A.G. Li et al. Agricultural and Forest Meteorology 106 2001 289–301 293
of the grain filling duration correspond to 0.5M. Here M
represents final grain weight g. Although total grain yield never reaches its asymptotic maximum M,
L measures the duration to 0.95M in this paper. The
equation of the modified logistic curve is shown below Y = M
P P +
e
− BX−L
2 where Y is the estimated grain weight g, X the ATU’s
from emergence, M the estimated final grain weight g, B the slope of logistic curve and related to the
grain filling rate, and L a measure of the completion of the grain filling process in ATUs. The grain filling
duration d was defined as the period between an in- dividual kernel weight of 0.003 g to 95 of the final
kernel weight. A significant difference in duration in this paper was defined by a difference in two kernels’
durations greater than standard errors of the comple- tion of individual kernel growth. After each model was
estimated, model adequacy was assessed by residual analysis. Following this, models were compared us-
ing a full model dummy variable procedure Bates and Watts, 1988. Duguid and Brûle-Babel 1994 have
defined the maximum rate of grain filling R based on logistic model parameters as: R =
1 4
MB . Although
an exact test for R is not possible, simultaneous con- trasts of parameters M and B provide an approximate
test. All computations were carried out using SAS 6.12 SAS Institute, 1989.
3. Results
3.1. Grain growth on various positions of a spike over four treatments
3.1.1. Kernel growth on the upper spikelet Only the first and second kernels in the upper
spikelet had enough data to fit the nonlinear cumu- lative logistic curves. Under ambient CO
2
and water stress conditions, the grain filling process of the first
kernel was different from that of the second kernel Table 1. This was caused by a lower grain filling rate
Table 2 and a longer grain filling duration within the second kernel Fig. 4A. We did not find a difference
in final kernel weight between the first and second kernels Table 1. We also detected a difference in
the grain filling process between the first and second kernels under elevated CO
2
and well-watered condi- tions Table 1, in which the first kernel was 2.0 mg
heavier than the second one Table 2 due to a longer grain filling duration Fig. 4A.
3.1.2. Kernel growth on the middle spikelet The ranking of kernel weights within a middle
spikelet was the second the first the third the fourth kernels and the ranking order was the same
over all four treatments Table 4. Differences in grain filling processes between the first and third, the
first and fourth, the second and third, the second and fourth, and the third and fourth kernels were detected
in all four treatments Table 1. Under ambient CO
2
and well-watered conditions, there was a difference in the grain filling process between the first and sec-
ond kernels Table 1, leading to a second kernel that was 3.8 mg heavier than the first one due to a
faster grain filling rate of 0.01 mg kernel
− 1
ATU
− 1
Table 4. Weights of the first and third kernels were not different under ambient CO
2
and drought stress conditions; the faster grain filling rate of the first
kernel Table 4 might outweigh the longer grain filling duration of the third kernel Fig. 4B. How-
ever, the weight of the first kernel was heavier than that of the third kernel due to a longer grain filling
duration under well-watered condition Fig. 4B and a faster grain filling rate under elevated CO
2
con- centration Table 4. The weight of the first kernel
was greater than that of the fourth kernel under all treatments due to a longer grain filling duration and
a faster grain filling rate associated with the first kernel Table 4. The second kernel were heavier
than the third and fourth kernel due to a faster grain filling rate in all treatments Tables 1 and 4. The
weight of the third kernel was greater than that of the fourth kernel due to a higher grain filling rate
regardless of the treatment Table 4. Moreover, a longer grain filling duration of the third kernel under
ambient CO
2
and drought stress also contributed to the greater kernel weight than those of the fourth
kernel Fig. 4B. Under the condition without water stress, the first kernel had the longest grain filling du-
ration, and the durations for second, third, and fourth kernels decreased gradually as the kernel number in-
creased Fig. 4B. However, this pattern did not hold under ambient CO
2
and drought stress conditions Fig. 4B.
