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Figure S1. Residual error plotted against expected values for the best fit model (Incomplete resource partitioning; equation 2 in text), fit with non-weighted least squares a), and weighted least squares (b). Weighted least squares was used to fit all models, to account for heteroscedasticity in the data. 1 Table S1. Log-likelihood (LL) and Akaike information criterion (AIC) values for the models presented in the text, fit to the data, using least squares (LS) and weighted least squares (Weighted LS). Model Full Model (Eq. 1) Niche partitioning removed (Eq. 2) Facilitation removed (Eq. 2) Facilitation, Unique niche removed Facilitation, Niche overlap removed LS LL -955.40 -968.26 -956.41 -964.69 -965.81 LS AIC 1936.7 1952.5 1936.8 1945.4 1953.6 2 Weighted LL -500.8108 -514.9386 -501.3982 -518.7444 -512.096 Weighted LS AIC 1027.6 1045.9 1026.8 1053.5 1046.2 Figure S2. Natural enemies recovered at the end of the experiment, divided by the number originally released, summed for true predators in (a) Block 1 and (c) Block 2, and for pupae of the parasitoid D. rapae in (b) Block 1 and (d) Block 2. Error bars represent means 1 s.e. True predator reproduction was common in the first trial, which encompassed early summer when predator reproduction is at its height (e.g., Snyder et al. 2006). Thus, predator densities generally exceeded the number initially added [Fig. S1(a)]. However, true predator reproduction rarely occurred in the second trial, conducted well into the summer drought typical for the region, and thus at a time when activity of most predators naturally declines. Thus, predator densities declined over the course of the second trial [Fig. S1(c)]. Per capita predator recovery at the end of Trial 1 generally decreased with increasing predator density, but predator density, predator diversity, or their interaction did not significantly impact predator densities in either trial [Table S1(a)]. As with true predators, per capita parasitoid reproduction was higher in Trial 1 than Trial 2 [Fig. S1(b, d); Table S1(b)]. However, parasitoid densities were not significantly impacted by predator diversity or density, or their interactions, in either trial [Table S1(b)]. Final / initial 30 a) Block 1, predators 18 20 12 10 6 0 0 0.3 2 c) Block 2, predators b) Block 1, parasitoid d) Block 2, parasitoid 0.2 1 0.1 0.0 0 4 8 16 4 32 Predator density Mono 3 Diverse 8 16 32 Table S2. Three-way ANOVA of the final densities of (a) true predators and (b) the aphid parasitoid D. rapae. a. True predators Source d.f. MS Diversity 1 3.329 Density 3 87.697 Block 1 352.676 Diversity × Density 3 9.047 Diversity × Block 1 3.806 Density × Block 3 87.323 Diversity × Density × Block 3 7.969 Error 48 41.3 F-ratio 0.081 2.123 8.539 0.219 0.092 2.114 0.193 P 0.778 0.110 0.005 0.883 0.763 0.111 0.901 F-ratio 0.005 .490 11.971 1.307 0.081 0.466 1.289 P 0.946 0.695 0.004 0.311 0.780 0.711 0.317 b. Parasitoid Source d.f. MS Diversity 1 0.073 Density 3 7.511 Block 1 183.659 Diversity × Density 3 20.056 Diversity × Block 1 1.242 Density × Block 3 7.143 Diversity × Density × Block 3 19.784 Error 14 15.342 4