Types of trees

This book is about evolution, and one of the fundamental features of evolutionary analysis is the tree. The terms tree and phylogeny are used quite loosely in the literature for the purposes of describing a number of quite distinct objects. Evolutionary trees are a subset of the group of objects that graph theorists know as trees, which are themselves connected graphs that do not contain cycles. An evolutionary tree typically has labelled leaf nodes (tips) and unlabelled internal nodes (an internal node may also be known as a divergence or coalescence). The leaf nodes are labelled with taxa, which might represent an individual organism, or a whole species, or more typically just a gene fragment, while the internal nodes represent unsampled (and thus inferred) common ancestors of the sampled taxa. For reasons mainly of history, the types of trees are many and varied; in the following we introduce the main types.

2.1.1 Rooted and unrooted trees

One of the more important distinctions is between rooted trees and unrooted trees (Figure 2.1). Both of the trees in Figure 2.1 describe the evolutionary relationships between four taxa labelled A to D.

A rooted tree has a notion of the direction in which evolution occurred. One internal node is identified as the root, and evolution proceeds from the root to the leaves. A tree is said to be binary if its internal nodes always have precisely two children. A rooted binary tree of n taxa can be described by 2n−1 nodes and 2n−2 branches, each with an associated branch length. A rooted binary tree is displayed in Figure 2.1a; note that the path length between two leaf nodes should be measured only by the sum of the lengths of the horizontal lines along the shortest path connecting the two leaves. The vertical lines exist purely for the purpose of visual layout. Taxon A is actually the shortest distance of all the taxa to taxon D, even though taxon A is the furthest from D vertically.

In contrast, an unrooted tree does not have a root and so does not admit any knowledge of which direction evolution ‘flows’. The starting point is not known, so the tree is generally drawn with the leaf nodes spread around the perimeter of the diagram.