294 A.G. Li et al. Agricultural and Forest Meteorology 106 2001 289–301
A.G. Li et al. Agricultural and Forest Meteorology 106 2001 289–301 295
Fig. 4. Grain filling durations in thermal units for individual kernels on the upper A, middle B, and lower spikelets C for different treatments. AD — ambient CO
2
and drought stress condition, AW — ambient CO
2
and well-watered condition, ED — elevated CO
2
and drought stress condition, EW — elevated CO
2
and well-watered condition.
296 A.G. Li et al. Agricultural and Forest Meteorology 106 2001 289–301
Table 2 Parameter estimates ±asymptotic standard errors for the upper
spikelet of the main stem over ambient A and elevated E CO
2
concentrations, and drought stress D and well-watered W treatments: maximum kernel weights mg per kernel M, slopes
of logistic curves B, grain filling rates R
a
, and proportion of variances explained by regressions var.
Treatment Parameter
Estimates First kernel
Second kernel AD
M 41.7±0.7
43.4±0.9 B
0.0104±0.0008 0.0083±0.0014
R 0.11
0.09 Var.
99 99
AW M
45.9±0.7 44.5±0.8
B 0.0085±0.0005
0.0091±0.0006 R
0.10 0.10
Var. 98
99 ED
M 43.8±0.6
45.7±1.0 B
0.0109±0.0007 0.0105±0.0011
R 0.12
0.12 Var.
99 98
EW M
48.5±0.8 46.5±0.8
B 0.0077±0.0005
0.0090±0.0006 R
0.09 0.10
Var. 99
99
a
R =
1 4
MB , the test of R is for difference in parameters M
and B.
3.1.3. Kernel growth on the lower spikelet Significant differences in grain filling processes
were found between the first and third, the first and fourth, the second and third, the second and fourth,
and the third and fourth kernels over all four growth conditions Table 1. As with the middle spikelet,
however, grain filling processes of the first and second kernels were not different except under ambient CO
2
and well-watered conditions Table 1. The ranking of the kernel weights in the lower spikelet was the same
as that of middle spikelet, i.e. the second the first the third the fourth kernels. The second kernel had
a faster grain filling rate Table 6, and a longer grain filling duration than the fourth kernel in all treatments
Fig. 4C. The first kernel weights under all four treatments were heavier than those of the third kernel
due to a faster grain filling rate under well-watered condition Tables 1 and 6 and a longer grain filling
duration under drought stress condition Fig. 4C. The weight of the first kernel was higher than that
of the fourth kernel due to both a longer grain filling duration and a faster grain filling rate Tables 1 and
6. The third kernel weighed more than the fourth kernel for various reasons. Under ambient CO
2
, the third kernel had a greater grain filling rate than the
fourth kernel, and difference in grain filling duration was not detected. Under elevated CO
2
and drought stress conditions, however, both a longer grain filling
duration and a faster grain filling rate contributed to the increase in weight of the third kernel Tables 1
and 6.
3.2. Effects of elevated CO
2
on the grain growth 3.2.1. Kernels on the upper spikelet
Elevated CO
2
affected grain filling processes of both the first and second kernels at the upper spikelet
under either drought stress or well-watered condition Table 3. Under drought stress condition, elevated
CO
2
increased the grain filling rate of the first and second kernels and led to final kernel weight increases
of 2.1 and 2.3 mg, respectively, compared to those un- der ambient CO
2
Table 2. Under well-watered con- dition, elevated CO
2
resulted in an increase in the first kernel weight of 2.6 mg due to a longer grain filling
Table 3 Individual kernel grain filling processes of the main stem upper
spikelet; maximum grain weights mg per kernel M, and grain filling rates R
a
contrast over ambient A and elevated E CO
2
concentrations, and drought stress D and well-watered W treat- ments
Contrasts First Kernel
Second Kernel d.f.
F d.f.
