Phylogenetics and rank of matrices

Abstract

Phylogenetics is the study of the evolutionary relationships of a group of species, and it is usually inferred from the DNA sequences of a set of living species. Thanks to the model developed by Darwin based on natural selection, we can construct phylogenetics trees that relate a set of contemporary species. Thus phylogenetics tries to reconstruct these trees. In order to do it is necessary to model evolution adopting a parametric statistic model. Using these models one is able to deduce polynomial relationships between the parameters of our model, known as phylogenetic invariants. The main goal of this work is to understand the relationship between phylogenetics and these algebraic techniques and to prove that using the rank of certain matrices we can find phylogenetic invariants that are useful for tree reconstruction.