Today, we will firstly consider the maximum likelihood method for the reconstruction of phylogenies. For this, we will introduce evolutionary models. Such a model is based on a rooted tree and a rate matrix which specifies the substitution matrices along the branches of the tree. Then we will introduce the likelihood of the tree and discuss the problem of optimizing the branch lengths.
Secondly, we will study distance based methods. The goal is to construct the most additive tree from a given set of evolutionary distances. We will use linear programming to tackle this problem. An example involving four species will be given.
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