title: Matchings and phylogenetic trees.
abstract: This paper presents a natural coordinate system for phylogenetic trees using a correspondence with the set of perfect matchings in the complete graph. This correspondence produces a distance between phylogenetic trees, and a way of enumerating all trees in a minimal step order. It is useful in randomized algorithms because it enables moves on the space of trees that make random optimization strategies "mix" quickly. It also promises a generalization to intermediary trees when data are not decisive as to their choice of tree, and a new way of constructing Bayesian priors on tree space.
authors.affiliation: Department of Mathematics, Sequoia Hall, Stanford University, Stanford, CA 94305-4065, USA.
authors.forename: P W
authors.initials: PW
authors.lastname: Diaconis
authors.forename: S P
authors.initials: SP
authors.lastname: Holmes
mesh_terms: D000818:Animals; D006801:Humans; D008962:Models, Theoretical; D010802:Phylogeny