Published in Agron. J. 96:1222-1230 (2004).
© American Society of Agronomy
677 S. Segoe Rd., Madison, WI 53711 USA
Agronomic Modeling
Simulating Seed Number in Grain Sorghum from Increases in Plant Dry Weight
T. J. Gerika,*,
W. D. Rosenthala,
R. L. Vanderlipb and
L. J. Wadec
a Texas Agric. Exp. Stn., Texas A&M Univ. Syst., Blackland Res. and Ext. Cent., 720 East Blackland Rd., Temple, TX 76502
b Dep. of Agron., Kansas State Univ., Manhattan, KS 66506
c School of Plant Biol., Univ. of Western Australia, Crawley, WA 6009, Australia
* Corresponding author (t-gerik{at}tamu.edu)
Received for publication May 30, 2002.
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ABSTRACT
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Simulation of seed number for crop models is important in identifying cultural practices, which enhance yield stability. Field and crop simulation studies examined the relationship between dry weight accumulation and seed number per plant to potentially improve the capability of the grain sorghum [Sorghum bicolor (L.) Moench] model, SORKAM, to simulate seed number. The best estimates of seed numbers were obtained from plant dry weight accumulated during the 360 growing degree day intervals encompassing panicle branch–spikelet formation (PBSI) and panicle elongation through anthesis (EAI). Comparison of observed vs. simulated seed numbers using SORKAM's original equations accounted for 57% of the variation in seed number, but it underestimated high seed numbers. Accumulated plant dry weight for the PBSI and EAI intervals accounted for 49 and 64% of the variation in seed number, respectively. Simulation of seed numbers improved when the more sensitive water stress coefficient (for leaf area, WATCOle) was applied to the interval (PBSI or EAI) experiencing the highest water stress while the less sensitive water stress coefficient (for dry weight, WATCOdw) was applied to the interval experiencing the lowest water stress. The slope from the regression of observed on simulated seed numbers was 0.80 (r2 = 0.57) for SORKAM with the WATCOle switch compared with 0.59 (r2 = 0.57) in the original SORKAM model. Hence, the timing and recovery of water stress during the panicle development period was important in estimating seed number of sorghum.
Abbreviations: E, SORKAM model containing Eq. [14], from A–480 to A+120 (600 GDD), approximating the time interval used to simulate seed number • EA, SORKAM with Eq. [17], from A–180 to A+180 (360 GDD), approximating the second half of the panicle development—panicle elongation through anthesis • EAI, interval encompassing panicle elongation through anthesis • GDD, growing degree days • PBS, SORKAM with Eq. [16], from A–540 to A–180 (360 GDD), approximating the first half of the panicle development—appearance of primary branches and spikelets appear on the developing panicle • PBSI, interval encompassing panicle branch and spikelet appearance • PBS/EA, SORKAM containing the empirically derived equations [i.e., representing panicle branch—spikelet appearance interval (A–540 to A–180) and panicle elongation–anthesis interval (A–180 to A+180)] with a switch to select the equations to simulate seed number. The switch compares the mean WATCO values for the two intervals and then directs the model to apply the equation associated with the interval where water stress was more severe (i.e., where the WATCO value was smaller) to simulate seed numbers for the whole 720-GDD interval • RMSE, root mean squared error • SORKAM, grain sorghum plant growth model • WATCO, water stress coefficient • WATCOdw, water stress coefficient for dry weight • WATCOle, water stress coefficient for leaf area • WATCOdw/le, the SORKAM with its original equations for estimating seed number but containing a switch that applies the water stress coefficient, WATCOdw or WATCOle, during the intervals of panicle branch–spikelet appearance (A–540 to A–180) and panicle elongation–anthesis (A–180 to A+180) depending on levels of water stress. The switch compares the mean WATCOle values of the two intervals and then applies WATCOle to the interval where water stress was more severe and WATCOdw to the interval where water stress was less severe. If water stress levels are equal, WATCOle is applied to both intervals
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INTRODUCTION
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SIMULATION MODELS were developed to predict crop growth, development, water use, and yield. SORKAM (Sorghum Growth Model–Kansas State and Texas A&M Universities) (Rosenthal et al., 1989), an improved version of the grain sorghum model SORGF (Arkin et al., 1976), plays an important role in helping to examine the influence of alternative sowing date, row spacing, plant density, soil properties, and irrigation timing on yield for sorghum in different regions of the world (Rosenthal et al., 1989; Rosenthal and Gerik, 1990; Vanderlip et al., 1995; Retta et al., 1990). SORKAM's ability to simulate seed number was reported by Heiniger et al. (1997), but given the importance of seed number, further examination is warranted.
