Supplementary Table S1. Yield and phenological parameters of 12 soybean cultivars grown under two [CO2] levels in two years: aCO2, ambient [CO2]; eCO2, elevated [CO2]. Ratio represents the difference between eCO2 and aCO2 for the numbers of days from VE to R1 and from R1 to R7, and the ratio of eCO2 to aCO2 for the other parameters. The values are the means of n = 4 or 5 plants. ***P < 0.001; **P < 0.01; *P < 0.05; +P < 0.1; ns, not significant. Cultivar CO2treatmet Aboveground biomass (g plan-1) Branch number per plant Node number of main stem Harvest index Pod number per plant Pod bumber per aboveground biomass Seed number per pod Single seed weight (mg) Number of days from VE to R1 Number of days from R1 to R7 Season 2013 2014 Yukihomare aCO2 31.3 38.4 3.3 5.0 9.0 8.8 0.63 0.52 32.3 54.0 1.03 1.41 1.96 1.71 313.0 220.2 29 28 44 55 eCO2 37.8 48.4 4.0 5.3 0.56 36.4 62.3 0.96 1.29 1.85 1.77 308.5 228.4 47 59 Ratio 1.21 1.26 1.23 1.05 0.98 0.88 0.99 1.13 1.15 0.94 0.91 1.04 -1.4 -0.3 2.4 Ohsuzu 63.9 74.9 5.4 6.5 14.0 13.5 0.61 0.59 56.4 64.3 0.86 1.78 1.65 394.8 421.4 38 41 68 75 69.5 84.4 4.8 7.5 13.8 13.3 0.53 0.54 66.5 0.70 0.79 1.84 1.58 411.7 439.5 39 40 71 76 1.09 0.89 0.92 0.95 0.8 -0.8 3.8 1.3 Ryuhou 75.4 78.4 6.4 6.0 14.8 0.58 61.0 63.0 0.81 0.80 1.93 2.02 378.3 355.6 36 62 73 96.0 95.2 14.6 70.6 64.5 0.74 0.68 2.38 375.7 349.8 65 72 1.27 1.00 1.06 0.90 0.97 1.16 1.02 0.84 1.18 -0.4 3.6 -1.0 Enrei 81.1 84.7 7.0 14.2 15.8 65.8 56.0 0.66 2.20 353.0 409.3 45 60 130.0 118.2 6.8 9.3 16.3 0.47 90.0 77.0 0.69 0.65 2.49 364.7 369.1 43 69 1.60 1.40 1.37 1.38 0.85 4.2 1.8 Miyagishirome 107.8 104.6 7.3 16.8 19.3 0.48 69.8 63.5 1.99 1.88 365.9 425.7 52 74 163.5 151.5 8.5 17.4 20.3 0.42 0.50 107.2 92.5 1.80 1.94 350.4 421.3 77 1.52 1.45 1.17 1.54 1.46 1.01 0.4 -0.5 -1.3 Mandarin 31.7 31.1 4.6 13.6 15.0 0.62 43.2 42.5 1.36 1.86 247.2 247.3 26 50 54.6 51.0 15.6 16.5 0.55 0.64 56.8 59.5 2.09 2.08 255.3 261.0 27 54 63 1.72 1.64 1.10 1.31 0.76 1.12 1.11 -0.6 4.5 Dunfield 68.4 64.0 4.4 16.6 17.3 0.51 111.3 1.39 1.74 2.12 1.61 171.4 201.5 89.2 77.8 5.6 8.3 17.2 0.43 97.6 120.3 1.55 2.19 1.57 181.5 212.6 49 58 1.22 1.08 3.0 Athow 62.8 74.0 3.4 18.5 0.60 77.3 2.58 2.50 224.2 245.9 77.4 78.9 3.5 18.6 19.0 67.2 79.3 0.87 2.64 2.47 240.6 250.1 1.07 0.83 0.0 1.0 2.8 Harosoy 54.5 42.1 17.0 67.0 1.59 2.35 2.16 191.5 190.9 85.1 69.3 5.2 5.5 18.8 20.5 100.6 97.0 2.31 2.14 201.2 215.4 1.56 1.50 Harosoy-dt1 35.2 21.7 8.0 0.67 41.0 41.8 1.25 274.7 263.8 66 49.7 32.8 5.8 49.0 52.8 2.26 277.7 270.7 67 1.51 1.44 1.20 0.3 Williams 87.1 74.7 6.3 19.5 70.5 76.0 2.66 2.67 258.7 224.3 35 30 110.6 99.3 21.0 90.5 100.8 0.82 2.89 244.1 223.8 33 1.33 1.28 1.6 2.5 0.6 0.5 Williams-dt1 49.6 56.2 10.8 51.6 71.3 2.41 239.6 206.4 31 83 63.3 60.2 60.0 75.0 2.39 1.92 217.1 32 87 ANOVA CO2 *** ns * ** Cultivar (CV) CO2ｘCV +

