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Experimental Design and Data Collection

We include data from 30 sites in 10 countries which are part of the Nutrient Network (NutNet) distributed experiment (Borer et al. 2014a; Borer et al. 2017) (Table S1). Sites were dominated by herbaceous or low-statured vegetation and spanned wide gradients in elevation (6 to 3500 m), latitude (52 oS to 69 oN), mean annual precipitation (249 to 1877 mm yr-1), mean annual temperature (-3 to 23 oC), and mean aboveground live biomass (34 to 900 g m-2). Local richness (4 to 43 species m-2) and total site richness (18 to 142 species site-1) were highly variable among sites. We used data from control plots at 30 sites and from two experiments at subsets of the sites: the Multiple-nutrient experiment (21 sites) and the Consumer-nutrient experiment (16 sites). Experimental duration at the time of sampling varied from 3-11 years (Table S1); inclusion of duration in statistical models did not qualitatively change results.

Multiple-nutrient Experiment: This experiment factorially combined three nutrient-addition treatments each at two levels (Control or Fertilized): Nitrogen addition (10 g N m-2 yr-1 as timed-release urea), Phosphorus addition (10 g P m-2 yr-1 as triple-super phosphate), and Potassium and Micronutrient addition (10 g K m-2 yr-1 as potassium sulfate and 100 g m-2 yr-1 of a micronutrient mix (6% Ca, 3% Mg, 12% S, 0.1% B, 1% Cu, 17% Fe, 2.5% Mn, 0.05% Mo, and 1% Zn). N, P, and K were applied annually, and the micronutrient mix was applied once at the start of the study.

Consumer-nutrient Experiment: This experiment factorially combines nutrient addition (Control or Fertilized) and vertebrate consumer presence (Control or Fenced). To do this, we combine the unfenced control and unfenced plots with all nutrients added from the Multiple Nutrient Experiment with two additional treatments using herbivore fencing: Fenced with no nutrients added and Fenced with all nutrients added. Fences were 2.1 m tall and excluded aboveground, non-climbing, vertebrate herbivores. The lower 0.9 m was composed of 1 cm woven wire mesh with a 0.3 m outward-facing flange stapled to the ground to exclude digging animals. The top 1.2 m was composed of five rows of wire. Minor variations in fence design are described by Borer et al (2014a).

Data Collection: We estimated SARs using data collected at five spatial scales: 0.01, 1, 6.25, 25, and 75 m2 (sampling scheme illustrated in Figure S1). We recorded the presence of all species in each 5 x 5 m plot (25 m2), a 2.5 x 2.5 m subplot nested within each 5 x 5 m plot (6.25 m2), a 1 x 1 m subplot nested within each 2.5 x 2.5 m plot (1 m2), and four 0.1 x 0.1 m subplots placed at the corners of the 1 m2 subplot (4 by 0.01 m2). We aggregated species lists across the three replicate 5 x 5 m plots to estimate species richness at the 75 m2 scale. We also sampled plant species abundances in the 1 m x 1 m subplot by visually estimating the areal cover of each species, allowing us to calculate Simpson’s evenness at the 1 m2 scale (Smith & Wilson 1996). We used the mean richness of the four 0.01 m2 subplots in our analyses, and we excluded a small number of 0.01 m2 subplots with a mean species richness of zero as log richness was undefined (0.1% of samples). We note here that the 75 m2 richness estimate is based on non-nested data and includes among block variability, as it is composed of three spatially separate 25 m2 plots. Nested and non-nested SAR’s typically have similar slopes in non-forested terrestrial habitats (Drakare et al. 2006). Furthermore, when we only used the fully nested samples with a maximum area of 25 m2, our results were qualitatively similar. One site did not collect species richness data at the 75 m2 scale (chilcas.ar) and had a maximum area of 18.75 m2 (area of three 2.5 m2 plots). Inclusion or exclusion of this site did not qualitatively change results. We calculated site richness (i.e., site species pool) as the total number of species found across all sampled plots and years at the site (Table S1). We sampled aboveground plant biomass by clipping all aboveground biomass (live and dead) in two 0.1 m x 1 m strips, sorting current year’s biomass (live biomass) from previous year’s biomass (dead biomass), drying the biomass to a constant mass at 60 oC, and weighing it to the nearest 0.01 g. Within each 1 m2 quadrat, we measured the proportion of photosynthetically active radiation (PAR) reaching the ground level and above the canopy.