A Bayesian hierarchical modeling approach for species diversity in ecology

Species diversity is the foundation of many ecological disciplines. This metric is often approximated using species richness and evenness, even though actual richness likely exceeds observations due to imperfect sampling methods. Estimating the “true” species richness, which includes identifying the number of missing species, has intrigued ecologists for decades. We adopted a parametric model that appeared in Fisher et al. (1943), which models the numbers of individuals from different species as random samples from a negative binomial distribution, and developed a Bayesian computational approach to directly estimate the distribution model parameters. The model parameters represent species abundance and evenness, and can be used to derive species richness. We evaluated our parametric approach using (1) a simulation study and (2) three historical data sets. Furthermore, we illustrated the hierarchical modeling approach to combine data from multiple parallel studies using a biannual fishery survey data set. Our parametric model formulation is computationally efficient, and the hierarchical structure facilitates embedding diversity estimation into broader application, such as assessing spatial and temporal trends in species diversity associated with environmental stressors. Additionally, because the two parameters of the negative binomial distribution model represent species abundance and evenness of a community, this parametric approach facilitates a deeper understanding of the ecological systems under study. The negative binomial distribution model works with a wide range of species frequency distribution types. As a result, our emphasis on a parametric model can help us characterize the structure of an ecosystem and provide a greater depth of ecologically meaningful information.