Experimental setup
To quantify diversity effects of the producer community, we measured and compared primary production at different levels of producer species richness. Specifically, we measured primary production as the resource uptake at the end of the simulations (see Supplementary 1), which we used as yield Y to calculate net diversity effects ΔY as ΔY = YO - YE (Loreau & Hector 2001). They capture the over- or underperformance of producer species mixtures in comparison to their monocultures as the difference between observed mixture yields YO and expected mixture yields YE, which are the sum of monoculture yields relative to their seeded proportion in mixture (i.e., their starting densities). To create a diversity gradient of the producer communities, we drew 30 random 16-species mixtures, all their monocultures, and five mixtures at each of three intermediate levels of species richness (2, 4, 8) that we randomly assembled from their respective 16-species species-pools.
To investigate the effects of multi-trophic interactions, we embedded the producer communities in food-webs at varying levels of animal richness (0, 10, 30, 50, 70). Systems without animals served as a null-model for the effects of multi-trophic interactions. Further, we included resource-use complementarity by manipulating the resource-use dissimilarity (RUD) of producer species over 16 steps (see below for a detailed description). We simulated all producer communities in a full factorial design for a total of 76,800 simulations, 960 for each possible combination of RUD and animal richness. We ran all simulations in Julia 1.2.0 (Bezanson et al. 2017) using the DifferentialEquations package (Rackauckas & Nie 2017). Simulations were limited to 150,000 time-steps, where they usually reached equilibrium. The code used for the simulations is available at <public.repository>.