1. 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 +

2. 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 aCO2, ambient [CO2]; eCO2, elevated [CO2]. Data are means ±SE (n=4). NSC was the sum of starch, sucrose, glucose and fructose.

3. 2014;
y = x
R2 = 0.961***
2014;
y = x
R2 = 0.599**
2013;
y = x
R2 = 0.725***
2013;
y = x
R2 = 0.816***
2013;
y = x
R2 =
2014;
y = x
R2 = 0.872***
2013;
y = x
R2 = 0.654**
2014;
y = 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.

4. Supplementary Table S2. Yield and phenological parameters for the 12 soybean cultivars grown under two levels of planting density in 2013 and 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 + *

5. 2013;
y = x
R2 = 0.847***
2013;
y = x
R2 = 0.736**
2014;
y = x
R2 =
2014;
y = x
R2 = 0.916***
2014;
y = 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.

6. 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

7. 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)

8. 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