Assessing the effect of model specification and prior sensitivity on Bayesian tests of temporal signal
Authors: Tay John H , Kocher Arthur , Duchene Sebastian 
Published: August 2024

Our understanding of the evolution of many microbes has been revolutionised by the molecular clock, a statistical tool to infer evolutionary rates and timescales from analyses of biomolecular sequences. In all molecular clock models, evolutionary rates and times are jointly unidentifiable and ‘calibration’ information must therefore be used.

For many organisms, sequences sampled at different time points can be employed for such calibration. Before attempting to do so, it is recommended to verify that the data carry sufficient information for molecular dating, a practice referred to as evaluation of temporal signal. Recently, a fully Bayesian approach, BETS (Bayesian Evaluation of Temporal Signal), was proposed to overcome known limitations of other commonly used techniques such as root-to-tip regression or date randomisation tests. BETS requires the specification of a full Bayesian phylogenetic model, posing several considerations for untangling the impact of model choice on the detection of temporal signal. Here, we aimed to (i) explore the effect of molecular clock model and tree prior specification on the results of BETS and (ii) provide guidelines for improving our confidence in molecular clock estimates.

Using microbial molecular sequence data sets and simulation experiments, we assess the impact of the tree prior and its hyperparameters on the accuracy of temporal signal detection. In particular, highly informative priors that are inconsistent with the data can result in the incorrect detection of temporal signal. In consequence, we recommend: (i) using prior predictive simulations to determine whether the prior generates a reasonable expectation of parameters of interest, such as the evolutionary rate and age of the root node, (ii) conducting prior sensitivity analyses to assess the robustness of the posterior to the choice of prior, and (iii) selecting a molecular clock model that reasonably describes the evolutionary process.

Author summary

Our knowledge of when historical and modern pathogens emerged and spread is largely grounded on molecular clock models. The inferences from these models assume that sequence sampling times must have captured a sufficient amount of evolutionary change, which is typically determined using tests of temporal signal, such as BETS. Although BETS is generally effective, here we show that it can incorrectly detect temporal signal if the chosen evolutionary model makes implausible statements about the evolutionary timescale, a situation that is difficult to diagnose, particularly with complex Bayesian models. We demonstrate that this problem is due to a statistical artefact, that we refer to as tree extension and that it can be minimised by conducting careful prior predictive simulations, and by eliciting biologically plausible priors in the model. Overall, our study provides guidelines for improving our statistical confidence in estimates of evolutionary timescales, with key applications for recently emerging pathogens and data sets involving ancient molecular data.