Data from: Properties of Markov chain Monte Carlo performance across many empirical alignments --part II

Nearly all current Bayesian phylogenetic applications rely on Markov chain
Monte Carlo (MCMC) methods to approximate the posterior distribution for
trees and other parameters of the model. These approximations are only
reliable if Markov chains adequately converge and sample from the joint
posterior distribution. While several studies of phylogenetic MCMC
convergence exist, these have focused on simulated datasets or select
empirical examples. Therefore, much that is considered common knowledge
about MCMC in empirical systems derives from a relatively small family of
analyses under ideal conditions. To address this, we present an overview
of commonly applied phylogenetic MCMC diagnostics and an assessment of
patterns of these diagnostics across more than 18,000 empirical analyses.
Many analyses appeared to perform well and failures in convergence were
most likely to be detected using the average standard deviation of split
frequencies, a diagnostic that compares topologies among independent
chains. Different diagnostics yielded different information about failed
convergence, demonstrating that multiple diagnostics must be employed to
reliably detect problems. The number of taxa and average branch lengths in
analyses have clear impacts on MCMC performance, with more taxa and
shorter branches leading to more difficult convergence. We show that the
usage of models that include both Γ-distributed among-site rate variation
and a proportion of invariable sites are not broadly problematic for MCMC
convergence but are also unnecessary. Changes to heating and the usage of
model-averaged substitution models can both offer improved convergence in
some cases, but neither are a panacea.