A road map for phylogenetic models of species trees.

The field of phylogenetics has burgeoned into a great diversity of statistical models, providing researchers with a vast amount of analytical tools for investigating the evolutionary theory. This abundance of theoretical work has the merit that many different aspects of evolution can be investigated using various types of data. However, empiricists may sometimes struggle to find the right model for their needs amid such variety. In particular, some computer programs gather the theory of many different models, published in hundreds of different papers, within the same operational framework. This makes it particularly difficult for users to obtain comprehensive information about the assumptions and structure of various models. Yet, a large part of phylogenetic models are structured in individual modules that can be linked together in the same conceptual framework, akin to some sort of phylogenetic supermodel. In this paper, we propose to browse through the network of phylogenetic models, emphasizing their modular structure, with the purpose to outline the commonalities and differences of individual models. Focusing on probabilistic models, we describe how to go from the model assumptions to the corresponding probability distributions as pedagogically as possible. To achieve this task, we resort heavily on graph theory to represent the probabilistic relationships among parameters and data, and present the models in their most elementary form (i.e. including parameters that are generally marginalized out), which simplifies the mathematics considerably. We concentrate on models designed for species trees, but evoke the link with other types of trees (e.g. gene trees).