Fredrik Ronquist

Efficiency of Markov chain Monte Carlo tree proposals in Bayesian phylogenetics.

The main limiting factor in Bayesian MCMC analysis of phylogeny is typically the efficiency with which topology proposals sample tree space. Here we evaluate the performance of seven different proposal mechanisms, including most of those used in current Bayesian phylogenetics software. We sampled 12 empirical nucleotide data sets--ranging in size from 27 to 71 taxa and from 378 to 2,520 sites--under difficult conditions: short runs, no Metropolis-coupling, and an oversimplified substitution model producing difficult tree spaces (Jukes Cantor with equal site rates). Convergence was assessed by comparison to reference samples obtained from multiple Metropolis-coupled runs. We find that proposals producing topology changes as a side effect of branch length changes (LOCAL and Continuous Change) consistently perform worse than those involving stochastic branch rearrangements (nearest neighbor interchange, subtree pruning and regrafting, tree bisection and reconnection, or subtree swapping). Among the latter, moves that use an extension mechanism to mix local with more distant rearrangements show better overall performance than those involving only local or only random rearrangements. Moves with only local rearrangements tend to mix well but have long burn-in periods, whereas moves with random rearrangements often show the reverse pattern. Combinations of moves tend to perform better than single moves. The time to convergence can be shortened considerably by starting with a good tree, but this comes at the cost of compromising convergence diagnostics based on overdispersed starting points. Our results have important implications for developers of Bayesian MCMC implementations and for the large group of users of Bayesian phylogenetics software.

The Phylogenetic Handbook: Bayesian phylogenetic analysis using MRBAYES

What is the probability that Sweden will win next year’s world championships in ice hockey? If you’re a hockey fan, you probably already have a good idea, but even if you couldn’t care less about the game, a quick perusal of the world championship medalists the last 15 years (Table 7.1) would allow you to make an educated guess. Clearly, Sweden is one of only a small number of teams that compete successfully for the medals. Let’s assume that all seven medalists the last 15 years have the same chance of winning, and that the probability of an outsider winning is negligible. Then the odds of Sweden winning would be 1:7 or 0.14. We can also calculate the frequency of Swedish victories in the past. Two gold medals in 15 years would give us the number 2:15 or 0.13, very close to the previous estimate. The exact probability is difficult to determine but most people would probably agree that it is likely to be in the vicinity of these estimates. You can use this information to make sensible decisions. If somebody offered you to bet on Sweden winning the world championships at the odds 1:10, for instance, you might not be interested because the return on the bet would be close to your estimate of the probability. However, if you were offered the odds 1:100, you might be tempted to go for it, wouldn’t you? As the available information changes, you are likely to change your assessment of the probabilities. Let’s assume, for instance, that the Swedish team made it to