The Geometry of Phylogenetic Trees

We consider a continuous space that models the set of all phylogenetic
trees having a fixed set of leaves.  This space has a natural metric of
nonpositive curvature (i.e., it is CAT(0) in the sense of Gromov), giving
a way of measuring distance between phylogenetic trees and providing some
procedures for averaging or otherwise doing statistical analyses on sets
of trees on a common set of species.

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.

This is joint work with Susan Holmes and Karen Vogtmann.