F AD–AW
3 12.15
∗∗∗
3 4.89
∗∗∗
AD–ED 3
9.76
∗∗∗
3 13.61
∗∗∗
AW–EW 3
21.34
∗∗∗
3 18.27
∗∗∗
ED–EW 3
8.98
∗∗∗
3 3.21
M
AD
–M
ED
1 5.22
∗
1 3.96
∗
R
AD
–R
ED
2 6.76
∗∗∗
2 15.48
∗∗∗
M
AW
–M
EW
1 5.28
∗
1 2.26
R
AW
–R
EW
2 5.90
∗∗∗
2 6.08
∗∗
M
AD
–M
AW
1 15.72
∗∗∗
1 0.68
R
AD
–R
AW
2 9.79
∗∗∗
2 0.36
M
ED
–M
EW
1 20.37
∗∗∗
1 0.43
R
ED
–R
EW
2 13.14
∗∗∗
2 2.63
a
R =
1 4
MB , the test of R is for difference in parameters M
and B.
∗
Significant at 0.05 level.
∗∗
Significant at 0.01 level.
∗∗∗
Significant at 0.001 level.
A.G. Li et al. Agricultural and Forest Meteorology 106 2001 289–301 297
duration, but had no effect on the second kernel weight Tables 2 and 3.
3.2.2. Kernels on the middle spikelet Elevated CO
2
influenced the grain filling processes of all the kernels on the middle spikelet over two
water regimes Table 5. Under drought stress condi- tions the weight of both the first and fourth kernels
increased 4.0 mg by elevated CO
2
, due to an enhanced grain filling rate. However, this did not occur under
well-watered conditions Table 4. Under drought stress condition, elevated CO
2
shortened the grain filling duration Fig. 4B and increased the grain
filling rate of the second and third kernels Tables 4 and 5. However, a faster grain filling rate may have
compensated for the shorter grain filling duration and difference in final kernel weight was not detectable
Table 4.
3.2.3. Kernels on the lower spikelet The grain filling processes of the first, second,
third and fourth kernels at the lower spikelet over two water treatments were influenced by elevated CO
2 Table 4
Parameter estimates ±asymptotic standard errors for the middle spikelet of the main stem over ambient A and elevated E CO
2
concentrations, and drought stress D and well-watered W treatments: maximum kernel weights mg per kernel M, slopes of logistic curves B and grain filling rates R
a
, and proportion of variances explained by regressions var. Treatments
Parameters Estimates
First kernel Second kernel
Third kernel Fourth kernel
AD M
47.3±0.9 52.1±1.4
45.6±1.8 31.5±1.2
B 0.0102±0.0008
0.0082±0.0009 0.0081±0.0013
0.0099±0.0017 R
0.12 0.11
0.09 0.08
Var. 98
97 95
97 AW
M 52.1±1.1
55.9±1.0 48.0±1.0
33.2±1.6 B
0.0073±0.0005 0.0079±0.0005
0.0087±0.0007 0.0092±0.0017
R 0.10
0.11 0.10
0.08 Var.
98 99
98 97
ED M
51.3±0.7 52.2±0.6
46.6±1.0 35.5±1.3
B 0.0101±0.0006
0.0106±0.0006 0.0103±0.0012
0.0101±0.0015 R
0.13 0.14
0.12 0.09
Var. 99
99 98
97 EW
M 53.9±0.9
56.3±1.0 48.2±0.9
36.1±1.5 B
0.0082±0.0005 0.0085±0.0006
0.0089±0.0006 0.0081±0.0013
R 0.11
0.12 0.11
0.07 Var.
99 99
99 98
a
R =
1 4
MB , the test of R is for difference in parameters M and B.
