Accounting for spatially autocorrelated errors is necessary to infer cross-scale biodiversity–ecosystem functioning patterns in natural world

Cross-scale biodiversity–ecosystem functioning (BEF) relationships are widely used to evaluate how biodiversity relates to ecosystem functioning across space. Theory predicts that when species turnover is incomplete across space, the BEF slope follows a characteristic hump-shaped scaling pattern, strengthening with increasing scale before weakening at broader scales. In real landscapes, however, biodiversity and ecosystem function often co-vary along environmental gradients, and spatial autocorrelation naturally increases with scale, potentially confounding regression-based BEF inference.

We combined simulations and field data to quantify how explicitly accounting for spatial autocorrelation (SAC) affects BEF scaling. In simulations, biodiversity and ecosystem function were generated under joint control of an environmental gradient and a spatial stochastic component, allowing SAC to emerge in both predictors and responses. In empirical analyses, we used forest inventory data from two temperate forests. We constructed a sequence of spatial scales by aggregating plots using a k-nearest-neighbor procedure, with k increasing from small to large neighborhoods. At each scale, we estimated BEF as the slope of species richness (SR) on biomass increment, while controlling for climate, soil, and trait covariates. We then contrasted non-spatial models with spatial models that include SAC in the residual structure, and quantified ΔBEF as the difference in SR slopes between spatial and non-spatial fits.

Across simulations and observations, ignoring SAC produced an apparently monotonic strengthening of BEF with scale. However, when SAC was included, the BEF scaling curve followed the predicted hump-shaped pattern. Moreover, ΔBEF increased with residual Moran’s I, indicating that stronger spatial dependence systematically inflates non-spatial BEF estimates as scale increases. Finally, the BEF slopes were negatively correlated with excess species richness and positively correlated with species turnover after correcting for SAC, consistent with the theory that species turnover plays a key role in BEF scaling. Our study emphasizes that accounting for SAC is essential for accurate BEF scaling and provides a useful approach for future studies.