The parsimony score of a character on a tree equals the number of state changes required to fit that character onto the tree. We show that for unordered, reversible characters this score equals the number of tree rearrangements required to fit the tr
ee onto the character. We discuss implications of this connection for the debate over the use of consensus trees or total evidence, and show how it provides a link between incongruence of characters and recombination.
We derive an invertible transform linking two widely used measures of species diversity: phylogenetic diversity and the expected proportions of segregating (non-constant) sites. We assume a bi-allelic, symmetric, finite site model of substitution. Li
ke the Hadamard transform of Hendy and Penny, the transform can be expressed completely independent of the underlying phylogeny. Our results bridge work on diversity from two quite distinct scientific communities.
The Robinson-Foulds (RF) distance is by far the most widely used measure of dissimilarity between trees. Although the distribution of these distances has been investigated for twenty years, an algorithm that is explicitly polynomial time has yet to b
e described for computing this distribution (which is also the distribution of trees around a given tree under the popular Robinson-Foulds metric). In this paper we derive a polynomial-time algorithm for this distribution. We show how the distribution can be approximated by a Poisson distribution determined by the proportion of leaves that lie in `cherries of the given tree. We also describe how our results can be used to derive normalization constants that are required in a recently-proposed maximum likelihood approach to supertree construction.
The Hadamard transform of cite{Hendy89a, Hendy89} provides a way to work with stochastic models for sequence evolution without having to deal with the complications of tree space and the graphical structure of trees. Here we demonstrate that the tran
sform can be expressed in terms of the familiar $bP[bt] = e^{bQ[bt]}$ formula for Markov chains. The key idea is to study the evolution of vectors of states, one vector entry for each taxa; we call this the $n$-taxon process. We derive transition probabilities for the process. Significantly, the findings show that tree-based models are indeed in the family of (multi-variate) exponential distributions.