Seed number of grain sorghum was determined during the panicle development and anthesis period. Lee et al. (1974) described panicle development beginning at panicle initiation—i.e., when the growing point changes from developing vegetative structures (leaves and stem) to reproductive structures typically 35 to 40 d after germination. They reported the appearance and development of the primary and secondary panicle branches and the spikelet primordial and glumes occurred in the first 21 d following panicle initiation. Thereafter, panicle structures increased in size—elongating and emerging from the leaf sheath of the panicle from the plant over the next 10 to 15 d. Both stages coincide with the period of rapid plant growth, when the leaves, stems and roots attain their maximum size (Vanderlip, 1972).
SORKAM assumes that plant growth and seed number are correlated during the panicle development–anthesis period by simulating seed number from mean daily dry weight accumulation during the panicle formation period—from 7 d after panicle initiation when seven to nine leaves have appeared to 10 d after anthesis (Vanderlip et al., 1984; Rosenthal et al., 1989). Cultivar-dependent coefficients relate daily aboveground dry weight to seed number as:
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where SNO is the number of seeds per plant that can be supported by the accumulated daily aboveground dry weight, DRIWT is the daily increase in aboveground dry weight (g plant–1), AVSD is an empirical cultivar- and temperature-dependent coefficient for relating the daily increase in aboveground dry weight to seed number, AVSNO is the weighted average seed number per plant, i is the day number starting with panicle initiation, and NND is the time interval (d) beginning 1 wk after growing point differentiation. These equations describe the relationship between increasing plant dry weight accumulation and seed number per plant in irrigated environments (Fischer et al., 1976; Wright et al., 1983) but do not address the wide range of planting dates and plant populations reported by Baker (1982). Similar relationships were used for maize (Zea mays L.) by Kiniry and Knievel (1995). Few values of AVSD are available (Rosenthal et al., 1989). In its current form, AVSD and AVSNO are probably less sensitive to environmental conditions (like water stress) when the structures responsible for seed number are forming (Heiniger et al., 1997).
Grain sorghum, like other cereals, approaches its genetic potential in seed number when growing conditions are favorable while unfavorable weather (water stress) or biotic stresses during the panicle development–anthesis interval lower final seed numbers. Water stress coefficients, like WATCO in SORKAM, modify the outcome of plant growth processes like crop phenology, leaf expansion, and dry weight accumulation in accordance with the crop's sensitivity to stress events (Rosenthal et al., 1989). In SORKAM, WATCO is derived from the fraction of plant available soil water in the root zone (PWHC). Separate WATCO coefficients are used to adjust plant growth, depending on the sensitivity of the process to water stress. For example, WATCOdw adjusts the daily increase in plant dry weight for water stress as:
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whereas WATCOle adjusts the daily increase in leaf area expansion for water stress as:
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The WATCOdw is more conservative in reducing accumulated dry weight than is WATCOle. WATCOdw uses a larger multiplier than WATCOle and is not triggered until the fraction of plant available soil water declines to 0.3 while WATCOle is more sensitive to water stress—being invoked when the fraction of plant available soil water reaches 0.5. Yet, evidence suggests that developmental periods immediately following panicle initiation (i.e., those associated with floral differentiation) are more sensitive to stress than developmental periods immediately before or after anthesis (Fischer, 1985). Meyer and Green (1980)(1981) reported greater sensitivity of reproductive tissue undergoing differentiation to water stress than somatic tissue.
