Abstract
When evolutionary distances between pairs of taxa can be estimated, they can be used to rapidly infer a phylogenetic tree. This chapter explains how distances should be defined and estimated, and then focus on the task of constructing a phylogenetic tree that corresponds to those distances. It discusses the properties that distances must satisfy in principle, and the classic approaches to tree inference, least squares and minimum evolution. The chapter focuses on the most commonly known methods, in particular neighbor joining and a wide range of algorithms inspired therefrom. It presents the major ideas underlying distance-based methodology. The study of tree distances is an old subject and is one of the foundations of mathematical phylogenetics. The component of a distance-based approach to tree inference is distance estimation. FastTree is faster and requires less memory than the distance-based methods, and it can easily handle datasets containing hundreds of thousands of sequences.