Graduate Computational Algebraic Geometry Seminar
Sonja Petrovic
UIC
Identifiability of two-tree mixtures under group-based models
Abstract: Phylogenetic data arising on two possibly different tree topologies might be mixed through several biological mechanisms, including incomplete lineage sorting
or horizontal gene transfer in the case of different topologies, or simply different substitution processes on characters in the case of the same topology.
Recent work on a 2-state symmetric model of character change showed such a mixture model has non-identifiable parameters, and thus it is theoretically
impossible to determine the two tree topologies from any amount of data under such circumstances.
In joint work with Allman, Rhodes and Sullivant, we investigate the question of identifiability for 2-tree mixtures of the 4-state group-based models, which
are more relevant to DNA sequence data. Using algebraic techniques, we show that the tree parameters are identifiable for the JC and K2P models. We also prove
that generic substitution parameters for the JC mixture models are identifiable, and for the K2P and K3P models obtain generic identifiability results for
mixtures on the same tree. This indicates that the full phylogenetic signal remains in such mixtures, and that the 2-state symmetric result is thus a
misleading guide to the behavior of other models.
The talk will be accessible to a general audience.
Thursday February 3, 2011 at 10:00 AM in SEO 1227