Susan Holmes, Stanford University.
"Confidence Regions for Phylogenetic trees"
Monday, October 16 2000
Communications 120 at 3:30 P.M.

Abstract

Joint work with Louis Billera and Karen Vogtmann, Mathematics Department, Cornell.

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.

New types of confidence statements are made possible in this cube complex.