Most phylogenetic analyses result in a sample of trees, but summarizing and visualizing these samples can be challenging. Consensus trees often provide limited information about a sample, and so methods such as consensus networks, clustering and multidimensional scaling have been developed and applied to tree samples. This paper describes a stochastic algorithm for constructing a principal geodesic or line through treespace which is analogous to the first principal component in standard principal components analysis. A principal geodesic summarizes the most variable features of a sample of trees, in terms of both tree topology and branch lengths, and it can be visualized as an animation of smoothly changing trees. The algorithm performs a stochastic search through parameter space for a geodesic which minimizes the sum of squared projected distances of the data points. This procedure aims to identify the globally optimal principal geodesic, though convergence to locally optimal geodesics is possible. The methodology is illustrated by constructing principal geodesics for experimental and simulated data sets, demonstrating the insight into samples of trees that can be gained and how the method improves on a previously published approach. A java package called GeoPhytter for constructing and visualizing principal geodesics is freely available from www.ncl.ac.uk/ ntmwn/geophytter.

SUMMARY: We describe an algorithm and software tool for comparing alternative phylogenetic trees. The main application of the software is to compare phylogenies obtained using different phylogenetic methods for some fixed set of species or obtained using different gene sequences from those species. The algorithm pairs up each branch in one phylogeny with a matching branch in the second phylogeny and finds the optimum 1-to-1 map between branches in the two trees in terms of a topological score. The software enables the user to explore the corresponding mapping between the phylogenies interactively, and clearly highlights those parts of the trees that differ, both in terms of topology and branch length. AVAILABILITY: The software is implemented as a Java applet at http://www.mrc-bsu.cam.ac.uk/personal/thomas/phylo_comparison/comparison_page.html. It is also available on request from the authors.

MOTIVATION: Several methods have recently been developed to analyse large-scale sets of physical interactions between proteins in terms of physical contacts between the constituent domains, often with a view to predicting new pairwise interactions. Our aim is to combine genomic interaction data, in which domain-domain contacts are not explicitly reported, with the domain-level structure of individual proteins, in order to learn about the structure of interacting protein pairs. Our approach is driven by the need to assess the evidence for physical contacts between domains in a statistically rigorous way. RESULTS: We develop a statistical approach that assigns p-values to pairs of domain superfamilies, measuring the strength of evidence within a set of protein interactions that domains from these superfamilies form contacts. A set of p-values is calculated for SCOP superfamily pairs, based on a pooled data set of interactions from yeast. These p-values can be used to predict which domains come into contact in an interacting protein pair. This predictive scheme is tested against protein complexes in the Protein Quaternary Structure (PQS) database, and is used to predict domain-domain contacts within 705 interacting protein pairs taken from our pooled data set.