Table 7. Elevated CO
2
increased the grain filling rate of the first and fourth kernels, and led to increases
in the final kernel weight of 2.8 and 6.3 mg under drought stress conditions, respectively, and 5.0 and
7.5 mg under well-watered conditions, respectively Tables 6 and 7. Elevated CO
2
increased the second kernel weight by 2.8 mg under drought stress condi-
tion which was due to an increased grain filling rate. This did not occur under the well-watered condition
though Tables 6 and 7. The fourth kernel was more responsive to elevated CO
2
than the other kernels. 3.3. Effects of drought stress on the grain growth
3.3.1. Kernels on the upper spikelet Drought stress affected grain filling processes of the
first kernel at ambient and elevated CO
2
levels, and of the second kernel at the ambient CO
2
level only Table 3. Under ambient and elevated CO
2
condi- tions, the first kernel weight increased 4.2 and 4.7 mg,
respectively, under well-watered conditions due to a longer grain filling duration Fig. 3a.
298 A.G. Li et al. Agricultural and Forest Meteorology 106 2001 289–301
Table 5 Individual kernel grain filling processes of the main stem middle section; maximum grain weights mg per kernel M, grain filling rates
R
a
and the completion of grain filling processes L contrast over ambient A and elevated E CO
2
concentrations, and drought stress D and well-watered W treatments
Contrasts Kernel 1
Kernel 2 Kernel 3
Kernel 4 d.f.
F d.f.
F d.f.
F d.f.
F AD–AW
3 11.88
∗∗∗
3 14.41
∗∗∗
3 9.00
∗∗∗
3 4.21
∗∗
AD–ED 3
9.29
∗∗∗
3 5.07
∗∗
3 3.46
∗
3 4.11
∗∗
AW–EW 3
18.79
∗∗∗
3 19.42
∗∗∗
3 8.41
∗∗∗
3 4.49
∗∗
ED–EW 3
4.66
∗∗∗
3 3.97
∗∗
3 2.64
∗
3 2.06
M
AD
–M
ED
1 11.98
∗∗∗
1 0.02
1 0.37
1 5.66
∗
R
AD
–R
ED
2 9.21
∗∗∗
2 6.48
∗∗
2 5.00
∗
2 4.04
∗
M
AW
–M
EW
1 1.67
1 0.05
1 0.01
1 1.58
R
AW
–R
EW
2 9.31
∗∗∗
2 5.57
∗∗
2 1.59
2 1.57
M
AD
–M
AW
1 12.34
∗∗∗
1 3.17
1 1.55
1 0.66
R
AD
–R
AW
2 12.17
∗∗∗
2 3.37
∗
2 0.82
2 1.02
M
ED
–M
EW
1 4.64
∗
1 8.11
∗∗
1 0.93
1 0.09
R
ED
–R
EW
2 5.00
∗∗
2 5.13
∗∗
2 2.40
∗
2 1.05
a
R =
1 4
MB , the test of R is for difference in parameters M and B.
∗
Significant at 0.05 level.
∗∗
Significant at 0.01 level.
∗∗∗
Significant at 0.001 level.
Table 6 Parameter estimates ±asymptotic standard errors for the lower spikelet of the main stem over ambient A and elevated E CO
2
concentrations, and drought stress D and well-watered W treatments: maximum kernel weights mg per kernel M, slopes of logistic curves B, grain filling rates R
a
, and proportion of variances explained by regressions var. Treatments
Parameters Estimates
First kernel Second kernel
Third kernel Fourth kernel
AD M
49.5±1.0 50.9±1.2
45.5±1.1 34.2±1.3
B 0.0087±0.000
0.0096±0.0009 0.0099±0.00096
0.0112±0.0019 R
0.11 0.12
0.11 0.10
Var. 99
98 98
97 AW
M 51.3±1.2
55.6±1.2 48.2±1.2
37.5±1.6 B
0.0077±0.000 0.0076±0.0005
0.0078±0.0006 0.0084±0.0013
R 0.10
0.11 0.09
0.08 Var.
98 99
98 98
ED M
52.3±0.9 53.7±0.9
46.9±1.1 40.5±1.2
B 0.0093±0.000
0.0094±0.0007 0.0106±0.0012
0.0108±0.0022 R
0.12 0.13
0.12 0.11
Var. 99
99 98
98 EW
M 56.3±1.0
56.5±1.0 50.6±1.2
45.0±2.3 B
0.0078±0.000 0.0079±0.0005
0.0083±0.0007 0.0090±0.0016
R 0.11
0.11 0.10
0.10 Var.
99 99
98 96
a
R =
1 4
MB , the test of R is for difference in parameters M and B.
