The analysis of biodiversity using rank abundance distributions.

Biodiversity is an important topic of ecological research. A common form of data collected to investigate patterns of biodiversity is the number of individuals of each species at a series of locations. These data contain information on the number of individuals (abundance), the number of species (richness), and the relative proportion of each species within the sampled assemblage (evenness). If there are enough sampled locations across an environmental gradient then the data should contain information on how these three attributes of biodiversity change over gradients. We show that the rank abundance distribution (RAD) representation of the data provides a convenient method for quantifying these three attributes constituting biodiversity. We present a statistical framework for modeling RADs and allow their multivariate distribution to vary according to environmental gradients. The method relies on three models: a negative binomial model, a truncated negative binomial model, and a novel model based on a modified Dirichlet-multinomial that allows for a particular type of heterogeneity observed in RAD data. The method is motivated by, and applied to, a large-scale marine survey off the coast of Western Australia, Australia. It provides a rich description of biodiversity and how it changes with environmental conditions.