  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.
