Regular Article: Geometry of the Space of Phylogenetic Trees

Authors:
Louis J. Billera;Susan P. Holmes;Karen Vogtmann
Affiliations:
Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York, 14853;INRA, Montpellier, France and Department of Statistics, Stanford University, Stanford, California, 94305, f1susan@stat.stanford.eduf1;Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York, 14853
Venue:
Advances in Applied Mathematics
Year:
2001

Citing 0
Cited 14

The Bergman complex of a matroid and phylogenetic trees

Journal of Combinatorial Theory Series B
The positive Bergman complex of an oriented matroid

European Journal of Combinatorics
Approximating geodesic tree distance

Information Processing Letters
Nested set complexes of Dowling lattices and complexes of Dowling trees

Journal of Algebraic Combinatorics: An International Journal
Speculation on the generality of the backward stepwise view of PCA

Proceedings of the international conference on Multimedia information retrieval
Visualizing phylogenetic treespace using cartographic projections

WABI'09 Proceedings of the 9th international conference on Algorithms in bioinformatics
Nonlinear network optimization: an embedding vector space approach

IEEE Transactions on Evolutionary Computation
A Fast Algorithm for Computing Geodesic Distances in Tree Space

IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
Geometries on spaces of treelike shapes

ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part II
Horoball hulls and extents in positive definite space

WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Computing Geodesic Distances in Tree Space

SIAM Journal on Discrete Mathematics
Shortest path problem in rectangular complexes of global nonpositive curvature

Computational Geometry: Theory and Applications
Tree-space statistics and approximations for large-scale analysis of anatomical trees

IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
Dimension reduction in principal component analysis for trees

Computational Statistics & Data Analysis

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.