The Geometry of the space of semi-labelled binary trees, and an application to computational biology.
by
Susan Holmes
Stanford University
Coauthors: Louis Billera (Mathematics, Cornell), Karen Vogtmann (Mathematics, Cornell)

We will present a geometric model of a space which parametrizes phylogenetic trees using both combinatorics and geometry. The geometry of the space gives a way of measuring a distance between phylogenetic trees as well as a way of `averaging' or `combining' several trees whose leaves are identicial. The convex hull of a set of trees can also be defined, thus making possible a ``peeling" procedure which finds the most central trees in a set, called the tree of greatest depth. This geometric model of tree space provides answers to questions concerning the number of `neighbors' to a given tree and the `curvature' of the boundaries between regions defining different trees that have been posed by biologists and statisticians over the last decade. It also provides a justification for disregarding portions of a collection of trees that agree, thus simplifying the space in which comparisons are to be made.

http://www-stat.stanford.edu/~susan/papers/june.pdf

Date received: September 24, 2000