Dimensions of phylogenetic network varieties

Abstract: Phylogenetic networks provide a means of describing the evolutionary history of taxa that have undergone “horizontal” events, such as hybridization or lateral gene transfer. The mutation process of a single site in shared DNA sequence for a set of such taxa can be modelled as a Markov process on a phylogenetic network, and the site-pattern probability distributions from such a model can be viewed as a projective variety. In this work, we have given an explicit description of the dimension of this variety for a given level-1 phylogenetic network under any group-based model of evolution. I will give an overview of the model from an algebraic perspective and describe our results, focussing on the toric fiber product of two ideals, and finish with some applications to identifiability problems. Joint work with Elizabeth Gross and Robert Krone.

Mathematics

Audience: researchers in the discipline

ANTLR seminar

Series comments: This is the Algebra, Number Theory, Logic and Representation theory seminar.