Supplementary Fig. S1. Photosynthetic rate and nonstructural carbohydrate (NSC) content on leaf dry mass base at flowering (A, C) and seed filling stage (B, D) of several soybean cultivars grown under two [CO2] levels in 2014. aCO2, ambient [CO2]; eCO2, elevated [CO2]. Data are means ±SE (n=4). NSC was the sum of starch, sucrose, glucose and fructose.

2014; y = - 0.099 + 1.054 x R2 = 0.961*** 2014; y = - 2.098 + 3.257 x R2 = 0.599** 2013; y = - 2.359 + 3.414 x R2 = 0.725*** 2013; y = - 0.083 + 0.959 x R2 = 0.816*** 2013; y = - 0.215 + 1.609 x R2 = 0.248+ 2014; y = - 0.12 + 1.164 x R2 = 0.872*** 2013; y = 0.243 + 0.817 x R2 = 0.654** 2014; y = - 2.141 + 3.529 x R2 = 0.401* Supplementary Fig. S2. Linear regressions between the relative increase in seed yield (eCO2/ aCO2) with elevated [CO2] and the relative changes in (A) the node number on the main stem, (B) aboveground biomass, (C) harvest index, and (D) pod number in 2013 (black circles) and 2014 (white circles). ***P < 0.001; **P < 0.01; *P < 0.05; +P < 0.1.

Supplementary Table S2. Yield and phenological parameters for the 12 soybean cultivars grown under two levels of planting density in 2013 and 2014. ND, normal plant density (= 9.52 plants per m2) ; LD, low plant density (= 4.76 plants per m2). Data are means (n = 3). Ratio represents the difference between LD and ND for the numbers of days from VE to R1 and from R1 to R7, and the ratio of LD to ND for the other parameters. ***P < 0.001; **P < 0.01; *P < 0.05; +P < 0.1; ns, not significant. Cultivar Plant density Aboveground biomass (g plant-1) Branch number per plant Node number of main stem Harvest index Pod number per plant Pod number per aboveground biomass Seed number per pod Single seed weight(mg) Number of days from VE to R1 Number of days from R1 to R7 2013 2014 Yukihomare ND 45.1 46.5 4.1 3 9 9.3 0.68 0.59 51.5 55.5 1.15 1.20 1.85 1.69 317.9 292.1 31 30 60 58 LD 70.7 48.6 5.1 3.8 9.2 9.7 0.69 81.1 57.9 1.16 1.19 1.87 1.83 318 269.2 57 Ratio 1.57 1.05 1.23 1.27 1.02 1.04 1 1.00 1.01 1.08 0.92 -1 Ohsuzu 93.3 122.4 5.5 6.8 14.4 14 0.62 0.6 104.6 115.5 1.12 0.94 1.68 1.62 329.4 391.8 45 47 63 68 148.9 166.7 6.3 7.9 14.1 15.2 0.61 0.58 166.0 158.3 0.95 1.71 1.58 318.7 382.5 62 1.6 1.36 1.17 0.98 1.09 0.96 1.59 1.37 0.97 Ryuhou 86.8 105.1 6.2 5.7 15 0.53 103.5 100.3 1.65 309.7 339.2 44 41 64 71 133.9 146.7 7 7.3 14.9 14.5 0.55 159.6 137.6 1.67 305.2 346 40 1.54 1.4 1.13 1.28 1.03 0.99 Enrei 88.8 108.8 5.6 6.7 15.5 15.7 0.52 99.9 97.8 0.91 1.66 1.60 321.3 358.9 48 74 147.9 185.3 8.5 16 0.51 165.6 160.9 0.87 1.64 333.1 360.3 1.7 1.3 Miyagishirome 72.4 131.5 18 19.1 0.29 0.46 81.2 101.3 1.11 0.77 0.79 1.77 342.9 337.1 59 54 87 127.7 239.7 8.6 18.8 20.1 154.7 186.5 0.81 1.73 342.2 333.6 72 1.76 1.82 1.39 1.90 1.84 Mandarin 58.4 56.1 3.3 14.8 17.1 74.3 1.33 1.96 1.95 248.6 229.1 28 65 102.6 97.4 4.9 4.2 16.5 17.3 139.5 123.1 2.01 2.02 247.1 235.2 1.74 1.49 1.29 1.72 Dunfield 84.2 83.6 6.6 18.1 18.5 0.56 119.5 106.4 1.42 2.09 2.19 189.2 204.7 38 129.5 122.5 7.6 19.6 193.7 157.1 1.50 179.4 202.7 39 1.47 1.22 1.06 0.83 1.48 Athow 74.1 85.2 4 19.2 21.6 0.57 114.7 2.21 2.34 183.1 190.1 32 80 112 126.5 4.4 5.9 18.7 21.5 0.63 162.8 148.4 1.46 1.21 2.26 2.52 191.4 194.2 29 1.51 1.1 1.07 Harosoy - 110.8 7.4 110.4 2.70 240.8 162.1 7.7 175.3 2.37 221.7 0.88 Harosoy-dt1 62.1 3.6 20.9 0.65 64.8 1.18 2.16 236.4 80.7 0.66 72.7 256.5 0.89 Williams 90.8 88.9 5.3 7.5 22.2 0.54 114.4 93.7 2.30 2.23 206.5 217.6 34 77 81 152 143.3 6.9 10.4 21 22.9 190.8 166.1 1.26 2.28 2.35 205.6 211.8 1.61 1.38 Williams-dt1 48.4 11 56.7 293.2 76 4.6 12.5 75.5 2.48 283.9 1.14 ANOVA Plant density (PD) *** ** ns Cultivar (CV) PDxCV + *

