Supplementary figures S1-S4 from The strength of the biodiversity–ecosystem function relationship depends on spatial scale

Our understanding of the relationship between biodiversity and ecosystem functioning (BEF) applies mainly to fine spatial scales. New research is required if we are to extend this knowledge to broader spatial scales that are relevant for conservation decisions. Here, we use simulations to examine conditions that generate scale dependence of the BEF relationship. We study scale by assessing how the BEF relationship (slope and <i>R</i><sup>2</sup>) changes when habitat patches are spatially aggregated. We find three ways for the BEF relationship to be scale-dependent: (i) variation among local patches in local (α) diversity, (ii) spatial variation in the local BEF relationship and (iii) incomplete compositional turnover in species composition among patches. The first two cause the slope of the BEF relationship to increase moderately with spatial scale, reflecting nonlinear averaging of spatial variation in diversity or the BEF relationship. The third mechanism results in much stronger scale dependence, with the BEF relationship increasing in the rising portion of the species area relationship, but then decreasing as it saturates. An analysis of data from the Cedar Creek grassland BEF experiment revealed a positive but saturating slope of the relationship with scale. Overall, our findings suggest that the BEF relationship is likely to be scale dependent.