A graphical null model for scaling biodiversity-ecosystem functioning relationships

1. Global biodiversity is declining at rates faster than at any other point in human history. Experimental manipulations at small spatial scales have demonstrated that communities with fewer species consistently produce less biomass than higher diversity communities. Understanding the consequences of the global extinction crisis for ecosystem functioning requires understanding how local experimental results are likely to change with increasing spatial and temporal scales and from experiments to naturally assembled systems. 2. Scaling across time and space in a changing world requires baseline predictions. Here, we provide a graphical null model for area scaling of biodiversity-ecosystem functioning relationships using observed macroecological patterns: the species-area curve and the biomass-area curve. We use species-area and biomass-area curves to predict how species richness-biomass relationships are likely to change with increasing sampling extent. We then validate these predictions with data from two naturally assembled ecosystems: a Minnesota savanna and a Panamanian tropical dry forest. 3. Our graphical null model predicts that biodiversity-ecosystem functioning relationships are scale-dependent. However, we note two important caveats. First, our results indicate an apparent contradiction between predictions based on measurements in biodiversity-ecosystem functioning experiments and from scaling theory. When ecosystem functioning is measured as per unit area (e.g. biomass per m(2)), as is common in biodiversity-ecosystem functioning experiments, the slope of the biodiversity ecosystem functioning relationship should decrease with increasing scale. Alternatively, when ecosystem functioning is not measured per unit area (e.g. summed total biomass), as is common in scaling studies, the slope of the biodiversity-ecosystem functioning relationship should increase with increasing spatial scale. Second, the underlying macroecological patterns of biodiversity experiments are predictably different from some naturally assembled systems. These differences between the underlying patterns of experiments and naturally assembled systems may enable us to better understand when patterns from biodiversity-ecosystem functioning experiments will be valid in naturally assembled systems. 4. Synthesis. This paper provides a simple graphical null model that can be extended to any relationship between biodiversity and any ecosystem functioning across space or time. Furthermore, these predictions provide crucial insights into how and when we may be able to extend results from small-scale biodiversity experiments to naturally assembled regional and global ecosystems where biodiversity is changing.