Abstract: With the increasing abundance of modern molecular sequence data and the dramatic expansion of the tree-like topological space describing historical relationships between species,reliable inference of phylogenetic trees continues to face enormous challenges.In recent years,the most advanced Hamiltonian Markov Monte Carlo(HMC) algorithm in the Markov Chain Monte Carlo(MCMC) family has been shown to be applicable to phylogenetic analysis,which can avoid the large amount of random walk behaviors present in traditional MCMC algorithms and speed up the mixing of Markov chains.However,in the more complex multimodal development tree space,the HMC algorithm cannot escape from the local high probability region by obtaining propo-sals from other modes.In order to improve the robustness of the algorithm,a hybrid path Hamiltonian Markov Monte Carlo(MPHMC) optimization strategy is proposed in this paper.Without adding additional computational cost,the algorithm samples paths with a non-HMC update component for discrete parameters,alternating with HMC deterministic updates,and introduces a branch rearrangement strategy with greater topological variation in the tree space,enabling freer traversal of the entire posterior distribution's tree space.Experiments on five empirical datasets demonstrate that the MPHMC method better samples from the correct posterior distribution,and the HMC single-path sampling algorithm may fail when run on larger datasets that are more difficult to sample,while the MPHMC method achieves a sampling efficiency gain over 14% than the widely used phylogenetic analysis tool,Mrbayes(MCMC).

Key words: MrBayes, Tree space, HMC, Multimodal posterior distribution, Mixed path