Sampling phylogenetic tree space with the generalized Gibbs sampler

A recent article published in Cladistics is critical of a number of heuristic methods for phylogenetic inference based on parsimony scores. One of my papers is among those criticized, and I would appreciate the opportunity to make a public response. The specific criticism is that I have re-invented an algorithm for economizing parsimony calculations on trees that differ by a subtree pruning and regrafting (SPR) rearrangement. This criticism is justified, and I apologize for incorrectly claiming originality for my presentation of this algorithm. However, I would like to clarify the intent of my paper, if I can do so without detracting from the sincerity of my apology. My paper is not about that algorithm, nor even primarily about parsimony. Rather, it is about a novel strategy for Markov chain Monte Carlo (MCMC) sampling in a state space consisting of trees. The sampler involves drawing from conditional distributions over sets of trees: a Gibbs-like strategy that had not previously been used to sample tree-space. I would like to see this technique incorporated into MCMC samplers for phylogenetics, as it may have advantages over commonly used Metropolis-like strategies. I have recently used it to sample phylogenies of a biological invasion, and I am finding many applications for it in agent-based Bayesian ecological modelling. It is thus my contention that my 2005 paper retains substantial value.