H-Representation of the Kimura-3 Polytope

2014/09/15 by Marie Mauhar, Mauhar, Marie, Joseph Rusinko +3
Agricultural and Biological Sciences · Biochemistry, Genetics and Molecular Biology · #14M25 #Algebraic Geometry (math.AG) #Biochemical and Structural Characterization #FOS: Biological sciences #FOS: Mathematics #Genomics and Phylogenetic Studies #Plant and animal studies #Populations and Evolution (q-bio.PE)

paper · pdf · doi:10.48550/arxiv.1409.4130

openalex publication_date 2014/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a group-based Markov model on a tree, one can compute the vertex representation of a polytope which describes the associated toric variety. The half-space representation, however, is not easily computable. In the case of ℤ₂ or ℤ₂×ℤ₂, these polytopes have applications in the field of phylogenetics. We provide a half-space representation for the m-claw tree where G=ℤ₂×ℤ₂, which corresponds to the Kimura-3 model of evolution.

Citations

• Phylogenetic Algebraic Geometry
• A simple method for estimating evolutionary rates of base substitutions through comparative studies of nucleotide sequences
• Invariant versus classical quartet inference when evolution is heterogeneous across sites and lineages

Related

• Geometry of the Kimura 3-parameter model
• Toric ideals of homogeneous phylogenetic models
• Phylogenetic ideals and varieties for the general Markov model
• Toric ideals of phylogenetic invariants
• A semialgebraic description of the general Markov model on phylogenetic trees