Mean and Variance of Phylogenetic Trees

Abstract.— We describe the use of the Fréchet 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 Fréchet mean is comparable to other summary methods, despite its stickiness property, and that the Fréchet variance is faster and more precise than commonly used variance measures. These mean and variance measures are more theoretically justified, and more robust, than previous estimates of this type, and can be estimated reasonably efficiently. This leads to applications such as mean hypothesis testing. (