Recent years have seen a rapid expansion of the model space explored in statistical phylogenetics, emphasizing the need for new approaches to model representation and software development. Clear communication and representation of the chosen model is crucial for: (1) reproducibility of an analysis, (2) model development and (3) software design. Moreover, a unified, clear and understandable framework formodel representation lowers the barrier for beginning scientists and non-specialists to grasp the model including the assumptions and parameter/variable dependencies.

Graphical models is such a unifying framework that has gained in popularity in the statistical literature in recent years. The core idea isto break complex models into conditionally independent distributions and the strength lies in, amongst others: comprehensibility, flexibility, adaptability and computational algorithms. Graphical models can be used to teach statistical models, to facilitate communication among phylogeneticists and in the development of generic software for simulation and statistical inference.

Here, we provide an introduction to graphical models for phylogeneticists and extend the standard graphical model representation to the realm of phylogenetics. We introduce a new graphical model component, tree plates, to capture the changing structure of the subgraph corresponding to a phylogenetic tree. We describe a range of phylogenetic models using the graphical model framework and built these into separate, interchangeable modules. Phylogenetic model graphs can be readily used in simulation, maximum likelihood inference, and Bayesian inference using either Metropolis-Hastings or Gibbs sampling of the posterior distribution.