Title: Comparing Trees using Distances, Trees and Multidimensional Scaling
Speaker: Susan Holmes (Stanford)
Abstract: Distances between trees have useful applications in combining phylogenetic trees built from multiple genes and in studying trees built from bootstrap samples and Bayesian posterior distributions. Until recently, computations of the distance between trees was intractable. We have developed an R package to compute the distance between trees based on a polynomial algorithm by M. Owen and S. Provan. Using this distance we are able to project trees from data with varying mutation rates, compare hierarchical clustering trees for Microarrays, and study influence functions for the data used to build the trees. The main tool for using the distances is multidimensional scaling, although the original tree metric delivers a treespace which is not Euclidean, it is itself negatively curved, the Euclidean approximations provided by MDS are very useful for making low dimensional graphics of tree projections. (This is joint work with John Chakerian)