Overview
Bayesian phylogenetics provides a probabilistic framework for inferring evolutionary trees by combining prior knowledge with observed sequence data through Bayes’ theorem. Rather than returning a single best tree, it produces a posterior distribution over tree topologies, branch lengths, and substitution model parameters. This distribution quantifies the uncertainty inherent in phylogenetic inference, allowing researchers to assign posterior probabilities to individual clades. The complexity of the parameter space necessitates Markov chain Monte Carlo (MCMC) sampling, which explores thousands or millions of trees and parameter values.
Key Concepts
MCMC algorithms, typically Metropolis-Hastings or Gibbs sampling, generate a chain of correlated samples from the posterior distribution. Convergence is assessed using diagnostics such as effective sample size (ESS) and potential scale reduction factor (PSRF). A burn-in period discards early samples before the chain reaches stationarity. Posterior probabilities on clades represent the proportion of sampled trees containing that clade and are more intuitive than bootstrap support values. The prior distribution can incorporate external information, such as fossil calibrations for molecular dating.
Practical Workflow
A Bayesian phylogenetic analysis in MrBayes begins by reading a sequence alignment in NEXUS format and specifying the substitution model, typically the best-fit model identified by ModelTest or jModelTest based on AIC. The MCMC settings are configured with two independent runs, each with four chains (one cold and three heated), to improve sampling of the posterior landscape. The analysis runs for 1–10 million generations with sampling every 1,000 generations. Convergence assessment is performed using the standard deviation of split frequencies (SDSF), which should approach values below 0.01 as the two runs converge on similar tree topologies. MrBayes outputs a parameter file that is examined in Tracer to confirm that effective sample sizes (ESS) exceed 200 for all continuous parameters, low ESS values indicate poor mixing and necessitate longer runs. The first 10–25% of samples are discarded as burn-in. Posterior probabilities for each clade are read directly from the consensus tree: values above 0.95 are considered strongly supported, 0.90–0.95 moderately supported, and below 0.90 weak. For BEAST analyses, the BEAUti interface provides step-by-step configuration of data partitions, clock models, and tree priors, with the added capability of estimating divergence times under relaxed clock models. Bayesian posterior probabilities are generally interpreted as the probability that a clade is true given the data and the model, distinct from bootstrap support, which measures reproducibility. Reporting the full posterior distribution rather than a single point estimate is a key advantage of the Bayesian framework.
Applications
Bayesian phylogenetics is particularly valued when uncertainty assessment is critical, such as in conservation genetics, epidemiological forecasting, and species delimitation. It excels at integrating multiple data types, including morphological characters and stratigraphic ranges. In practice, Bayesian analyses complement DNA sequencing studies and scale well with data from next-generation sequencing. They are frequently applied to resolve relationships in bacterial genetics, where horizontal gene transfer and recombination create conflicting phylogenetic signals that Bayesian models can accommodate.
