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Background  Bayesian MCMC has become a common approach for phylogenetic inference. But the growing size of molecular sequence data sets has created a pressing need to improve the computational efficiency of Bayesian phylogenetic inference algorithms.    Results  This paper develops a new algorithm to improve the efficiency of Bayesian phylogenetic inference for models that include a per-branch rate parameter. In a Markov chain Monte Carlo algorithm, the presented proposal kernel changes evolutionary rates and divergence times at the same time, under the constraint that the implied genetic distances remain constant. Specifically, the proposal operates on the divergence time of an internal node and the three adjacent branch rates. For the root of a phylogenetic tree, there are three strategies discussed, named Simple Distance, Small Pulley and Big Pulley. Note that Big Pulley is able to change the tree topology, which enables the operator to sample all the possible rooted trees consistent with the implied unrooted tree. To validate its effectiveness, a series of experiments have been performed by implementing the proposed operator in the BEAST2 software.    Conclusions  The results demonstrate that the proposed operator is able to improve the performance by giving better estimates for a given chain length and by using less running time for a given level of accuracy. Measured by effective samples per hour, use of the proposed operator results in overall mixing more efficient than the current operators in BEAST2. Especially for large data sets, the improvement is up to half an order of magnitude.

Improving the performance of Bayesian phylogenetic inference under relaxed clock models