Evaluation of proposal distributions on clock-constrained trees in Bayesian phylogenetic inference

Bayesian Markov chain Monte Carlo (MCMC) has become one of the principle methods of performing phylogenetic inference. Implementing the Markov chain Monte Carlo algorithm requires the definition of a proposal distribution which defines a transition kernel over the state space. The precise form of this transition kernel has a large impact on the computational efficiency of the algorithm. In this paper we investigate the efficiency of a number of different proposal distributions for clock-constrained phylogenetic trees (i.e. constrained by a strict or relaxed molecular clock). Clock-constrained trees have become increasingly important in phylogenetic inference, especially in the context of divergence time estimation and their constraints require substantially different proposal algorithms to unrooted phylogenetic trees. We investigated the efficiency of seven proposal moves on clock-constraint trees first on a small data set and then on six additional data sets. In contrast to the results for the case of MCMC on unconstrained phylogenetic trees we found that subtree swapping moves perform better than subtree prune and regraft algorithms and moderate proposals dominate bold proposals. However, the results varied with the data set we analyzed and the intermediate subtree swap proposal distribution which we introduce in this paper was the only one with a continuous high level of efficiency.