### Geometry of the space of phylogenetic trees

#### Louis J. Billera, Susan P. Holmes and and Karen Vogtmann

*Advances in Applied Math ***27**, 733-767 (2001)

We consider a continuous space which models the set of all
phylogenetic trees having a fixed set of leaves. This space has a natural metric
of nonpositive curvature, giving a way of measuring distance between phylogenetic
trees and providing some procedures for averaging or combining several trees
whose leaves are identical. This geometry also shows which trees appear within
a fixed distance of a given tree and enables construction of convex hulls of
a set of trees.

This geometric model of tree space provides a setting in which
questions that have been posed by biologists and statisticians over the last
decade can be approached in a systematic fashion. For example, it provides a
justification for disregarding portions of a collection of trees that agree,
thus simplifying the space in which comparisons are to be made.