THEORY

Introduction

The concept of likelihood refers to situations that typically arise in natural sciences in which given some data D, a decision must be made about an adequate explanation of the data. Thus, a specific model and a hypothesis are formulated in which the model as such is generally not in question. In the phylogenetic framework, one part of the model is that sequences actually evolve according to a tree. The possible hypotheses include the different tree structures, the branch lengths, the parameters of the model of sequence evolution, and so on. By assigning values to these elements, it is possible to compute the probability of the data under these parameters and to make statements about their plausibility. If the hypothesis varies, the result is that some hypotheses produce the data with higher probability than others. Coin-tossing is a standard example. After flipping a coin n = 100 times, h = 21 heads and t = 79 tails were observed. Thus, D = (21,79) constitutes a sufficient summary of the data. The model then states that, with some probability, θ ∈ [0,1] heads appear when the coin is flipped. Moreover, it is assumed that the outcome of each coin toss is independent of the others, that θ does not change during the experiment, and that the experiment has only two outcomes (head or tail). The model is now fully specified.