Abstract
AIM: Ecosystem stability and its link with biodiversity have mainly been 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. METHODS: 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). RESULTS: We show that the link between the two relationships strongly depends on whether the temporal fluctuations of the ecosystem property of interest are more correlated within than between species. If fluctuations are correlated within species but not between them, then the IAR is strongly constrained by the SAR. If instead individual fluctuations are only correlated by spatial proximity, then the IAR is unrelated to the SAR. We apply these two correlation assumptions to explore the effects of species loss and habitat destruction on stability, and find a rich variety of multi-scale spatial dependencies, with marked differences between the two assumptions. MAIN CONCLUSIONS: The dependence of ecosystem stability on biodiversity across spatial scales is governed by the spatial decay of correlations within and between species. Our work provides a point of reference for mechanistic models and data analyses. More generally, it illustrates the relevance of macroecology for ecosystem functioning and stability.