Semi-algebraic phylogenetic reconstruction

Phylogenetics studies the evolutionary history of species on our planet. The evolution of species can be represented in a phylogenetic tree in which the leaves represent the current species and the interior nodes represent their common ancestors. This study is based on the genome of species and it applies not only to the study of evolutionary relationships among organisms that host genes, but also to the study of genes themselves, making phylogenetics a useful tool to determine the origin of pathogens or for the traceability of cancer cells, among other applications.

To model evolution, DNA sequences are often assumed to evolve according to a Markov process in a phylogenetic tree governed by a model of nucleotide substitutions. These processes can be viewed as polynomial maps in terms of the substitution parameters and the study of these maps and the algebraic varieties parameterized by them can be used to reconstruct phylogenetic trees. In this talk we will also see that the addition of semi-algebraic conditions that characterize those biologically meaningful points in the varieties can improve phylogenetic reconstruction methods. Finally, we will present results of new phylogenetic reconstruction methods on real and simulated data.