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>.