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Session S34 - Symbolic and Numerical Computation with Polynomials

Wednesday, July 14, 14:30 ~ 15:00 UTC-3

Distance to the stochastic part of phylogenetic varieties

Marina Garrote-López

Universitat Politècnica de Catalunya, Spain   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The main goal of phylogenetic reconstruction is to recover the evolutionary history of a group of living species by using solely the information of their genome. 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 distribution at the leaves of the trees and one might be able to obtain polynomial relationships among the probabilities of different characters. The study of these polynomials and the geometry 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 with biological sense and explore the extent to which restricting to these subsets can provide insight into existent methods of phylogenetic reconstruction. We will analyse the projection into these subsets, which can be seen as an optimization problem and can be solved using nonlinear programming algorithms. As these algorithms do not guarantee a global solution, we use a different approach that allows us to find a global optimum. Numerical algebraic geometry and computational algebra play a fundamental role here. We will show some results on trees evolving under groups-based models and, in particular, we will explore the long-branch attraction phenomenon.

Joint work with Marta Casanellas (Universitat Politècnica de Catalunya) and Jesús Fernández-Sánchez (Universitat Politècnica de Catalunya).

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