Dispersal ability determines the scaling properties of species abundance distributions: a case study using arthropods from the Azores

Species abundance distributions (SAD) are central to the description of diversity and have played a major role in the development of theories of biodiversity and biogeography. However, most work on species abundance distributions has focused on one single spatial scale. Here we used data on arthropods to test predictions obtained with computer simulations on whether dispersal ability influences the rate of change of SADs as a function of sample size. To characterize the change of the shape of the SADs we use the moments of the distributions: the skewness and the raw moments. In agreement with computer simulations, low dispersal ability species generate a hump for intermediate abundance classes earlier than the distributions of high dispersal ability species. Importantly, when plotted as function of sample size, the raw moments of the SADs of arthropods have a power law pattern similar to that observed for the SAD of tropical tree species, thus we conjecture that this might be a general pattern in ecology. The existence of this pattern allows us to extrapolate the moments and thus reconstruct the SAD for larger sample sizes using a procedure borrowed from the field of image analysis based on scaled discrete Tchebichef moments and polynomials.