Distances between Extension Spaces of Phylogenetic Trees

TL;DR

This paper introduces a new method to measure distances between phylogenetic trees with different leaf sets using BHV extension spaces, enabling analysis of diverse gene trees.

Contribution

It defines a novel distance metric for trees with non-identical leaves and develops a gradient algorithm to compute it efficiently.

Findings

The algorithm scales well with large datasets.

Applied to gene trees across multiple life domains.

Provides an interpretable approach to evolutionary divergence.

Abstract

Phylogenetic trees summarize evolutionary relationships between organisms, and tools to analyze collections of phylogenetic trees enable contrasts between different genes' ancestry. The BHV metric space has enabled the analysis of collections of trees that share a common set of leaves, but many genes are not shared, even between closely related species. BHV extension spaces represent trees with non-identical leaf sets in a common BHV space, but limited analytical tools exist for extension spaces. We define the distance between two phylogenetic trees with non-identical leaf sets as the shortest BHV distance between their extension spaces, and develop a reduced gradient algorithm to compute this distance. We study the scalability of our algorithm and apply it to analyze gene trees spanning multiple domains of life. Our distance and algorithm offer a fully general, interpretable approach to analyzing both ancient and recent evolutionary divergence.