Mean and Variance of Phylogenetic Trees

Understand

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.