Livestock grazing is a major driver shaping grassland biodiversity, functioning, and stability. Whether grazing impacts on grassland ecosystems are scale-dependent remains unclear. Here, we conducted a sheep-grazing experiment in a temperate grassland to test grazing effects on the temporal stability of productivity across scales. We found that grazing increased species stability, but substantially decreased local community stability due to reduced asynchronous dynamics among species within communities. The negative effect of grazing on local community stability propagated to reduce stability at larger spatial scales. By decreasing biodiversity both within and across communities, grazing reduced biological insurance effects and hence the up-scaling of stability from species to communities and further to larger spatial scales. Our study provides the first evidence for the scale-dependence of grazing effects on grassland stability through biodiversity. We suggest that ecosystem management should strive to maintain biodiversity across scales to achieve sustainability of grassland ecosystem functions and services.

All the response variables have been natural log-transformed. They are unitless, except for "d_abun" with a percentage (%).