Geometry of the space of phylogenetic trees. (English) Zbl 0995.92035

Adv. Appl. Math. 27, No. 4, 733-767 (2001); erratum ibid. 29, No. 1, 136 (2002).
Summary: 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 spaces 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.


92D15 Problems related to evolution
05C05 Trees
05C90 Applications of graph theory


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