  Recent years have seen a rapid expansion of the model space explored in
statistical phylogenetics, emphasizing the need for new approaches to
statistical 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 for model representation lowers the
barrier for beginners and non-specialists to grasp complex phylogenetic models,
including their assumptions and parameter/variable dependencies.
  Graphical modeling is a unifying framework that has gained in popularity in
the statistical literature in recent years. The core idea is to break complex
models into conditionally independent distributions. The strength lies in the
comprehensibility, flexibility, and adaptability of this formalism, and the
large body of computational work based on it. Graphical models are well-suited
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 introduce modules to simplify the representation of standard
components in large and complex models. Phylogenetic model graphs can be
readily used in simulation, maximum likelihood inference, and Bayesian
inference using, for example, Metropolis-Hastings or Gibbs sampling of the
posterior distribution.
