Integrative Biology 200B University of California, Berkeley "Ecology and Evolution" Spring 2009 Lab 13: Coalescence Today we are going to use Mesquite to investigate coalescence. We will simulate a coalescent process for several alleles on a population tree. We will compare these simulated allele trees to the population trees and calculate several values that indicate something about the nature of the coalescent. We will also look at the effect of generations and population size on the coalescence process. Finally we will compare an actual gene tree for a group of alleles to several population trees. Establishing an Association The first thing that we are going to do is establish an association between populations and the alleles that they contain. This is a necessary step for any comparison between two groups of taxa. In this case one group of taxa is the populations and the other is the alleles found in those populations. It could just as well be a pair of mutualists, organisms and their parasites, species and duplicated gene families that they contain or even geographic areas and the species that reside in them. Open the file Coalesence example 1 in Mesquite. Open the tree. As you can see, there is not a lot of information here, just a tree with three taxa. Now we are going to create a set of alleles for the taxa in this tree. Select Taxa&Trees > New Block of Taxa. Call the block Alleles to separate it from the Populations block, and let’s start with 7 alleles. Let’s assign two alleles each to populations 1 and 2, and three alleles to population 3. Rename the alleles Allele 1a, Allele 1b, Allele 2a, etc. To establish the association select Taxa&Trees > New Association. Select Populations as the first block. In general it is easier if you select your containing taxa as your first block. Give the association a creative name. The Populations Taxa block will appear at the front of your screen, but now it will have a column for associated alleles and an association editor on the right for creating your associations. Select Population 1, go to the Association editor and select the two alleles from population 1, then press the arrow at the top of the association editor. Those two alleles should appear in the Alleles column next to population 1. Do the same for populations 2 and 3. You can use the plus and minus buttons to edit the associations, if you make any mistakes. Save your work and open the nexus file in a text editor. You will see four blocks in addition to the Mesquite Block: Two taxa blocks, one for the populations and one for the genes; a tree block for the population tree; and an association block explaining the association between the populations and their alleles. This block is in the standard format for associations in Nexus files. It is not as widely accepted as other aspects of the nexus file format, so be sure to check your documentation about file formats, if you are using another program. Simulating Coalescence on the Population Tree Now we are going to let Mesquite simulate a coalescent process for these eight genes on the population tree. This works by considering the chance of any two alleles coming together in a single haploid population as 1/Ne per generation. It goes back generation by generationcalculating the probability of each allele lineage coalescing until they have all come together, although by default it actually uses an exponential approximation of that process. Select Taxa&Trees > Multi Tree Window. Select Alleles, because we will be making trees of Alleles on the Taxon tree. Then choose Simulated Trees : Coalescence Contained within Current Tree. Let’s start with 10000 as our Ne. Just make 20 trees to keep the amount that you have to look at for this one lab down. Look at the trees. Use Multi-tree > Number of columns and Multi-tree > Number of rows to adjust the number of rows and columns and change the window size so that you can easily view many trees at once. How often are the alleles of each species monophyletic? How often does the gene topology reflect the true topology of the populations? Comparing the Depth of the Coalescence In the simulated trees window select Drawing> Branches Proportional to Length and Drawing > Tree Form > Curvogram. You can now clearly visualize when the different simulations completely coalesce. As you can see, some come together shortly before the initial split in lineages 200 generations ago (in Mesquite for the coalescence, branch length equals generations), but some diverged much longer ago. Let’s look at how the coalescence depth varies among our different simulations. In the Population tree window select Analysis > New Bar & Line Chart for > Trees, alleles, Simulated trees: Coalescence contained within current tree, 10000 for population size,Tree depth and let’s do 1000 trees for the simulation. There you go. There are no simulations that coalesce until after 200 generations ago. Where is the peak? What is the oldest coalescence that your simulation found? Visualizing the Comparison between Population Trees and Allele Trees We can make a pretty tree that shows the coalescence process within the population tree. In the Population Tree window select Drawing > Tree Form > Contained Gene (or Other) Tree. Use the branch lengths, and autoresolve Polytomies (although you won’t have any Polytomies from the simulation). Choose Simulated trees: Coalescence contained within current tree, 10000. Now doesn’t that look cool? You can see how the simulated gene tree fits together with the population tree. You can scan through the different simulations using the arrows in the box on the bottom right. Many of the controls normally found in the Drawing and Tree menus will now be found in the Contained menu. Select Contained > Display Contained Tree. A new window will appear showing the simulated tree that you are viewing. In this window use the second drawing menu to set branches proportional to lengths and tree form > curvogram. Scan through the different examples. Can you tell which simulations would require allele losses by looking at the reconstruction within the population tree? Quantifying the Comparison between Population Trees and Allele Trees Mesquite can also calculate two values that compare allele trees to populations. The first is s. The population tree is not used to calculate s, so it does
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