Heiniger et al. (1997) compared simulated seed number from SORKAM with field observations using 20 Kansas data sets. They reported that the model accounted for 50% of the variation in observed in seed number, but it underestimated seed number by 400 seed per plant. This raises the following questions: Does the sensitivity of reproductive tissues to stress change with development? Are reproductive tissues forming immediately after panicle initiation more or less sensitive to water stress than the reproductive tissues formed before and immediately following anthesis? This study was conducted to further evaluate SORKAM's ability to simulate seed number and determine if alternative methods could improve the model's reliability for simulating seed number of grain sorghum.
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MATERIALS AND METHODS
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Field Study Procedures
Field experiments were conducted to explore the relationship between plant dry matter accumulation during grain formation and final seed number for the period used by SORKAM (480 GDD before anthesis, A–480, to 120 GDD after anthesis, A+120) with shorter, discrete intervals during the panicle development period. Two sorghum hybrids of slightly different maturity were grown on a Houston Black clay (fine, montmorrillonitic, thermic, Udic Pellustert) soil at the Blackland Research Center, Temple, TX, in four plant densities in spring and autumn plantings. The experiments were sown on 16 Mar. 1989 and 1 Aug. 1989 in six-row plots that were 18.0 m long, with five replicates arranged in a randomized complete block design. The hybrids, ‘Cargill 4462’ and ‘Cargill 6670’, were planted and hand-thinned after emergence to establish four population densities of 5, 12, 19, and 26 plants m–2 in rows spaced 0.69 m apart. The site received a preplant application of N (urea) and P (0–46–0) at rates of 350 and 57 kg ha–1, and supplementary irrigation was applied as needed to prevent the occurrence of water stress symptoms, i.e., leaf curling. Plants were inspected regularly for the presence of insects and sprayed, if necessary. No visual symptoms of water stress, nutritional disorders, or insect damage were observed. The experiments were harvested on 10 July 1989 and 15 Nov. 1989, respectively. Other cultural details are found in Rosenthal et al. (1993).
Field Study: Sampling and Data Collection
Times of emergence, panicle initiation, flowering, and physiological maturity were recorded for each plot. Maximum and minimum air temperatures were measured and used to calculate daily growing degree days (GDD) above a base temperature of 7°C (Vanderlip and Arkin, 1977). Leaf area, plant dry weight, and light interception were recorded at weekly intervals from panicle initiation to 10 d after anthesis. Crop development and sampling occasions are summarized in Tables 1 and 2, respectively, relative to the number of days and GDD from sowing.
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Table 1. The occurrence and duration in days and growing degree days (GDD) of phenological stages for sorghum hybrids Cargill 4462 (C4462) and Cargill 6670 (C6670) in spring and autumn sowings.
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Table 2. The occurrence in days and growing degree days (GDD) to successive dry weight sampling for sorghum hybrids Cargill 4462 (C4462) and Cargill 6670 (C6670) in the spring and autumn sowings.
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On each sampling occasion, total aboveground dry weight was estimated from a 0.5-m2 area. Plants were counted, pulled from the soil, and their roots removed and discarded. Samples were divided into green leaf, stem, and panicle (when exerted) for both main stems and tillers. Green leaf area was measured with a LI-COR 3000 leaf area meter (LI-COR, Lincoln, NE). The samples were oven-dried at 60°C for 48 h and dry weights of the components recorded.
At maturity, a 1.0-m2 sample was taken from each plot for dry weight components as described above. Heads from an additional 2.0-m2 of plot were also collected from each plot, and plant number, panicle number, panicle dry weight, grain yield, and 1000-grain weight were recorded for the combined sample (3.0 m2). Seed number per plant was calculated from plant number, 1000-grain weight, and grain yield.
