Scaling up Bayesian population phylogenomics through virtual dimension reduction

Population phylogenomics uses sampled genomes to jointly infer population genetic processes (ancestral and contemporary population sizes, historical gene flow) and a phylogenetic tree relating species or populations including species split times. This challenging problem has been tackled most successfully in the Bayesian framework under the multispecies coalescent (MSC) model via Markov chain Monte Carlo (MCMC) computational algorithms. However, MCMC methods suffer from two serious problems: (i) mixing difficulties due to the high-dimensional state space with complex constraints, and (ii) the intrinsically serial nature of MCMC algorithms that defies parallelisation. To deal with both issues, we develop a new method, called Virtual Dimension Reduction allowing Parallelisation (VDRoP), that achieves the same MCMC mixing efficiency as dimension reduction through analytical integration of parameters, but without sacrificing parallel computation and without the restriction to conjugate priors. We implement the new method in the Bayesian program BPP and apply it to genomic datasets from Adansonia baobab trees, Anopheles mosquitoes, and Heliconius butterflies. The new algorithms reduce the run-time of MCMC analyses by 3 to 8 fold and improve the mixing efficiency by up to 50 fold for representative empirical datasets.