Rank abundance distributions (RADs) are a description of community structure common to every ecological sample where counts are recorded and are useful for managing and understanding biodiversity. We use RADs to describe patterns of biodiversity in samples with high numbers of unique species. We use a novel statistical method to analyse RADs and demonstrate prediction methods for attributes of biodiversity. The RAD is defined by the total abundance (Ni), species richness (Si) and the vector of relative abundances (nij) and the joint probability distribution of these quantities is modelled. Models were fitted to benthic biological data sampled on the Western Australian coast from depths of 100 to 1500 m and a latitudinal range of 22 to 35oS, using topographic and oceanographic data as covariates. Predictions from fitted models give attributes of biodiversity derived from RADs at a regular grid over the sampled area. The Leeuwin current and Leeuwin undercurrent appear to be key structuring forces for the predicted biodiversity attributes. The predictions show that benthic biodiversity is complex and varies with a number of different covariates. The predictions are unique, as they characterise important aspects of biodiversity and how it varies with large spatial scales. The predictions enable the complete reconstruction of the expected RAD at any point where covariates are available with estimates of uncertainty.