Modelling species diversity through species level hierarchical modelling

Summary.  Understanding spatial patterns of species diversity and the distributions of individ‐ual species is a consuming problem in biogeography and conservation. The Cape floristic region of South Africa is a global hot spot of diversity and endemism, and the Protea atlas project, with about 60 000 site records across the region, provides an extraordinarily rich data set to model patterns of biodiversity. Model development is focused spatially at the scale of 1′ grid cells (about 37 000 cells total for the region). We report on results for 23 species of a flowering plant family known as Proteaceae (of about 330 in the Cape floristic region) for a defined subregion. Using a Bayesian framework, we developed a two‐stage, spatially explicit, hierarchical logistic regression. Stage 1 models the potential probability of presence or absence for each species at each cell, given species attributes, grid cell (site level) environmental data with species level coefficients, and a spatial random effect. The second level of the hierarchy models the probability of observing each species in each cell given that it is present. Because the atlas data are not evenly distributed across the landscape, grid cells contain variable numbers of sampling localities. Thus this model takes the sampling intensity at each site into account by assuming that the total number of times that a particular species was observed within a site follows a binomial distribution. After assigning prior distributions to all quantities in the model, samples from the posterior distribution were obtained via Markov chain Monte Carlo methods. Results are mapped as the model‐estimated probability of presence for each species across the domain. This provides an alternative to customary empirical ‘range‐of‐occupancy’ displays. Summing yields the predicted richness of species over the region. Summaries of the posterior for each environmental coefficient show which variables are most important in explaining the presence of species. Our initial results describe biogeographical patterns over the modelled region remarkably well. In particular, species local population size and mode of dispersal contribute significantly to predicting patterns, along with annual precipitation, the coefficient of variation in rainfall and elevation.