Scalable Bayesian divergence time estimation with ratio transformations

<div class="page"> <div class="layoutArea"> <div class="column"> <p><span>Divergence time estimation is crucial to provide temporal signals for dating bio</span><span>logically important events, from species divergence to viral transmissions in space and </span><span>time. With the advent of high-throughput sequencing, recent Bayesian phylogenetic </span><span>studies have analyzed hundreds to thousands of sequences. Such large-scale analyses</span><span> </span><span>challenge divergence time reconstruction by requiring inference on highly-correlated</span><span> </span><span>internal node heights that often become computationally infeasible. To overcome this</span><span> </span><span>limitation, we explore a ratio transformation that maps the original </span><span>N - </span><span>1 internal</span><span> </span><span>node heights into a space of one height parameter and </span><span>N - </span><span>2 ratio parameters. To</span><span> </span><span>make the analyses scalable, we develop a collection of linear-time algorithms to com</span><span>pute the gradient and Jacobian-associated terms of the log-likelihood with respect to </span><span>these ratios. We then apply Hamiltonian Monte Carlo sampling with the ratio trans</span><span>form in a Bayesian framework to learn the divergence times in four pathogenic viruses</span><span> </span><span>(West Nile virus, rabies virus, Lassa virus and Ebola virus) and the coralline red algae.</span><span>  </span><span>Our method both resolves a mixing issue in the West Nile virus example and improves</span><span>  </span><span>inference efficiency by at least 5-fold for the Lassa and rabies virus examples as well</span><span>  </span><span>as for the algae example. Our method now also makes it computationally feasible to</span><span>  </span><span>incorporate mixed-effects molecular clock models for the Ebola virus example, confirms</span><span>  </span><span>the findings from the original study and reveals clearer multimodal distributions of the</span><span>  </span><span>divergence times of some clades of interest.</span></p> </div> </div> </div>