Mean and Variance of Phylogenetic Trees

TL;DR

This paper introduces the use of Frechet mean and variance in BHV treespace for summarizing phylogenetic tree diversity, demonstrating their advantages over traditional methods in speed, precision, and robustness.

Contribution

It presents a novel application of Frechet mean and variance in BHV treespace, offering more robust and efficient summaries of phylogenetic trees compared to existing methods.

Findings

Frechet mean is comparable to other summary methods.

Frechet variance is faster and more precise.

Frechet mean tends to be more binary than consensus trees.

Abstract

We describe the use of the Frechet mean and variance in the Billera-Holmes-Vogtmann (BHV) treespace to summarize and explore the diversity of a set of phylogenetic trees. We show that the Frechet mean is comparable to other summary methods, and, despite its stickiness property, is more likely to be binary than the majority-rules consensus tree. We show that the Frechet variance is faster and more precise than commonly used variance measures. The Frechet mean and variance are more theoretically justified, and more robust, than previous estimates of this type, and can be estimated reasonably efficiently, providing a foundation for building more advanced statistical methods and leading to applications such as mean hypothesis testing.