Analysis of Seed Number and Increase in Dry Weight
Total aboveground dry weights were sorted within each of the four plant density categories. An exponential equation was fitted to the relationship between total aboveground dry weight and GDD for each of the 16 combinations of planting date, plant density, and hybrid, using the regression procedures of SYSTAT (Wilkinson, 1990) to normalize cumulative plant dry weight and minimize sample-to-sample variation in plant density among sampling times using the following equation:
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where W is the dry weight (g m–2); a, b, and c are fitted coefficients; and GDD is the cumulative growing degree days from emergence at 7°C base temperature. This enabled us to better calculate the plant dry weight for any date or combination of dates by substituting the corresponding GDD in Eq. [7] into the appropriate equation representing the appropriate combination for planting date, plant density, and hybrid. The plant dry weight (g plant–1) was then determined by dividing the calculated dry weights (g m–2) from the fitted equation by the plant number at final harvest (plant m–2). Aboveground plant dry weights (g plant–1) were then calculated for 120-, 360-, and 600-GDD intervals spanning the grain formation period from panicle initiation through flowering (see Table 3) and then used to compute the linear relationship between accumulated plant dry matter and seed number for the corresponding segment of the grain formation period, using the regression procedures of SYSTAT (Wilkinson, 1990):
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where N is the number of seeds per plant at harvest, a and b are fitted coefficients, and I is the accumulated aboveground dry weight (g plant–1).
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Table 3. Accumulated growing degree day (GDD) periods for sorghum hybrids Cargill 4462 (C4462) and Cargill 6670 (C6670) in spring and autumn sowings for 120-GDD intervals from 600 GDD before anthesis (A–600) to 240 GDD following anthesis (A+240) used to represent phenological stages for calculation of accumulated aboveground dry weight to estimate seed number of grain sorghum.
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Analyzing SORKAM's Seed Number Prediction
Simulations of seed number per plant were performed using SORKAM's original seed number equations (Eq. [1] and [2]) and with equations derived from regressions of plant dry weight on seed number (Eq. [8]) from field plantings described above. The field plantings (i.e., containing plant populations ranging from 5 to 26 plants m–2 and high fertility and irrigation) provided the opportunity to develop these relationships under stress-free conditions, hence representing the potential (or maximum) ability of the plant to accumulate dry matter and to develop the panicle and maximize seed number per plant. Thus, we were able to substitute these empirically derived equations in SORKAM for the original equations without compromising the model's ability to accumulate dry matter or modify dry matter accumulation (and seed number per plant) for water stress or other stresses and situations.
Data from 16 data sets representing 14 sites in U.S. Great Plains and two sites in Australia that were grown under irrigated and dryland conditions and representing a wide range in grain production (Table 4) were compared with simulated seed numbers from SORKAM containing different equations and alternative configurations. The suitability of SORKAM's water stress coefficients for dry weight (WATCOdw) and leaf expansion (WATCOle) were also examined in these comparisons by substituting Eq. [3] and [4] with Eq. [5] and [6].
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Table 4. Details of the 16 data sets used from which observed seed numbers were obtained for SORKAM validation and comparison modifications to the SORKAM.
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Alternative Simulation Periods and Computational Switch
A computational switch was added to SORKAM to determine if the empirically derived equations and/or WATCO coefficients applied to different segments of the panicle development period improved SORKAM's ability to simulate seed number. The panicle development period was separated into two periods—one encompassing panicle initiation and primary and secondary branch development (PBS) and the second encompassing panicle elongation and anthesis (EA).
Comparisons between observed and simulated seed number per plant were performed with linear regression to ascertain the model's precision and accuracy (Smith and Rose, 1995). A perfect fit between observed vs. simulated values would yield a regression coefficient (b1) of unity, intercept (b0) of zero, and coefficient of determination (r2) of 1.00. The bias and root mean squared error (RMSE) were also calculated to ascertain the strength of the relationship between the observed and simulated data (Wallach and Goffinet, 1987; Retta et al., 1990).