2013; y = 0.276 + 0.817 x R2 = 0.847*** 2013; y = -0.717 + 1.469 x R2 = 0.736** 2014; y = 0.403 + 0.870 x R2 = 0.248+ 2014; y = 0.007 + 0.984 x R2 = 0.916*** 2014; y = -0.1432 + 1.109 x R2 = 0.834*** Supplementary Fig. S3. Linear regressions  between the relative increase in seed yield (low density, LD / normal density, ND) caused by low planting density for (A) branch number, (B) aboveground biomass, and (C) pod number in 2013 (black circles) and 2014 (white circles). ***P < 0.001; +P < 0.1. Data for 2013 only, n = 9.

aIdentified by Ziska et al. (2001). Supplementary Table S3. Descriptions of the 12 soybean cultivars used in this study. aIdentified by Ziska et al. (2001). Cultivar Country Maturity group Determinacy aCharacteristics Yukihomare Japan II Determinate Ohsuzu III Ryuhou IV Enrei Miyagishirome VII Mandarin USA I Indeterminate High CO2 responsive Dunfield Low CO2 responsive Athow Harosoy Harosoy-dt1 Williams Moderate CO2 responsive Williams-dt1

Normal density Low density July 3, 2014 (30 days after sowing) 0.3m 0.15m July 16, 2014 (43 days after sowing) Supplementary Fig. S4. Pictures of plant canopy of two densities at 30 days after sowing and 43 days after sowing of a cultivar ‘Ryuhou’ . These were taken by a camera for measurement of canopy coverage ratio (GACS1, Kimura-Kougei)

Supplementary Table S4. Monthly mean temperature, solar radiation, and precipitation in 2013 and 2014. Air temperature (°C) June July August September October 5-month mean Chamber 2013 22.1 23.4 25.4 21.9 15.3 22.2 2014 24.2 24.4 20.1 14.9 21.1 Field 19.6 21.8 23.5 19.1 13.2 19.4 20.2 22.7 17.1 11.1 18.8 30-year mean 17.8 21.3 22.9 18.2 11.5 18.3 Solar radiation (MJ m-2 d-1) 20.4 12 16.6 12.2 8.3 13.9 18.6 18.4 11.6 15.2 15.1 15 11.8 9.8 13.8 Precipitation (mm) 71.5 261.5 236 95 130 158.8 37.5 503.5 202.5 210 255.5 241.8 108.1 196.4 181.9 155.9 92.5 146.9