AbstractPlant community productivity generally increases with biodiversity, but the strength of this relationship exhibits strong empirical variation. In meta‐food‐web simulations, we addressed if the spatial overlap in plants' resource access and animal space‐use can explain such variability. We found that spatial overlap of plant resource access is a prerequisite for positive diversity–productivity relationships, but causes exploitative competition that can lead to competitive exclusion. Space‐use of herbivores causes apparent competition among plants, resulting in negative relationships. However, space‐use of larger top predators integrates sub‐food webs composed of smaller species, offsetting the negative effects of exploitative and apparent competition and leading to strongly positive diversity–productivity relationships. Overall, our results show that spatial overlap of plants' resource access and animal space‐use can greatly alter the strength and sign of such relationships. In particular, the scaling of animal space‐use effects opens new perspectives for linking landscape processes without effects on biodiversity to productivity patterns.