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RESULTS AND DISCUSSION
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Field Study: Accumulated Dry Weight versus Seed Number
Cargill 4462 flowered 4 d earlier than Cargill 6670 in the first (spring) planting and 3 d earlier in the second (fall) planting (Table 1). Both hybrids flowered 2 wk earlier when planted in autumn. Growing degree days from planting to panicle initiation and anthesis were similar for planting times, averaging 677 and 1217 GDD, respectively, and reflecting the warmer temperatures during the vegetative period for the autumn crop. Also, the times from panicle initiation to anthesis when potential seed numbers are set were similar over planting dates and cultivars—averaging 30 d or 540 GDD. In contrast, the spring crop experienced warmer temperatures requiring 14 fewer days but required 111 more GDD for the grain to reach maturity from anthesis.
Regression of accumulated dry matter on temperature (expressed as GDD) accounted for 80 to 93% of the variation in accumulated dry weight (Fig. 1 and Table 5). These equations offered a reliable means to estimate accumulated dry weight for discrete periods during panicle formation to study the relationship between seed number and dry matter accumulation.
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Fig. 1. Accumulation of aboveground dry weight (g/m2) with growing degree days from sowing (GDD) for sorghum hybrids Cargill 4462 and Cargill 6670 in spring and autumn sowings at each of two plant densities. The symbols represent actual data, and the curves are derived from the exponential equations presented in Table 5.
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Table 5. Exponential regressions of dry weight (W) on accumulated growing degree days (GDD) for two sorghum hybrids at two sowing times in each of four plant densities grown under irrigated conditions.
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Lee et al. (1974) described panicle development and its key stages. They found that the appearance of panicle branches, the initiation of spikelet primordia, and the completion of spikelet appearance and start of panicle elongation occurred in sequence at 5, 10, and 21 d post panicle initiation, which corresponds to 90, 180, and 380 GDD from panicle initiation or 450, 360, or 160 GDD from anthesis for the hybrids and planting dates in this study.
The panicle development period was divided into 120-, 360-, and 600-GDD intervals to examine the relationship between dry weight production and seed number for different stages of panicle development for the field studies. Intercepts (b0), regression coefficient (b1), and coefficient of determination (r2) were similar for equations of spring and autumn planting and hybrids (data not shown). Hence, data were combined to simplify the examination of the relationships between dry weight accumulation and seed number (Table 6). All equations produced reasonable predictions of seed number regardless if accumulated dry weight periods were divided into 120 or 360 intervals or encompassed longer 600-GDD periods when grown under optimum (i.e., well-watered) conditions. The goodness of fit (r2) ranged from 0.59 to 0.87 for equations associated with the intervals examined, confirming there is a high level of association between accumulated dry matter during panicle development and seed number. But equations exhibiting the best fit (i.e., those with the lowest intercept, b0, and highest coefficient of determination, r2) appeared to be those that included stages of spikelet formation and anthesis [i.e., from 360 GDD from anthesis (A–360) to 180 GDD following anthesis (A+180)] (Fig. 2 and Table 6).
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Table 6. Linear regressions of seed number per plant at harvest (N) and accumulation in plant dry weight (I) representing 120, 360, and 600 growing degree day (GDD) periods from 600 GDD before anthesis (A–600) to 240 GDD after anthesis (A+240). Subroutines for the prediction of potential floret number and final seed number were prepared using equations 16 and 17, respectively.
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Fig. 2. The relationship between final seed number per plant and cumulative aboveground dry weight during 360 growing degree day (GDD) interval for panicle branch–spikelet formation (A–540 to A–180) and panicle elongation–anthesis (A–180 to A+180) for sorghum hybrids Cargill 4462 and Cargill 6670 in spring and autumn sowings at each of four plant densities (5, 12, 19, and 26 plants/m2).
