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. Oaks et al. (2013) assessed the ability of an approximate-Bayesian method (msBayes) to estimate such a pattern of simultaneous divergence across taxa, to which Hickerson et al. (2014) responded. Both papers agree the method is sensitive to prior assumptions and often erroneously supports shared divergences; the papers differ about the explanation and solution. Oaks et al. (2013) suggested the method's behavior is caused by the strong weight of uniform priors on divergence times leading to smaller marginal likelihoods of models with more divergence-time parameters (Hypothesis 1); they proposed alternative priors to avoid strongly weighted posteriors. Hickerson et al. (2014) suggested numerical approximation error causes msBayes analyses to be biased toward models of clustered divergences (Hypothesis 2); they proposed using narrow, empirical uniform priors. Here, we demonstrate that the approach of Hickerson et al. (2014) does not mitigate the method's tendency to erroneously support models of clustered divergences, and often excludes the true parameter values. Our results also show that the tendency of msBayes analyses to support models of shared divergences is primarily due to Hypothesis 1. This series of papers demonstrate 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, 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.
Comment: 24 pages, 4 figures, 1 table, 14 pages of supporting information with 10 supporting figures