Toric ideals of homogeneous phylogenetic models

Details Toric ideals of homogeneous phylogenetic models Toric ideals of homogeneous phylogenetic models

2004-01-15

arxiv.org/abs/math/0401175v1

Proceedings of the 2004 international symposium on symbolic and algebraic computation

Mathematics

Combinatorics

6 pages, 17 figures

Scientific paper

10.1145/1005285.1005308

We consider the phylogenetic tree model in which every node of the tree is observed and binary and the transitions are given by the same matrix on each edge of the tree. We are able to compute the Grobner basis and Markov basis of the toric ideal of invariants for trees with up to 11 nodes. These are perhaps the first non-trivial Grobner bases calculations in 2^11 indeterminates. We conjecture that there is a quadratic Grobner basis for binary trees. Finally, we give a explicit description of the polytope associated to this toric ideal for an infinite family of binary trees and conjecture that there is a universal bound on the number of vertices of this polytope for binary trees.

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