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SORKAM: Simulated versus Observed Seed Number
Simulated seed numbers with SORKAM using WATCOdw and its original seed number equations were compared with observed seed numbers from field observations of 16 independent data sets. Only one data set was common with the observed vs. simulated seed number comparisons by Heiniger et al. (1997). In addition, three empirical equations derived from the field study that appeared to be good predictors of seed number (see Table 6: Eq. [14], [16], and [17]) were substituted for the original seed number equations in SORKAM to determine if they might improve the model's capability for simulating seed number. Time intervals of these equations overlapped with those originally used by SORKAM [i.e., from panicle initiation (A–540) to 10 d post anthesis (A+180)] in the following manner: (i) Equation no. 14 (E), from A–480 to A+120 (600 GDD), approximated the time interval used to simulate seed number in SORKAM; (ii) Equation no. 16 [PBS], from A–540 to A–180 (360 GDD), approximated the first half of the panicle development—appearance of primary branches and spikelets appear on developing panicle; and (iii) Equation no. 17 [EA], from A–180 to A+180 (360 GDD), approximated the second half of the panicle development—panicle elongation through anthesis.
Linear regression of observed on simulated seed number revealed that the original equations in SORKAM accounted for 57% of the variation in observed seed number (Fig. 3a). The regression coefficient (b1) was significantly less than unity. Thus, the model underpredicted seed number when growing conditions were favorable and observed numbers were high. These findings were similar to those reported by Heiniger et al. (1997). Likewise, incorporating the empirically derived seed number equation, E, in SORKAM (using WATCOdw to modify dry weight accumulation and seed number for water stress) mirrored the findings with SORKAM. Yet, the equation derived representing the first half of panicle development, representing panicle branch–spikelet appearance (PBS), overpredicted seed number when growing conditions were poor and observed seed numbers were low (Fig. 3b). The intercept (b0) and bias were higher, and the regression coefficient (b1) and coefficient of determination (r2) and RMSE were lower for PBS than SORKAM. The equation representing the second half of panicle development (i.e., panicle elongation–anthesis, EA) underestimated seed numbers when growing conditions were good and observed seed numbers were high (Fig. 3c). The intercept and regression coefficients derived with EA were lower than those for SORKAM although the coefficient of determination (r2) was slightly higher.
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Fig. 3. The relationship between simulate and observed seed number per plant for the current SORKAM model with the equation for the interval including panicle branch formation through anthesis (e.g., E; see Eq. [14] in Table 6), the SORKAM model with the equation for the interval including panicle branch–spikelet formation (e.g., PBS; see Eq. [16] in Table 6), and the SORKAM growth model with the panicle elongation–anthesis interval (e.g., EA; see Eq. [17] in Table 6). SORKAM simulations in this figure use the stress coefficient for dry weight (WATCOdw) to modify simulated seed number for water stress.
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The sensitivity of the developing panicle to water stress and the resulting effects on seed number are well known (Eastin et al., 1983; Fischer, 1985). Examination of mean and minimum values of SORKAM's water stress coefficients for dry weight (WATCOdw; Table 7) and leaf area (WATCOle; Table 8) calculated for data sets used to test the model confirm the occurrence of water stress during panicle development and anthesis at several sites. Values for WATCOdw during the panicle branch–spikelet appearance period (A–540 to A–180) and the panicle elongation–anthesis period (A–180 to A+180) were higher than WATCOle at most sites, confirming that WATCOle was more responsive to the water deficits. Could a more responsive treatment of accumulated dry matter to water stress improve simulation of seed number associated with SORKAM, PBS, or EA? To answer the question, we replaced WATCOdw used to modify the incremental dry weight increase to simulate seed number with WATCOle.
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Table 7. Mean and minimum values for SORKAM water stress coefficients for dry weight during the 360 growing degree day (GDD) intervals during panicle branch/spikelet appearance (WATCOdw1) and during panicle elongation/anthesis (WATCOdw2) for each of 16 validation sites.
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Table 8. Mean and minimum values for SORKAM water stress coefficients for leaf expansion during the 360 growing degree day (GDD) intervals during panicle branch/spikelet appearance (WATCOle1) and during panicle elongation/anthesis (WATCOle2) for each of 16 validation sites.
