The Ultrametric Constraint and its Application to Phylogenetics
This work addresses the challenge of combining phylogenetic trees into larger supertrees for biologists, representing an incremental improvement through a novel constraint method.
The paper tackled the problem of constructing phylogenetic supertrees by enforcing the ultrametric property through a constraint programming encoding, resulting in an efficient constraint-based solution that handles variants of the supertree construction problem.
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.