Zusammenfassung für den Vortrag am 14.10.2021 (14:00 Uhr)Seminar on Nonlinear Algebra
Marina Garrote-López (MPI MIS, Leipzig)
Algebraic and semi-algebraic phylogenetic reconstruction
To model evolution, one usually assumes that DNA sequences evolve according to a Markov process on a phylogenetic tree ruled by a model of nucleotide substitutions. This allows to define a joint distribution at the leaves of the trees and to obtain polynomial relationships among these joint probabilities. The study of these polynomials and of the algebraic varieties defined by them can be used to reconstruct phylogenetic trees.
However, not all points in these algebraic varieties have biological sense. In this talk, we will discuss the importance of studying the subset of these varieties that has biological sense and we will prove that, in some cases, considering this subset is fundamental for the phylogenetic reconstruction problem. Finally, we will present a new phylogenetic quartet reconstruction method which is based on the algebraic and semi-algebraic description of distributions that arise from the general Markov model on a quartet tree.