PhylogeneticTrees is a package for phylogenetic algebraic geometry. This package calculates generating sets for phylogenetic ideals and their joins and secants. Additionally, the package computes lower bounds for the dimensions of secants and joins of phylogenetic ideals.
This package handles a class of commonly used tree-based Markov models called group-based models. These models are subject to the Fourier-Hadamard coordinate transformation, which make the parametrizations monomial and the ideals toric. See the following for more details:  and .
For these models, the PhylogeneticTrees package includes two methods for computing a generating set for ideals of phylogenetic invariants. The first method calls FourTiTwo to compute the generating set of the toric ideal. The second implements a theoretical construction for inductively determining the ideal of phylogenetic invariants for any $k$-valent tree from the $k$-leaf claw tree as described in Theorem 24 of .
This package also handles the joins and secants of these ideals by implementing the elimination method described in .
In cases where computing a generating set for a join or secant ideal is infeasible, the package provides a probabilistic method, based on Terracini’s Lemma, to compute a lower bound on the dimension of a join or secant ideal.
 S.N. Evans and T.P. Speed, it Invariants of some probability models used in phylogenetic inference, Ann. Statist. 21 (1993), no. 1, 355–377, and
 L. Székely, P.L. Erdös, M.A. Steel, and D. Penny, A Fourier inversion formula for evolutionary trees, Applied Mathematics Letters 6 (1993), no. 2, 13–17.
 Bernd Sturmfels and Seth Sullivant, Toric ideals of phylogenetic invariants, J. Comp. Biol. 12 (2005), no. 2, 204–228.
 Bernd Sturmfels and Seth Sullivant, Combinatorial secant varieties, Quarterly Journal of Pure and Applied Mathematics 2 (2006), 285–309.
Version 2.0 of this package was accepted for publication in volume 11 of The Journal of Software for Algebra and Geometry on 8 August 2020, in the article Phylogenetic trees. That version can be obtained from the journal or from the Macaulay2 source code repository.
This documentation describes version 2.0 of PhylogeneticTrees.
The source code from which this documentation is derived is in the file PhylogeneticTrees.m2.