Vol. 11, No. 1, 2021

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Phylogenetic trees

Hector Baños, Nathaniel Bushek, Ruth Davidson, Elizabeth Gross, Pamela E. Harris, Robert Krone, Colby Long, Allen Stewart and Robert Walker

Vol. 11 (2021), 1–7
DOI: 10.2140/jsag.2021.11.1
Abstract

We introduce the package PhylogeneticTrees for Macaulay2, which allows users to compute phylogenetic invariants for group-based tree models. We provide some background information on phylogenetic algebraic geometry and show how the package PhylogeneticTrees can be used to calculate a generating set for a phylogenetic ideal as well as a lower bound for its dimension. Finally, we show how methods within the package can be used to compute a generating set for the join of any two ideals.

Keywords
phylogenetic trees, secant ideals, algebraic statistics, toric ideals
Mathematical Subject Classification 2010
Primary: 13P25
Secondary: 05C05, 14M25, 92D15
Supplementary material

Invariants for group-based phylogenetic models

Milestones
Received: 16 November 2016
Revised: 4 January 2020
Accepted: 8 August 2020
Published: 23 January 2021
Authors
Hector Baños
School of Mathematics
Georgia Institute of Technology
Atlanta, GA
United States
Nathaniel Bushek
Department of Mathematics and Physics
The College of St. Scholastica
Duluth, MN
United States
Ruth Davidson
Department of Mathematics
University of Illinois Urbana-Champaign
Urbana, IL
United States
Elizabeth Gross
Department of Mathematics
University of Hawaii‘i at Manoa
Honolulu, HI
United States
Pamela E. Harris
Department of Mathematics and Statistics
Williams College
Williamstown, MA
United States
Robert Krone
Department of Mathematics
UC Davis
Davis, CA
United States
Colby Long
Department of Mathematics and Computational Sciences
The College of Wooster
308 E. University Street
Wooster, OH 44691
United States
Allen Stewart
Department of Mathematics
Seattle University
Seattle, WA
United States
Robert Walker
Department of Mathematics
University of Wisconsin–Madison
Madison, WI
United States