<p> ELECTRONIC SUPPLEMENTARY MATERIAL</p><p>Table S1. ANOVAS for effects of mixture richness (two or three species, SR), atmospheric CO2</p><p> concentration (CO2), soil heterogeneity (SH) and their interactions on relative yield total</p><p>(RYT) and Dmax. All the terms are tested against the overall model residual. P values</p><p> below 0.05 are shown in boldface.</p><p>Source of variation RYT* Dmax MS F P MS F P df SR 1 4.11 10-3 0.74 0.394 1.45 10-2 0.72 0.401 -2 CO2 1 5.47 10 9.81 0.003 0.31 15.37 <0.001 SH 1 4.35 10-3 0.78 0.381 8.15 10-3 0.40 0.529 -4 -4 SR  CO2 1 8.63 10 0.16 0.695 7.56 10 0.04 0.848 SR  SH 1 7.93 10-5 0.01 0.905 1.57 10-4 0.01 0.930 -4 -2 CO2  SH 1 1.55 10 0.03 0.868 1.53 10 0.76 0.388 -3 -3 SR  SH CO2 1 5.81 10 1.04 0.312 4.18 10 0.21 0.652 Residual 56 5.57 10-3 2.03 10-2 * ANOVA results are shown for sqrt-transformed data. Homogeneous Heterogeneous 1200 1200 Total d cd cd c cd 1000 c c bc 1000 c 800 ab 800 a b 600 600 ab a 400 400 ) ) 2 200 200 2 - - m m</p><p> g 0 0 g ( (</p><p> s Pl Lo Hl Lopl Plhl Lohl Plohl Pl Lo Hl Lopl Plhl Lohl Plohl s s s a a</p><p> m 800 800 m o Belowground o i bc c i B bc bc B d cd bc 600 cd 600 cd ab bc a 400 400 ab a 200 200</p><p>0 0 Pl Lo Hl Lopl Plhl Lohl Plohl Pl Lo Hl Lopl Plhl Lohl Plohl Species composition</p><p>Figure S1. Differences among composition (SC) levels for total and belowground biomass compared across soil heterogeneity levels. For each soil heterogeneity level, different lowercase letters indicate significant differences among SC levels (P < 0.05, Tukey’s HSD test after a Two-</p><p> way ANOVA with SC and [CO2] as main factors). The effects of [CO2], and of the [CO2]  SC</p><p> interaction, were not significant in any case (F[CO2] < 3.2 , df = 6, 42, P > 0.080; F[CO2]  SC < 0.7 , df = 6, 42, P > 0.646). Data were log-transformed prior to ANOVA analyses. Data represent means + 1 SE (n = 8). Ambient CO2 (37.5 Pa) Elevated CO2 (70 Pa) 1200 1200 Total Homogeneous Heterogeneous 1000 1000</p><p>800 800</p><p>600 600</p><p>400 400</p><p>200 200</p><p>0 0 1 2 3 1 2 3 500 500 Aboveground</p><p>400 400 ) ) 2 2 - - m m</p><p> g g 300 300 ( (</p><p> s s s s a a 200 200 m m o o i i B B 100 100</p><p>0 0</p><p>200 200</p><p>400 400</p><p>600 600 Belowground 800 800 1 2 3 1 2 3 Species richness</p><p>Figure S2. Total (upper panels), aboveground (central panels) and belowground (lower panels)</p><p> biomass of the assemblages compared among richness, [CO2] and heterogeneity levels.</p><p>Data are means + 1 SE (n = 12, 12 and 4 for the 1, 2 and 3 species richness levels,</p><p> respectively). Ambient CO2 (37.5 Pa) Elevated CO2 (70 Pa) 20 20 ) ) Homogeneous e e Heterogeneous m m 18 18 u u l l o o v v</p><p>% % 16 16 ( (</p><p> e e r r u u t t 14 14 s s i i o o m m</p><p> l l 12 12 i i o o S S 10 10 Pl Lo Hl Lopl Plhl Lohl Plohl Pl Lo Hl Lopl Plhl Lohl Plohl Species composition</p><p>Figure S3. Volumetric soil moisture (0-12 cm depth) in the microcosms at harvest. Data represent means + 1 SE (n = 4). The main effects of [CO2] and of the interaction Species</p><p>Composition (SC)  [CO2] were marginally significant (F[CO2] = 3.75, df = 1,84, P = 0.056; FSC </p><p>[CO2] = 2.42, df = 4,84, P = 0.055). The rest of main effects and interactions were not significant</p><p>(P > 0.266 in all cases). Lo = Lolium perenne monoculture, Pl = Plantago lanceolata monoculture, Hl = Holcus lanatus monoculture, Lopl = Lolium + Plantago mixtures, Plhl =</p><p>Plantago + Holcus mixtures, Lohl = Lolium + Holcus mixtures, and Plohl = Plantago + Lolium +</p><p>Holcus mixtures.</p>