Biomass-diversity responses and spatial dependencies in disturbed tallgrass prairies

Monotonic, hump-shaped and zero-correlation productivity-diversity relationships have been found to date in many ecosystems. This diversity of responses has puzzled ecologists in their search for general principles on ecosystem functioning. Some state that the scale of observation is crucial in defining this relationship. We have developed a spatial model of tallgrass prairies where biomass and litter dynamics are defined by uncoupled difference equations. In this system, we periodically apply prescribed fire as a disturbance that propagates through neighboring cells. The model shows percolation thresholds at points where small-scale spatial heterogeneity and large-scale, global correlation coexist, resulting in power-law distributions in available areas for non-dominant species. These points maximize the biomass-diversity relationship. Our results suggest that spatial dependencies and the disturbance heterogeneity hypothesis are the cornerstone processes accounting for unimodality in productivity-diversity relationships.