Stochasticity conditions for Phylogenetic Reconstruction

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Sala Seminari "-1"
Ore: 14:30

Relatrice: 

• Marina Garrote López (CRM Barcelona)

Abstract:

Strong evidences suggest that all living organisms share a common ancestor and therefore are related by evolutionary relationships. These relationships are usually expressed in the form of a phylogenetic tree.
Nowadays there are more and more mathematicians and statisticians who collaborate with biologists in order to solve the major problems of phylogenetics. Many different areas of mathematics are involved in phylogenetic studies and recently developed techniques from algebraic geometry have already been used in the study of phylogenetic reconstruction methods.
One main goal of phylogenetic reconstruction is recovering the ancestral relationships among a group of current species. In order to reconstruct phylogenetic trees it is usual to model evolution adopting a parametric statistical model which allows us to define a joint probability distribution at the leaves of the trees. When these models are algebraic, one is able to deduce polynomial relationships between these probabilities, known as phylogenetic invariants. One can study these polynomials and the geometry of the algebraic varieties that arise from them and use it to reconstruct phylogenetic trees.
There is a special situation when these theoretical probabilities can be placed into a matrix that has to be positive-semidefinite of low rank, say k, in order to correspond to a distribution arising from a hidden Markov process on a certain phylogenetic tree with stochastic parameters. The corresponding (k+1)-minors are phylogenetic invariants and their vanishing provide interesting information about the tree topology. But unfortunately these conditions and polynomial relationships are not always satisfied when working with real or simulated data. In this talk we will discuss how can we deal with this data and theoretical conditions and the importance of the stochasticity of the parameters in phylogenetic inference.
The aim of our research is to use phylogenetic invariants and the stochasticity of the parameters of the general Markov model to provide insight into phylogenetic inference and to design new methods for phylogenetic reconstruction.

Contact person: Claudio Fontanari