Between geometry and biology: the problem of universality of the species-area relationship

The species-area relationship (SAR) is considered to be one of a few generalities in ecology, yet a universal model of its shape and slope has remained elusive. Recently Harte et al. (2009) argued that the slope of the SAR for a given area is driven by a single parameter, the ratio between total number of individuals and number of species (i.e. the mean population size across species at a given scale). We provide a geometric interpretation of this dependence. At the same time, however, we show that this dependence cannot be universal across taxa: if it holds for a taxon composed from two subsets of species and also for one of its subsets, it cannot simultaneously hold for the other subset. Using three datasets, we show that the slope of the SAR considerably varies around the prediction. We estimate the limits of this variation using geometric considerations, providing a theory based on species spatial turnover at different scales. We argue that the SAR cannot be strictly universal, but ...