A vector representation for phylogenetic trees

Good representations for phylogenetic trees and networks are important for enhancing storage efficiency and scalability for the inference and analysis of evolutionary trees for genes, genomes and species. We propose a new representation for rooted phylogenetic trees that encodes a tree on [Formula: see text] ordered taxa as a vector of length [Formula: see text] in which each taxon appears exactly twice. Using this new tree representation, we introduce a novel tree rearrangement operator, termed an <i>HOP</i>, that results in a tree space of linear diameter and quadratic neighbourhood size. We also introduce a novel metric, the <i>HOP distance</i>, which is the minimum number of HOPs to transform a tree into another tree. The HOP distance can be computed in near-linear time-a rare instance of tree rearrangement distance that is tractable. Our experiments show that the HOP distance is better correlated to the Subtree-Prune-and-Regraft distance than the widely used Robinson-Foulds distance. We also describe how the proposed tree representation can be further generalized to tree-child networks, showcasing its versatility and potential applications in broader evolutionary analyses.This article is part of the theme issue '"A mathematical theory of evolution": phylogenetic models dating back 100 years'.