THEORY

Introduction

One of the first steps in the analysis of aligned nucleotide or amino acid sequences typically is the computation of the matrix of genetic distances (or evolutionary distances) between all pairs of sequences. In the present chapter we discuss two questions that arise in this context. First, what is a reasonable definition of a genetic distance, and second, how to estimate it using statistical models of the substitution process.

It is well known that a variety of evolutionary forces act on DNA sequences (see Chapter 1). As a result, sequences change in the course of time. Therefore, any two sequences derived from a common ancestor that evolve independently of each other eventually diverge (see Fig. 4.1). A measure of this divergence is called a genetic distance. Not surprisingly, this quantity plays an important role in many aspects of sequence analysis. First, by definition it provides a measure of the similarity between sequences. Second, if a molecular clock is assumed (see Chapter 11), then the genetic distance is linearly proportional to the time elapsed. Third, for sequences related by an evolutionary tree, the branch lengths represent the distance between the nodes (sequences) in the tree. Therefore, if the exact amount of sequence divergence between all pairs of sequences from a set of n sequences is known, the genetic distance provides a basis to infer the evolutionary tree relating the sequences.