Poor Fit to the Multispecies Coalescent is Widely Detectable in Empirical Data

Model checking is a critical part of Bayesian data analysis, yet it remains largely unused in systematic studies. Phylogeny estimation has recently moved into an era of increasingly complex models that simultaneously account for multiple evolutionary processes, the statistical fit of these models to the data has rarely been tested. Here we develop a posterior predictive simulation-based model check for a commonly used multispecies coalescent model, implemented in *BEAST, and apply it to 25 published data sets. We show that poor model fit is detectable in the majority of data sets; that this poor fit can mislead phylogenetic estimation; and that in some cases it stems from processes of inherent interest to systematists. We suggest that as systematists scale up to phylogenomic data sets, which will be subject to a heterogeneous array of evolutionary processes, critically evaluating the fit of models to data is an analytical step that can no longer be ignored. [Gene duplication and extinction; gene tree; hybridization; model fit; multispecies coalescent; next-generation sequencing; posterior predictive simulation; species delimitation; species tree.].