Implications of uniformly distributed, empirically informed priors for phylogeographical model selection: a reply to Hickerson et al.

Establishing that a set of population-splitting events occurred at the same time can be a potentially persuasive argument that a common process affected the populations. Recently, Oaks et al. () assessed the ability of an approximate-Bayesian model-choice method (msBayes) to estimate such a pattern of simultaneous divergence across taxa, to which Hickerson et al. () responded. Both papers agree that the primary inference enabled by the method is very sensitive to prior assumptions and often erroneously supports shared divergences across taxa when prior uncertainty about divergence times is represented by a uniform distribution. However, the papers differ about the best explanation and solution for this problem. Oaks et al. () suggested the method's behavior was caused by the strong weight of uniformly distributed priors on divergence times leading to smaller marginal likelihoods (and thus smaller posterior probabilities) of models with more divergence-time parameters (Hypothesis 1); they proposed alternative prior probability distributions to avoid such strongly weighted posteriors. Hickerson et al. () suggested numerical-approximation error causes msBayes analyses to be biased toward models of clustered divergences because the method's rejection algorithm is unable to adequately sample the parameter space of richer models within reasonable computational limits when using broad uniform priors on divergence times (Hypothesis 2). As a potential solution, they proposed a model-averaging approach that uses narrow, empirically informed uniform priors. Here, we use analyses of simulated and empirical data to demonstrate that the approach of Hickerson et al. () does not mitigate the method's tendency to erroneously support models of highly clustered divergences, and is dangerous in the sense that the empirically derived uniform priors often exclude from consideration the true values of the divergence-time parameters. Our results also show that the tendency of msBayes analyses to support models of shared divergences is primarily due to Hypothesis 1, whereas Hypothesis 2 is an untenable explanation for the bias. Overall, this series of papers demonstrates that if our prior assumptions place too much weight in unlikely regions of parameter space such that the exact posterior supports the wrong model of evolutionary history, no amount of computation can rescue our inference. Fortunately, as predicted by fundamental principles of Bayesian model choice, more flexible distributions that accommodate prior uncertainty about parameters without placing excessive weight in vast regions of parameter space with low likelihood increase the method's robustness and power to detect temporal variation in divergences.