A.G. Li et al. Agricultural and Forest Meteorology 106 2001 289–301 291
2. Materials and methods
2.1. Experimental facilities and design Spring wheat cv. Yecora Roja was planted on
the demonstration farm at the University of Arizona Maricopa Agricultural Center using a split-block de-
sign of four replications Fig. 1. Mainplots were atmospheric CO
2
concentrations of 550 mmol mol
− 1
elevated or 370 mmol mol
− 1
ambient. The ele- vated CO
2
concentration was maintained using the free air CO
2
enrichment FACE system. Subplots were two levels of irrigation treatments: well-watered
which allowed only 30 of the available water in the rooted zone to be depleted as determined from
estimates of potential evapotranspiration obtained from an on-farm meteorological station, and drought
stressed or limited-water treatment which supplied only half as much as the well-watered treatment at
each irrigation. Water was supplied by a sub-surface drip irrigation system 0.5 m tube spacing, 0.3 m emit-
ter spacing, 0.2 m depth. The cumulative irrigation amounts from emergence to harvest were 600 and
275 mm for well-watered and drought stress treat-
Fig. 1. FACE facilities in the field.
ments, respectively Lewin et al., 1992. The wheat was planted on 15 December 1992 and emerged on
1 January 1993. Final harvest was on 24 May 1993. Enrichment of CO
2
in the elevated CO
2
plots started on the day of emergence. Plants were grown in rows
spaced 0.25 m apart with 130 plants m
− 2
and received 277 kg N ha
− 1
and 44 kg P ha
− 1
over the growing season. Air temperature was measured 2 m above the
soil surface. Accumulated thermal units ATUs were calculated as:
ATU = X
T
max
+ T
min
2 −
T
b
1 where T
max
and T
min
represent daily maximum and minimum air temperatures based on hourly readings,
respectively. T
b
= 0 is the base temperature for wheat
Bauer et al., 1985. 2.2. Sample collection and processing
Anthesis began on 23 April and 50 of the spikes had flowered by 26 April. Sampling started 6 days
after anthesis with nine plants per subplot sampled every 3–4 days until maturity Fig. 2. The main stem
292 A.G. Li et al. Agricultural and Forest Meteorology 106 2001 289–301
Fig. 2. Wheat plants harvested from each treatment.
Fig. 3. The illustration of spikelets removed from the main stem spike a and numbering specific floret positions b.
was identified and spikelet numbers on a spike were counted. The spike was separated into three sections:
the upper section containing about one quarter of the spikelets, the middle section containing about one half
of the spikelets, and the lower section containing about one quarter of the spikelets Fig. 3a. Three spikelets:
the middle spikelet of the middle section, the second spikelet of the upper section from the middle, and the
second spikelet of the lower section from the middle, were removed from the spike of the main stem for
each plant Fig. 3a. Samples were dried for 14 days at 70
◦
C in an oven, put into a desiccator and allowed to cool. Then each kernel was weighed to nearest of
0.1 mg. Starting from proximal kernels to distal ones, the kernels were named the first, second, third, and
fourth kernels within a spikelet Fig. 3b.
2.3. Mathematical analysis The weights of individual kernels from the up-
per, middle, and lower spikelets of the main stem spike were fitted into a nonlinear cumulative logistic
model as a function of ATUs using SAS proc NLIN method = Marquardt. The common logistic model
was modified by introducing a constant P =19 value Li et al., 2000. This change enables us to estimate
grain filling duration to any fractional point instead
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
