Our understanding of the origins, the functions and/or the structures of biological sequences strongly depends on our ability to decipher the mechanisms of molecular evolution. These complex processes can be described through the comparison of homologous sequences in a phylogenetic framework. Moreover, phylogenetic inference provides sound statistical tools to exhibit the main features of molecular evolution from the analysis of actual sequences. This chapter focuses on phylogenetic tree estimation under the maximum likelihood (ML) principle. Phylogenies inferred under this probabilistic criterion are usually reliable and important biological hypotheses can be tested through the comparison of different models. Estimating ML phylogenies is computationally demanding, and careful examination of the results is warranted. This chapter focuses on PhyML, a software that implements recent ML phylogenetic methods and algorithms. We illustrate the strengths and pitfalls of this program through the analysis of a real data set. PhyML v3.0 is available from (http://atgc_montpellier.fr/phyml/).
