Beyond species area curves: application of a scale-free measure for spatial variability of species richness

We report a novel pattern in species richness, complementary to the well-known species—area relationship. We show that, as sample area increases, the variation in relative richness decreases among otherwise comparable spatial units. This pattern holds for southern African birds, French birds, Cape Proteaceae and the trees of Barro Colorado Island. We propose a scale-free method for quantifying this pattern by measuring the multifractal intensity of species richness, which is the multi-scale tendency of adjacent patches with the same area to differ in richness. By this measure, spatial variability is strongest for Cape Proteaceae and weakest for Barro Colorado Island trees. Our results have implications for area-dependent estimates of species-richness, for example in reserve planning and in simulation-based studies. They imply that such estimates are most accurate for large areas, and will be subject to substantial uncertainty when the multifractal intensity is high and the area is small. For comparative purposes, multifractal intensity may be used as a supplement or as an alternative to mean richness, as well as for other ecological densities, such as biomass distribution and local abundance.