Linear invariants for the equal-input evolutionary model

Abstract

Mathematical models for describing biological systems are becoming more and more important nowadays. In this thesis we will study Markov processes on phylogenetic trees and deeply study the equal-input model, which is the first non-trivial model that presents the interesting properties of simple models. We will study widely this model, talking about its invariants, computing the linear ones for the case of n = 5 and studying the linear equations that satisfy all the distributions arising from it. We will also talk about some notions of phylogenetic trees and the distinction between topology and model invariants, understanding the generalization of these processes to phylogenetic mixtures.