Introduction

Our goal in this chapter is to formulate probabilistic models for phylogeny and show how trees can be inferred from sets of sequences, either by maximum likelihood or by sampling methods. We also review the phylogenetic methods of the previous chapter, and show that they often have probabilistic interpretations, though they are not usually presented this way.

Overview of the probabilistic approach to phylogeny

The basic aim of probability-based phylogeny is to rank trees either according to their likelihood P(data∣tree), or, if we are taking a more Bayesian view, according to their posterior probability P (tree∣data). There may be subsidiary aims, such as finding the likelihood or posterior probability of some particular taxonomic feature, such as a grouping of a set of organisms on a single branch. To achieve any of these aims, we must be able to define and compute P(x•∣T, t•), the probability of a set of data given a tree. Here the data are a set of n sequences xj for j = 1…n, which we write compactly as x•. T is a tree with n leaves with sequence j at leaf j, and the t• are the edge lengths of the tree. To define P(x•∣T, t•) we need a model of evolution, i.e. of the mutation and selection events that change sequences along the edges of a tree.