Phylogenetics in a warm place: computational aspects of the Tropical Grassmannian

TL;DR

This paper explores the tropical Grassmannian as a geometric framework for phylogenetic trees, offering computational methods and insights that bridge algebraic geometry and evolutionary biology.

Contribution

It reviews the structure of the tropical Grassmannian and introduces algorithms for its computational analysis, facilitating phylogenetic inference.

Findings

Tropical Grassmannian models phylogenetic tree space effectively.

Algorithms for sampling from the tropical Grassmannian are developed.

The approach offers a new geometric perspective for phylogenetics.

Abstract

Phylogenetic trees provide a fundamental representation of evolutionary relationships, yet the combinatorial explosion of possible tree topologies renders inference computationally challenging. Classical approaches to characterizing tree space, such as the Billera-Holmes-Vogtmann (BHV) space, offer elegant geometric structure but suffer from statistical and computational limitations. An alternative perspective arises from tropical geometry, the tropical Grassmannian tropGr(2,n), introduced by Speyer and Sturmfels, which coincides with phylogenetic tree space. In this paper, we review the structure of the tropical Grassmannian and present algorithmic methods for its computational study, including procedures for sampling from the tropical Grassmannian. Our aim is to make these concepts accessible to evolutionary biologists and computational scientists, and to motivate new research directions at the interface of algebraic geometry and phylogenetic inference.