Practical guidelines for Bayesian phylogenetic inference using Markov chain Monte Carlo (MCMC)

Phylogenetic estimation is, and has always been, a complex endeavor. Estimating a phylogenetic tree involves evaluating many possible evolutionary histories that could explain a set of observed data, typically by using a model of evolution. Values for all model parameters need to be estimated as well. Bayesian phylogenetic inference is a state-of-the-art statistical method which allows us to co-estimate a phylogeny, evolutionary parameters, and obtain a detailed representation of the uncertainty associated with the estimates. Bayesian inferences commonly involve complex demographic models for the estimation of a tree, or incorporate data beyond genetic sequences, such as information from the fossil record. All Bayesian phylogenetic tree estimation software use the Markov Chain Monte Carlo (MCMC) algorithm, a method for approximating the posterior distribution of parameters in a mathematical model. While many researchers use MCMC in phylogenetic analyses, interpreting results and diagnosing problems with MCMC remain vexing issues to many biologists. We thus offer an overview of how MCMC is used in Bayesian phylogenetic inference, with a particular emphasis on complex hierarchical models, such as the fossilized birth-death (FBD) model. We will discuss strategies to diagnose common MCMC problems and troubleshoot difficult analyses, in particular convergence issues. We will show how the study design, the choice of models and priors, but also technical features of the inference tools themselves can all be adjusted to obtain the best results. Finally, we will also discuss the unique challenges created by the incorporation of fossil information in phylogenetic inference, and present tips to address them.