Graduate Computational Algebraic Geometry Seminar
Sonja Petrovic
UIC
Identifiability of phylogenetic mixtures
Abstract: This talk will present recent results on model parameter
identifiability for algebraic statistical models arising in
phylogenetics.
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. 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 two relevant models. We also prove
that generic substitution parameters for one of the mixture models are
identifiable, and for two other 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.
Joint work with Elizabeth Allman, John Rhodes, and Seth Sullivant.
Thursday April 1, 2010 at 11:00 AM in SEO 612