Colby Long, Ph.D.

Title: Algebraic Invariants in Phylogenetics

Abstract.  Phylogenetics is the study of the evolutionary relationships among organisms. A central challenge in the field is to use biological data for a given set of organisms in order to determine the evolutionary tree that describes their history. One approach for doing so is to build tree-based models of DNA sequence evolution and then to select the model that best fits the data according to some criteria. Once a model is selected, the tree parameter of the model is assumed to describe the history of the taxa under consideration. However, in order for such a method to be reliable, the tree parameter of the model must be identifiable.  In this talk, we will discuss how phylogenetic invariants, algebraic relationships among DNA site-pattern frequencies, can be used to establish model identifiability. We’ll also discuss some invariants-based methods for phylogenetic inference.