Using coverage-based rarefaction to infer non-random species distributions

Understanding how species are non-randomly distributed in space and how the resulting spatial structure responds to ecological, biogeographic, and anthropogenic drivers is a critical piece of the biodiversity puzzle. However, most metrics that quantify the spatial structure of diversity (i.e., community differentiation), such as Whittaker's beta-diversity, depend on sampling effort and are influenced by species pool size, species abundance distributions, and numbers of individuals. Null models are useful for identifying the degree of differentiation among communities due to spatial structuring relative to that expected from sampling effects, but do not accommodate the influence of sample completeness (i.e., the proportion of the species pool in a given sample). Here, we develop an approach that makes use of individual- and coverage-based rarefaction and extrapolation, to derive a metric, beta(C), which captures changes in intraspecific aggregation independently of changes in the species pool size. We illustrate the metric using spatially explicit simulations and two case studies: (1) a re-analysis of the "Gentry" plot data set consisting of small forest plots spanning a latitudinal gradient from North to South America and (2) comparing a large plot in high diversity tropical forests of Barro Colorado Island, Panama, with a plot in a lower diversity temperate forest in Harvard Forest, Massachusetts, USA. We find no evidence for systematic changes in spatial structure with latitude in these data sets. As it is rooted in biodiversity sampling theory and explicitly controls for sample completeness, our approach represents an important advance over existing null models for spatial aggregation. Potential applications range from better descriptors of biogeographic diversity patterns to the consolidation of local and regional diversity trends in the current biodiversity crisis.