Geometry of the Space of Phylogenetic Trees |
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Authors: | Louis J. Billera Susan P. Holmes Karen Vogtmann |
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Affiliation: | a Department of Mathematics, Malott Hall, Cornell University, Ithaca, New York, 14853;b INRA, Montpellier, France;Department of Statistics, Stanford University, Stanford, California, 94305, f1 |
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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. |
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Keywords: | phylogenetic trees semi-labeled trees associahedron CAT(0) space consensus bootstrap |
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