole phylogeny, while Pairwise Comparisons breaks a phylogeny down into a number of comparisons between pairs of taxa. On the other hand, Pairwise Comparisons rely on looking for significance by counting changes in characters, while Pagel’s test uses comparison of likelihood scores for the same purpose. Both these methods will be described in more detail below. A third method, Maddison's test, uses changes in number of characters, but makes the calculation over the whole phylogeny. This test is available in MacClade, but not Mesquite, so we won't be using it today. We will do all these analyses on the Concentrated Changes example data set from the the Mesquite examples. Open this file in Mesquite. Go to the Show State Names Editor Window and rename each of the two characters and states as follows: Character 1 = dependent character, Fruit Type, state 0 = ancestral, fleshy, state 1 = derived, dry; Character 2 = independent character, Ecology, state 0 = tropical rainforest, state 1 = open savanna. Save your work (but only this one time). Comparing Reconstructions Visually The first thing that we will do is look at the distribution of the two characters against each other in one window, so that you might more clearly see their differences. Open the Tree Window. Go to Tree>mirror tree window. A new window will appear with the trees facing each other. Expand the window so that you can see what’s going on. First let’s compare parsimony reconstructions of our two characters. Select Mirror> left side >trace character history, and select Parsimony ancestral states. Do the same for the right tree. You will see character 1 traced in both trees. Use the Trace character box for the right tree to switch to character 2. Now you can clearly see that Character 1 only switches from state 0 to state 1 in lineages that are in state 1 for character 2. You can also modify the reconstructions for each of these trees. For example let's look at the likelihood reconstructions. You will see separate trace menus for each tree. For both trees go to trace>Reconstruction Method>Likelihood Ancestral States, and select Current probability models. It may be helpful if you set the Tree Form to Balls and Sticks. You can set the Likelihood model to Mk2 by going to trace>Probability Model>assym. 2 param. Don't for get to do this for both trees. You can also use this method to compare different reconstructions of a single character. Why don't you compare the 2 parameter reconstruction of character 1 to the mk1 reconstruction? Pairwise ComparisonsOne possible approach for detecting correlation between two characters is to break the tree down into a number of non-overlapping series of branches that connect two taxa. You then ask how often the taxon with the higher state of the independent character also has the higher (positive) or lower (negative) state of the dependent character. Because the branches don’t overlap you can just compare this to a standard nonparametric distribution and yet be certain that any correlations are independent of the phylogeny. This can also work for discrete characters by looking at the number of times one particular state for one character will be associated with one particular state of another character while the other taxon of each pair has the opposite set of character states. There are a number of different possible pairs for any given tree. Mesquite gives you three ways to select your pairs. It can either pick sets of pairs that maximize the total number of pairs, those that maximize the total pairs with differences in one character or those that maximize the total pairs with differences in both characters. In any case it can come up with multiple possible pairs and you can pan through multiple options. First open the original tree window and select analysis > pairwise comparisons. For our first set of comparisons let’s just take the maximum possible number: select most pairs and hit OK. Now the tree will appear greatly changed. All those colored lines are the different pairs of taxa. How many pairs of taxa are there? The numbers up above the tips are the character states for the characters you’re comparing. Down in the bottom right are three boxes indicating the characters being compared and the choice of pairs. As you can see right now you are comparing character 1 as the independent character and character 2 as the dependent. That is the opposite of what you want, since it appears that the state of character 2 effects the state of character 1, not the other way around. Switch the characters to make the appropriate comparison. The third box has the details of the comparison. There is only one possible set of pairs for the most trees criterion of pair choice. Below that is a summary of the comparisons: Positive (Green): cases in which one of the taxa has a 1 for both characters and the other taxon has a 0 for both. (00 vs 11); Negative(Red): cases in which one of the taxa has a 1 for one character and a 0 for the other and the other taxon has the opposite. (01 vs 10); Neutral(Grey): cases in which the taxa disagree in the independent character, but have the same dependent character. (01 vs 11) or (00 vs 10); Remainder(Blue): cases in which the independent character is the same for both taxa. The last thing in the box is the p-value, which is very low for this comparison. Now let’s try another set of pairs. Go to Pairs > pair selector > Pairs contrasting in state for one character. A number of pairs box will appear. This time the program found a bunch
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