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Replacing WATCOdw with WATCOle improved the performance of SORKAM for simulating seed number by increasing the regression coefficient and lowering the intercept, but the goodness of fit (r2) remained unchanged, and the regression coefficient remained considerably below unity (Fig. 3a and 4a). It did not change the overall performance of EA since regression coefficients (b1) remained the same (Fig. 3c and 4c). Replacing WATCOdw with WATCOle improved the performance of PBS to simulate seed number by increasing the regression coefficient (b1) from 0.47 to 0.63 and increasing the goodness of fit (r2) from 0.49 to 0.69 (Fig. 3b and 4b). Despite modest improvements, substituting WATCOdw with WATCOle did little to improve SORKAM's overall ability to simulate seed number, whether the SORKAM, PBS, or EA versions of the model, comprising the different periods involving panicle development and anthesis, were used. However, PBS seemed to better simulate seed number than SORKAM and EA when observed seed numbers were high while SORKAM and EA seemed to better simulate seed numbers than PBS when observed seed numbers were low (Fig. 3 and 4).
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Fig. 4. The relationship between simulated and observed seed number per plant for the current SORKAM, the SORKAM model with the equation for the interval including panicle branch–spikelet formation (e.g., PBS; see Eq. [16] in Table 6), and the SORKAM growth model with the panicle elongation–anthesis interval (e.g., EA; see Eq. [17] in Table 6). SORKAM simulations in this figure use the stress coefficient for leaf expansion (WATCOle) to modify simulated seed number for water stress.
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To account for the differences associated with PBS and EA, we a constructed a version of SORKAM (PBS/EA) containing the empirically derived equations [i.e., representing panicle branch–spikelet appearance interval (PBS, A–540 to A–180) and panicle elongation–anthesis interval (EA, A–180 to A+180)] with a switch to select the equations to simulate seed number. The switch compared the mean WATCO values for the two intervals and then directed the model to apply the equation associated with the interval where water stress was more severe (i.e., where the WATCO value was smaller) to simulate seed numbers for the whole 720-GDD interval. If WATCO coefficients for the two intervals were equal, the switch directed the model to apply the equation associated with the panicle branch–spikelet appearance interval to simulate seed number. Both coefficients, WATCOle and WATCOdw, were evaluated to ascertain which one, if any, might better enable PBS/EA to simulate seed number.
The PBS/EA model with WATCO switch improved SORKAM's ability to simulate seed number. Regression of observed on simulated seed numbers yielded regression coefficients approaching unity when using either WATCOdw or WATCOle in compensating for water stress (Fig. 5a and 5b)—clearly better than SORKAM, PBS, and EA (Fig. 3 and 4). The intercept (b0) and bias of observed on simulated seed number with the PBS/EA and WATCOle (Fig. 5a) were smaller than the intercept for PBS/EA and WATCOdw (Fig. 5b). These findings suggests that PBS/EA model with the WATCOle may better simulate seed number than PBS/EA with WATCOdw. Yet, the coefficient of determination (r2) of PBS/EA with WATCOle was similar to the original SORKAM regardless of the water stress coefficients applied.
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Fig. 5. The relationship between observed and simulated seed number per plant for SORKAM model containing the WATCO switch to apply the empirically derived equation for the panicle branch–elongation interval (PBS; Eq. [16], Table 6) or the panicle elongation–anthesis interval (EA; Eq. [17], Table 6) using (a) the water stress coefficient for leaf area (WATCOle), (b) the water stress coefficient for dry weight (WATCOdw), or (c) the original SORKAM equations and replacing WATCOle with WATCOdw in the PBS or EA interval, whichever is greater, but applying WATCOle to simulation of seed numbers to both intervals when water stress is equal.
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Obviously, physiologically descriptive equations, like those in the original SORKAM, for simulating seed number better serve the model, the modeler, and the user, if the results are comparable to empirically derived functions. The success with PBS/EA containing WATCOle to simulate seed number suggests that the effects of water stress cannot be uniformly applied to the key intervals [i.e., panicle branch–spikelet appearance (A–540 to A–180) and panicle elongation–anthesis (A–180 to A+180)] associated with simulation of seed number but should be handled differently, depending on the interval and severity of the stress.
