The relationship between the spatial scaling of biodiversity and ecosystem stability

Ecosystem stability and its link with biodiversity have been mainly studied at the local scale. Here we present a simple theoretical model to address the joint dependence of diversity and stability on spatial scale, from local to continental. The notion of stability we use is based on the temporal variability of an ecosystem-level property, such as primary productivity. In this way, our model integrates the well-known species-area relationship (SAR) with a recent proposal to quantify the spatial scaling of stability, called the invariability-area relationship (IAR). To explore the possible links between the two relationships, we contrast two assumptions about the spatial decay of correlations. In case species differences determine spatial decorrelation, the IAR is a duplicate of the SAR; in case decorrelation is directly determined by spatial separation, the IAR is unrelated to the SAR. We apply the two model variants to explore the effects of species loss and habitat destruction on stability, and find a rich variety of multi-scale spatial dependencies. Our work emphasizes the importance of studying diversity and stability across spatial scales, and provides a point of reference for mechanistic models and data analyses.