A combinatorial method for connecting BHV spaces representing different numbers of taxa

TL;DR

This paper introduces a combinatorial approach to connect BHV tree spaces of different dimensions, enabling the comparison and integration of phylogenetic trees with varying numbers of taxa within a unified framework.

Contribution

It presents a novel combinatorial method for transitioning between BHV tree spaces of different maximal dimensions, facilitating tree comparison and consensus methods.

Findings

Enables transition between BHV spaces with different taxa counts

Removes obstacles for embedding problems like supertree and consensus

Supports integration of trees with varying numbers of taxa

Abstract

The phylogenetic tree space introduced by Billera, Holmes, and Vogtmann (BHV tree space) is a CAT(0) continuous space that represents trees with edge weights with an intrinsic geodesic distance measure. The geodesic distance measure unique to BHV tree space is well known to be computable in polynomial time, which makes it a potentially powerful tool for optimization problems in phylogenetics and phylogenomics. Specifically, there is significant interest in comparing and combining phylogenetic trees. For example, BHV tree space has been shown to be potentially useful in tree summary and consensus methods, which require combining trees with different number of leaves. Yet an open problem is to transition between BHV tree spaces of different maximal dimension, where each maximal dimension corresponds to the complete set of edge-weighted trees with a fixed number of leaves. We show a combinatorial method to transition between copies of BHV tree spaces in which trees with different numbers of taxa can be studied, derived from its topological structure and geometric properties. This method removes obstacles for embedding problems such as supertree and consensus methods in the BHV treespace framework.