Relevant phylogenetic invariants of evolutionary models

TL;DR

This paper demonstrates that for phylogenetic reconstruction, it suffices to consider edge invariants derived from tree edges, simplifying the algebraic approach to evolutionary models like Jukes-Cantor and Kimura.

Contribution

It proves that edge invariants alone are sufficient for phylogenetic reconstruction, analogous to Buneman's theorem, streamlining algebraic methods in phylogenetics.

Findings

Edge invariants are sufficient for phylogenetic reconstruction.

Applicable to common evolutionary models like Jukes-Cantor and Kimura.

Simplifies algebraic approach in phylogenetics.

Abstract

Recently there have been several attempts to provide a whole set of generators of the ideal of the algebraic variety associated to a phylogenetic tree evolving under an algebraic model. These algebraic varieties have been proven to be useful in phylogenetics. In this paper we prove that, for phylogenetic reconstruction purposes, it is enough to consider generators coming from the edges of the tree, the so-called edge invariants. This is the algebraic analogous to Buneman's Splits Equivalence Theorem. The interest of this result relies on its potential applications in phylogenetics for the widely used evolutionary models such as Jukes-Cantor, Kimura 2 and 3 parameters, and General Markov models.