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Binary phylogenetic trees inferred from biological data are central tounderstanding the shared evolutionary history of organisms. Inferring theplacement of latent nodes in a tree by any optimality criterion (e.g., maximumlikelihood) is an NP-hard problem, propelling the development of myriadheuristic approaches. Yet, these heuristics often lack a systematic means ofuniformly sampling random trees or effectively exploring a tree space thatgrows factorially, which are crucial to optimisation problems such as machinelearning. Accordingly, we present Phylo2Vec, a new parsimonious representationof a phylogenetic tree. Phylo2Vec maps any binary tree with $n$ leaves to aninteger vector of length $n$. We prove that Phylo2Vec is both well-defined andbijective to the space of phylogenetic trees. The advantages of Phylo2Vec aretwofold: i) easy uniform sampling of binary trees and ii) systematic ability totraverse tree space in very large or small jumps. As a proof of concept, we usePhylo2Vec for maximum likelihood inference on five real-world datasets and showthat a simple hill climbing-based optimisation efficiently traverses thevastness of tree space from a random to an optimal tree.

Phylo2Vec: a vector representation for binary trees