There is still considerable debate about which mechanisms drive the relationship between biodiversity and ecosystem function (BEF). Although most scientists agree on the existence of two underlying mechanisms, complementarity and selection, experimental studies keep producing contrasting results on the relative contributions of the two effects. We present a spatially explicit resource competition model and investigate how the strength of these effects is influenced by trait and environmental variability, resource distribution, and species pool size. Our results demonstrate that the increase of biomass production with increasing species numbers depends on the concurrence of environmental and trait variability: BEF relationships are stronger if functionally different species coexist in a landscape with heterogeneous resource supply. These large biodiversity effects arise from complementarity effects, whereas selection effects are maximized when broad trait ranges coincide with narrow ranges of resource supply ratios. Our results will therefore help to resolve the debate on complementarity and selection mechanisms.