ABSTRACT


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. Return to Applied Math Colloquium home page 