Geometry of the Kimura 3-parameter model
Algebraic Geometry
2007-05-23 v1 Commutative Algebra
Populations and Evolution
Abstract
The Kimura 3-parameter model on a tree of n leaves is one of the most used in phylogenetics. The affine algebraic variety W associated to it is a toric variety. We study its geometry and we prove that it is isomorphic to a geometric quotient of the affine space by a finite group acting on it. As a consequence, we are able to study the singularities of W and prove that the biologically meaningful points are smooth points. Then we give an algorithm for constructing a set of minimal generators of the localized ideal at these points, for an arbitrary number of leaves n. This leads to a major improvement of phylogenetic reconstruction methods based on algebraic geometry.
Cite
@article{arxiv.math/0702834,
title = {Geometry of the Kimura 3-parameter model},
author = {Marta Casanellas and Jesus Fernandez-Sanchez},
journal= {arXiv preprint arXiv:math/0702834},
year = {2007}
}
Comments
26 pages with 4 figures