Data from: Quantifying MCMC exploration of phylogenetic tree space

In order to gain an understanding of the effectiveness of phylogenetic
Markov chain Monte Carlo (MCMC), it is important to understand how quickly
the empirical distribution of the MCMC converges to the posterior
distribution. In this paper we investigate this problem on phylogenetic
tree topologies with a metric that is especially well suited to the task:
the subtree prune-and-regraft (SPR) metric. This metric directly
corresponds to the minimum number of MCMC rearrangements required to move
between trees in common phylogenetic MCMC implementations. We develop a
novel graph-based approach to analyze tree posteriors and find that the
SPR metric is much more informative than simpler metrics that are
unrelated to MCMC moves. In doing so we show conclusively that topological
peaks do occur in Bayesian phylogenetic posteriors from real data sets as
sampled with standard MCMC approaches, investigate the efficiency of
Metropolis-coupled MCMC (MCMCMC) in traversing the valleys between peaks,
and show that conditional clade distribution (CCD) can have systematic
problems when there are multiple peaks.