Adaptive dating and fast proposals: Revisiting the phylogenetic relaxed clock model

Relaxed clock models enable estimation of molecular substitution rates across lineages and are widely used in phylogenetics for dating evolutionary divergence times. Under the (uncorrelated) relaxed clock model, tree branches are associated with molecular substitution rates which are independently and identically distributed. In this article we delved into the internal complexities of the relaxed clock model in order to develop efficient MCMC operators for Bayesian phylogenetic inference. We compared three substitution rate parameterisations, introduced an adaptive operator which learns the weights of other operators during MCMC, and we explored how relaxed clock model estimation can benefit from two cutting-edge proposal kernels: the AVMVN and Bactrian kernels. This work has produced an operator scheme that is up to 65 times more efficient at exploring continuous relaxed clock parameters compared with previous setups, depending on the dataset. Finally, we explored variants of the standard narrow exchange operator which are specifically designed for the relaxed clock model. In the most extreme case, this new operator traversed tree space 40% more efficiently than narrow exchange. The methodologies introduced are adaptive and highly effective on short as well as long alignments. The results are available via the open source optimised relaxed clock (ORC) package for BEAST 2 under a GNU licence (https://github.com/jordandouglas/ORC).Author summary: Biological sequences, such as DNA, accumulate mutations over generations. By comparing such sequences in a phylogenetic framework, the evolutionary tree of lifeforms can be inferred and historic divergence dates can be estimated. With the overwhelming availability of biological sequence data, and the increasing affordability of collecting new data, the development of fast and efficient phylogenetic algorithms is more important than ever. In this article we focus on the relaxed clock model, which is very popular in phylogenetics. We explored how a range of optimisations can improve the statistical inference of the relaxed clock. This work has produced a phylogenetic setup which can infer parameters related to the relaxed clock up to 65 times faster than previous setups, depending on the dataset. The methods introduced adapt to the dataset during computation and are highly efficient when processing long biological sequences.