10 Likelihood lab

10 Likelihood lab - Integrative Biology 200A...

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University of California, Berkeley "PRINCIPLES OF PHYLOGENETICS" Spring 2008 Lab 10: Maximum Likelihood and Modeltest In this lab we’re going to use PAUP* to find a phylogeny using molecular data and Maximum Likelihood as the optimality criterion. The computer evaluates the likelihood of each tree, including topology and branch lengths, one at a time. It calculates the probability of each base pair changing in such a way as to generate the states observed at the tips of the branches based on the tree and a set of parameters describing how the bases change with time. The likelihood of a data set for a given tree is the product of these probabilities for all the base pairs. The computer chooses the topology and branch lengths that produce the highest likelihood for the data set. So what parameters of nucleotide change do we use and what values do we give them? This is called the model of nucleotide change and today we will pick a model using ModelTest. There are an infinite number of possible models. Many have been implemented in various programs, many have been suggested and never implemented, and even more have never been conceived. Today we are only going to deal with a few models that are implemented in PAUP* and evaluated by ModelTest . A model is considered nested within another model if its parameters are a limited set of the parameters in the other model. For example the Jukes-Cantor model, which assumes that every nucleotides has the same rate of change to any other, is nested within the Kimura two parameter model, which assumes different transition and transversion rates. A model without any invariant sites would be nested within one with some percentage of invariant sites. Any two models are not necessarily nested. Adding parameters to a model always increases the maximum likelihood of the data. However, if a model has too many parameters, then maximum likelihood becomes unreliable. Therefore to accept a new parameter into your model it must produce a significant increase in the likelihood. How do you tell if a difference in likelihood is significant? Well, I’m sure you’ll be shocked to learn that there is a formula. It is called the Likelihood Ratio Test (LRT). For a given model with likelihood, Λ 1 , nested within another model with likelihood, Λ 2 , with n less parameters: Χ 2 (chi squared) = 2 * ( ln ( Λ 2 ) – ln ( Λ 1 )) with n degrees of freedom. You can use this equation to pick the most inclusive model that can not be significantly improved on. The only drawback of this equation is that you can not use it to compare different trees, because different trees are not different models – they are more like alternative parameter values. Therefore, you have to compare the different models on a single tree, and which tree to compare them on may not be obvious. Luckily, you tend to get similar results as long as you use a reasonable tree.
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10 Likelihood lab - Integrative Biology 200A...

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