The biodiversity and ecosystem functioning (BEF) relationship is expected to be scale-dependent. The autocorrelation of environmental heterogeneity is hypothesized to explain this scale dependence because it influences how quickly biodiversity accumulates over space or time. However, this link has yet to be demonstrated in a formal model. Here we use a Lotka-Volterra competition model to simulate community dynamics when environmental conditions vary across either space or time. Species differ in their optimal environmental conditions, which results in turnover in community composition. We vary biodiversity by modelling communities with different sized regional species pools and ask how the amount of biomass per unit area depends on the number of species present, and the spatial or temporal scale at which it is measured. We find that more biodiversity is required to maintain functioning at larger temporal and spatial scales. The number of species required increases quickly when environmental autocorrelation is low, and slowly when autocorrelation is high. Both spatial and temporal environmental heterogeneity led to scale dependence in BEF, but autocorrelation had larger impacts when environmental change was temporal. These findings show how the biodiversity required to maintain functioning is expected to increase over space and time.
