Gromov meets Phylogenetics - new Animals for the Zoo of Biocomputable Metrics on Tree Space

TL;DR

This paper introduces a new class of metrics for unrooted phylogenetic trees based on Gromov-Hausdorff distance, which are computationally efficient, robust under NNI-operations, and exhibit unique local behavior.

Contribution

The paper proposes novel Gromov-Hausdorff based metrics for phylogenetic trees that are efficiently computable and distinct from existing metrics, with analysis of their performance.

Findings

Metrics can be computed via linear or quadratic programming.

Metrics are robust under NNI-operations.

Performance analyzed on random trees and caterpillars.

Abstract

We present a new class of metrics for unrooted phylogenetic $X$-trees derived from the Gromov-Hausdorff distance for (compact) metric spaces. These metrics can be efficiently computed by linear or quadratic programming. They are robust under NNI-operations, too. The local behavior of the metrics shows that they are different from any formerly introduced metrics. The performance of the metrics is briefly analised on random weighted and unweighted trees as well as random caterpillars.