Computing at Glasgow University
Paper ID: 8979

The Ultrametric Constraint and its Application to Phylogenetics
Moore,N.C.A. Prosser,P.

Publication Type: Journal
Appeared in: Journal of Artificial Intelligence Research, Volume 32
Page Numbers : 901-938
Publisher: AAAI Press
Year: 2008
ISBN/ISSN: ISSN 11076-9757

A phylogenetic tree shows the evolutionary relationships among species. Internal nodes of the tree represent speciation events and leaf nodes correspond to species. A goal of phylogenetics is to combine such trees into larger trees, called supertrees, whilst respecting the relationships in the original trees. A rooted tree exhibits an ultrametric property; that is, for any three leaves of the tree it must be that one pair has a deeper most recent common ancestor than the other pairs, or that all three have the same most recent common ancestor. This inspires a constraint programming encoding for rooted trees. We present an efficient constraint that enforces the ultrametric property over a symmetric array of constrained integer variables, with the inevitable property that the lower bounds of any three variables are mutually supportive. We show that this allows an efficient constraint-based solution to the supertree construction problem. We demonstrate that the versatility of constraint programming can be exploited to allow solutions to variants of the supertree construction problem.

Keywords: supertrees construction constraint programming tree of life ultrametric

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