A hierarchical Bayesian model to incorporate uncertainty into methods for diversity partitioning.

Recently there have been major theoretical advances in the quantification and partitioning of diversity within and among communities, regions, and ecosystems. However, applying those advances to real data remains a challenge. Ecologists often end up describing their samples rather than estimating the diversity components of an underlying study system, and existing approaches do not easily provide statistical frameworks for testing ecological questions. Here we offer one avenue to do all of the above using a hierarchical Bayesian approach. We estimate posterior distributions of the underlying "true" relative abundances of each species within each unit sampled. These posterior estimates of relative abundance can then be used with existing formulae to estimate and partition diversity. The result is a posterior distribution of diversity metrics describing our knowledge (or beliefs) about the study system. This approach intuitively leads to statistical inferences addressing biologically motivated hypotheses via Bayesian model comparison. Using simulations, we demonstrate that our approach does as well or better at approximating the "true" diversity of a community relative to naïve or ad-hoc bias-corrected estimates. Moreover, model comparison correctly distinguishes between alternative hypotheses about the distribution of diversity within and among samples. Finally, we use an empirical ecological dataset to illustrate how the approach can be used to address questions about the makeup and diversities of assemblages at local and regional scales.