Department of Statistics, The Ohio State University
Statistics and Biostatistics Colloquium Series

Graphs are used to represent a variety of relationships among biological data. The phylogenetic tree is one such graph whose purpose is to convey the pattern of descent relating a collection of species. On a phylogenetic tree, extant species are positioned as leaves, or pendent vertices in the language of graph theory. Crucially, ancestral species populate the interior of this graph and by definition are not observed. The goal of phylogenetic reconstruction is to identify from data where the speciation events away from these common ancestors have occurred, thereby recovering the latent structure of the tree. This talk is concerned with the recovery of such latent structure using the machinery of spectral graph theory. I first show how a celebrated result of Miroslav Fiedler on the use of eigenvectors to cut graphs extends to the latent tree case where only the pendent vertices have been supplied. I then discuss how this extension can be used in practice to reconstruct a phylogeny from pairwise distance data. Finally, I connect these results to an application of classical multidimensional scaling in numerical taxonomy. I will attempt to argue that, at least for treelike data, multidimensional scaling can be seen as inferential as well as descriptive. This is joint work with Alexander Griffing.

Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.