A.G. Li et al. Agricultural and Forest Meteorology 106 2001 289–301 299
Table 7 Individual kernel grain filling processes of the main stem lower spikelets; maximum grain weights mg per kernel M, and grain filling
rates R
a
contrast over ambient A and elevated E CO
2
concentrations, and drought stress D and well-watered W treatments Contrasts
Kernel 1 Kernel 2
Kernel 3 Kernel 4
d.f. F
d.f. F
d.f. F
d.f. F
AD–AW 3
10.93
∗∗∗
3 11.23
∗∗∗
3 10.07
∗∗∗
3 2.78
∗
AD–ED 3
16.13
∗∗∗
3 7.94
∗∗∗
3 5.69
∗∗∗
3 5.67
∗∗∗
AW–EW 3
27.44
∗∗∗
3 13.77
∗∗∗
3 13.61
∗∗∗
3 9.46
∗∗∗
ED–EW 3
7.76
∗∗∗
3 5.96
∗∗∗
3 6.49
∗∗∗
3 2.89
∗
M
AD
–M
ED
1 4.41
∗
1 4.58
∗
1 0.84
1 8.97
∗∗
R
AD
–R
ED
2 9.55
∗∗∗
2 4.69
∗∗
2 2.75
2 7.46
∗∗∗
M
AW
–M
EW
1 9.77
∗∗
1 0.27
1 1.71
1 7.69
∗∗
R
AW
–R
EW
2 15.95
∗∗∗
2 4.05
2 6.69
∗∗∗
2 8.61
∗∗∗
M
AD
–M
AW
1 1.20
1 8.22
∗∗
1 2.33
1 1.50
R
AD
–R
AW
2 3.64
∗
2 8.02
∗∗∗
2 6.25
∗∗
2 1.84
M
ED
–M
EW
1 8.39
∗∗
1 3.78
1 5.53
∗
1 4.25
∗
R
ED
–R
EW
2 6.07
∗∗
2 4.41
∗
2 5.21
2 3.55
∗ a
R =
1 4
MB , the test of R is for difference in parameters M and B.
∗
Significant at 0.05 level.
∗∗
Significant at 0.01 level.
∗∗∗
Significant at 0.001 level.
3.3.2. Kernels on the middle spikelet Drought stress influenced the grain filling pro-
cesses of all the kernels on the middle spikelet under both elevated and ambient CO
2
levels with the excep- tion of the fourth kernel at elevated CO
2
condition Table 5. The first kernel weight increased 4.8 and
2.6 mg under ambient CO
2
and elevated CO
2
levels, respectively, due to a prolonged grain filling dura-
tion Fig. 4B. The final weight of the second kernel increased 4.1 mg in the well-watered treatment at
elevated CO
2
again due to a prolonged grain fill- ing duration Fig. 4B. The third and fourth kernels
were less responsive to drought stress conditions than the first and second kernels in this experiment
Table 5.
3.3.3. Kernels on the lower spikelet All the grain filling processes of the individual ker-
nels at the lower spikelet were influenced by drought stress conditions over both CO
2
levels Table 7. Well-watered conditions increased the final kernel
weights of the first, third, and fourth kernels under elevated CO
2
due to a longer grain filling duration Fig. 4C, but not under ambient CO
2
Tables 6 and 7. The final weight of the second kernel increased
by well-watered condition due to a longer grain fill- ing duration under the ambient CO
2
condition only Tables 6 and 7. Water treatment had the most effect
on the fourth kernel weight.
4. Discussion
