The power and pitfalls of Dirichlet-multinomial mixture models for ecological count data

The Dirichlet-multinomial mixture model (DMM) and its extensions provide powerful new tools for interpreting the ecological dynamics underlying taxon abundance data. However, like many complex models, how effectively they capture the many features of empirical data is not well understood. In this work, we expand the DMM to an infinite mixture model (iDMM) and use posterior predictive distributions (PPDs) to explore the performance in three case studies, including two amplicon metagenomic time series. We avoid concentrating on fluctuations within individual taxa and instead focus on consortial-level dynamics, using straight-forward methods for visualizing this perspective. In each study, the iDMM appears to perform well in organizing the data as a framework for biological interpretation. Using the PPDs, we also observe several exceptions where the data appear to significantly depart from the model in ways that give useful ecological