Insights from a general, full-likelihood Bayesian approach to inferring shared evolutionary events from genomic data: Inferring shared demographic events is challenging.

Factors that influence the distribution, abundance, and diversification of species can simultaneously affect multiple evolutionary lineages within or across communities. These include changes to the environment or inter-specific ecological interactions that cause ranges of multiple species to contract, expand, or fragment. Such processes predict temporally clustered evolutionary events across species, such as synchronous population divergences and/or changes in population size. There have been a number of methods developed to infer shared divergences or changes in population size, but not both, and the latter has been limited to approximate methods. We introduce a full-likelihood Bayesian method that uses genomic data to estimate temporal clustering of an arbitrary mix of population divergences and population-size changes across taxa. Using simulated data, we find that estimating the timing and sharing of demographic changes tends to be inaccurate and sensitive to prior assumptions, which is in contrast to accurate, precise, and robust estimates of shared divergence times. We also show that previous estimates of co-expansion among five Alaskan populations of three-spine sticklebacks (Gasterosteus aculeatus) were likely driven by prior assumptions and ignoring invariant characters. We conclude by discussing potential avenues to improve the estimation of synchronous demographic changes across populations.