Using invariants for phylogenetic tree construction

TL;DR

This paper introduces the use of phylogenetic invariants, specific polynomials in probability distributions, for constructing phylogenetic trees, highlighting algebraic, statistical, and computational challenges and open problems.

Contribution

It provides a comprehensive introduction and survey of phylogenetic invariants, emphasizing their practical application in tree construction and discussing current challenges.

Findings

Survey of existing literature on phylogenetic invariants

Identification of algebraic and computational challenges

Outline of open problems in the field

Abstract

Phylogenetic invariants are certain polynomials in the joint probability distribution of a Markov model on a phylogenetic tree. Such polynomials are of theoretical interest in the field of algebraic statistics and they are also of practical interest--they can be used to construct phylogenetic trees. This paper is a self-contained introduction to the algebraic, statistical, and computational challenges involved in the practical use of phylogenetic invariants. We survey the relevant literature and provide some partial answers and many open problems.