Molecular phylogenetic reconstruction aim at recovering the evolutionary tree (or phylogeny) of a set of homologous sequences. The maximum likelihood method seems to be the most reliable approach. Unfortunately, the computing time required by classical methods to pinpoint the phylogeny of maximum likelihood quickly becomes unacceptable as the number of sequences increases. Therefore, such methods cannot deal with large data sets. Two kinds of methods are available for reconstructing large phylogenies according to the maximum likelihood principle: distance based methods and quartet methods. Both divide the original problem in sub-problems made of few sequences that they can rapidly solve (according to the maximum likelihood principle). They then combine the solution of those sub-problems in a solution to the original one. After a presentation of main phylogenetic reconstruction methods, we describe a new quartet method (Weight Optimization) that has both better theoretical properties and better topological accuracy than Quartet Puzzling (a widely used quartet method). We then explain why quartet methods are not adapted to infer large phylogenies according to the maximum likelihood principle and how they can be used, efficiently, to solve other kind of problems. Finally, we propose an approach combining distance methods and maximum likelihood in an original way. This approach, called TripleML, improves the reliability of distance-based methods by replacing the distance they use by distances obtained via a local optimization of the likelihood of triplets of taxa (or set of taxa).
