A consensus tree method takes a collection of phylogenetic trees and outputs a single “representative” tree. The first consensus method was proposed by Adams in 1972. Since then a large variety of different methods have been developed, and there has been considerable debate over how they should be used. This paper has two goals. First, we survey the main consensus tree methods used in phylogene...

We study the problem of distinguishing between two distributions on a metric space; i.e., given metric measure spaces (X, d, μ1) and (X, d, μ2), we are interested in the problem of determining from finite data whether or not μ1 is μ2. The key is to use pairwise distances between observations and, employing a reconstruction theorem of Gromov, we can perform such a test using a two sample Kolmogo...

The Yule (pure-birth)model is the simplest nullmodel of speciation; each lineage gives rise to a new lineage independentlywith the same rateλ.We investigate the expected length of an edge chosen at random from the resulting evolutionary tree. In particular, we compare the expected length of a randomly selected edge with the expected length of a randomly selected pendant edge.We provide some exa...

As the number of sequenced genomes has grown, we have become increasingly aware of the impact of horizontal gene transfer on our understanding of genome evolution. Methods for detecting horizontal gene transfer from sequence abound. Among the most accurate are methods based on phylogenetic tree inference, but even these can perform poorly in some cases, such as when multiple trees fit the data ...

Amalgamating smaller evolutionary trees into a single parent tree is an important task in evolutionary biology. Traditionally, the (supertree) methods used for this amalgamation take a collection of leaf-labelled trees as their input. However, it has been recently highlighted that, in practice, such an input is somewhat limiting and that one would like supertree methods for collections of trees...

We study the geometry of metrics and convexity structures on the space of phylogenetic trees, which is here realized as the tropical linear space of all ultrametrics. The CAT(0)-metric of Billera-Holmes-Vogtman arises from the theory of orthant spaces. While its geodesics can be computed by the Owen-Provan algorithm, geodesic triangles are complicated. We show that the dimension of such a trian...

The path-difference metric is one of the oldest distances for the comparison of fully resolved phylogenetic trees, but its statistical properties are still quite unknown. In this paper we compute the mean value of the square of the path-difference metric between two fully resolved rooted phylogenetic trees with n leaves, under the uniform distribution. This complements previous work by Steel an...

A (pseudo-)metric D on a finite set X is said to be a ‘tree metric’ if there is a finite tree with leaf set X and nonnegative edge weights so that, for all x, y ∈ X , D(x, y) is the path distance in the tree between x and y. It is well known that not every metric is a tree metric. However, when some such tree exists, one can always find one whose interior edges have strictly positive edge weigh...