First steps toward the geometry of cophylogeny

TL;DR

This paper introduces the emerging field of cophylogenetics, focusing on the algebraic and geometric properties of related evolving trees like hosts and parasites, and proposes foundational concepts and open problems.

Contribution

It pioneers the algebraic geometric approach to cophylogenetics, defining spaces, invariants, and reconstruction methods for related evolutionary trees.

Findings

Proposed the concept of cophylogenetic tree spaces

Introduced algebraic invariants for cophylogenetics

Outlined open problems in the field

Abstract

Here we introduce researchers in algebraic biology to the exciting new field of cophylogenetics. Cophylogenetics is the study of concomitantly evolving organisms (or genes), such as host and parasite species. Thus the natural objects of study in cophylogenetics are tuples of related trees, instead of individual trees. We review various research topics in algebraic statistics for phylogenetics, and propose analogs for cophylogenetics. In particular we propose spaces of cophylogenetic trees, cophylogenetic reconstruction, and cophylogenetic invariants. We conclude with open problems.