Power-Law Species-Area Relationships and Self-Similar Species Distributions Within Finite Areas

The species-area relationship (SAR) is often expressed as a power law, which indicates scale invariance. It has been claimed that the scale invariance---or self-similarity at the community level---is not compatible to the self-similarity at the level of spatial distribution of individual species, because the power law would only emerge if distributions for all species had identical fractal dimensions. Here we show that even if species differ in their fractal dimensions, the resulting SAR is approximately linear on a log-log scale because observed spatial distributions are inevitably spatially restricted – a phenomenon we term the finite area effect. Using distribution atlases, we demonstrate that the apparent power law of SARs for central European birds is attributable to this finite-area effect affecting species that indeed reveal self-similar distributions. We discuss implications of this mechanism producing the SAR.