To further test this hypothesis, we developed another model, WATCOdw/le, using SORKAM with its original equations and containing a switch that changed the water stress coefficients, WATCOdw and WATCOle, used during the intervals of panicle branch–spikelet appearance (A–540 to A–180) and panicle elongation–anthesis (A–180 to A+180), depending on levels of water stress. The switch compared the mean WATCOle values of the two intervals and then applied WATCOle to the interval where water stress was more severe and WATCOdw to the interval where water stress was less severe. If water stress levels were equal, WATCOle was applied to both intervals.
Regressing the observed on simulated values from WATCOdw/le revealed a significant improvement in the model's ability to simulate seed number over the original version of SORKAM (Fig. 3a and 5c). The results showed that the regression coefficient from WATCOdw/le was higher than that from SORKAM (b1 = 0.80 vs. 0.59) and the intercept lower (b0 = 647 vs. 969) although coefficients of determination (r2) were similar. Although the intercept was not as low and the regression coefficient not as close to ideal (b1 = 1.00) with WATCOdw/le as it was with SK-PBS/EA, the bias and RMSE from SK-Wdw/le were lower (Fig. 5a and 5c).
Both approaches, SK-PBS/EA and SK-Wdw/le, improved SORKAM's ability to simulate seed number over the original SORKAM. However, their differences were small, so recommending one method over another is not as important as the need to differentiate the impact of water stress on dry matter accumulation during the two periods associated with panicle development: (i) associated with panicle branch/spikelet development, and (ii) associated with panicle elongation. Applying a more sensitive approach or water stress coefficient to the period experiencing the greatest stress clearly improved our ability to simulate seed number of grain sorghum.
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SUMMARY
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The accumulation dry weight during panicle development and anthesis growth of well-watered, field-grown grain sorghum accounted for 60 to 87% of the variation in seed number. Yet, in-depth analyses of 120- and 360-GDD intervals during panicle development revealed that accumulated dry weights during the later stages of panicle development better estimated seed number than the intervals immediately following panicle initiation.
Comparing observed vs. simulated seed numbers from 16 independent data sets confirmed Heiniger et al. (1997) findings that SORKAM underestimated seed numbers. Examination of SORKAM's water stress coefficients from these experiments revealed that the highest stresses usually occurred during the latter part of the simulation period, but there were instances when stresses were more severe in the early stages. Modifying SORKAM to substitute a more sensitive water stress coefficient (i.e., the stress coefficient for leaf area) for the coefficient for the less sensitive water stress coefficient (i.e., the stress coefficient for dry weight) or a more sensitive empirical method for estimating seed number during the panicle branch/spikelet development interval and panicle elongation interval experiencing the highest water stress revealed that the timing and/or recovery of water stress when seed numbers are determined during the panicle initiation through anthesis period is important in simulating seed number.
Although seed number may be reduced by a variety of environmental and biotic factors, only environmental factors, which directly affect dry weight accumulation in the current SORKAM model (light interception, radiation use efficiency, and water stress), were considered in this study. Variations in assimilate supply after the critical anthesis period would not affect seed number but would be manifest in seed size. This study illustrates that dry weight accumulation following panicle initiation reasonably predicts final seed number of grain sorghum, but the relationship between dry weight and seed numbers for the intervals associated with panicle branch–spikelet appearance and panicle elongation–anthesis seems to differ in sensitivity and/or recovery from to water stress.
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ACKNOWLEDGMENTS
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We express our appreciation to the Queensland Department of Primary Industries who permitted Dr. Wade to work for 12 months at the Blackland Research Center in Temple, TX. Financial support was provided by the Central Queensland Grain Sorghum Marketing Board (now GRAINCO) and Texas Agricultural Experiment Station.
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NOTES
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Contribution no. 97-272-J from the Kansas Agric. Exp. Stn.
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ABSTRACT
INTRODUCTION
