Sequential Bayesian Phylogenetic Inference

The ideal approach to Bayesian phylogenetic inference is to estimate all parameters of interest jointly in a single hierarchical model. However, this is often not feasible in practice due to the high computational cost. Instead, phylogenetic pipelines generally consist of sequential analyses, whereby a single point estimate from a given analysis is used as input for the next analysis (e.g., a single multiple sequence alignment is used to estimate a gene tree). In this framework, uncertainty is not propagated from step to step, which can lead to inaccurate or spuriously confident results. Here, we formally develop and test a sequential inference approach for Bayesian phylogenetic inference, which uses importance sampling to generate observations for the next step of an analysis pipeline from the posterior distribution produced in the previous step. Our sequential inference approach presented here not only accounts for uncertainty between analysis steps but also allows for greater flexibility in software choice (and hence model availability) and can be computationally more efficient than the traditional joint inference approach when multiple models are being tested. We show that our sequential inference approach is identical in practice to the joint inference approach only if sufficient information in the data is present (a narrow posterior distribution) and/or sufficiently many important samples are used. Conversely, we show that the common practice of using a single point estimate can be biased, for example, a single phylogeny estimate can transform an unrooted phylogeny into a time-calibrated phylogeny. We demonstrate the theory of sequential Bayesian inference using both a toy example and an empirical case study of divergence-time estimation in insects using a relaxed clock model from transcriptome data. In the empirical example, we estimate 3 posterior distributions of branch lengths from the same data (DNA character matrix with a GTR+Gamma+I substitution model, an amino acid data matrix with empirical substitution models, and an amino acid data matrix with the PhyloBayes CAT-GTR model). Finally, we apply 3 different node-calibration strategies and show that divergence time estimates are affected by both the data source and underlying substitution process to estimate branch lengths as well as the node-calibration strategies. Thus, our new sequential Bayesian phylogenetic inference provides the opportunity to efficiently test different approaches for divergence time estimation, including branch-length estimation from other software.