Published online 1 September 2007
Published in Crop Sci 47:2078-2088 (2007)
© 2007 Crop Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
SEED PHYSIOLOGY, PRODUCTION & TECHNOLOGY
Simulating Source-Limited and Sink-Limited Kernel Set with CERES-Maize
J. I. Lizasoa,
A. E. Fonsecab and
M. E. Westgateb,*
a Dep. of Agronomy, Univ. of Florida, Gainesville, FL 32611-0500
b Dep. of Agronomy, Iowa State Univ., Ames, IA 50011
* Corresponding author (westgate{at}iastate.edu).
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ABSTRACT
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CERES-Maize simulates kernel set as a source-limited process based on average plant growth rate during the lag phase after flowering. Yet the number of kernels formed by maize (Zea mays L.) also depends on timely interaction between male and female flowers, which can limit formation of reproductive sinks under some conditions. Failure to account for sink-limited kernel set may contribute to simulation error observed under conditions that affect dynamics of pollen shed or silking, but do not alter crop growth rate. We developed algorithms for a Flowering Model to simulate sink-limited kernel set from flowering dynamics. This model was calibrated against kernel production in hybrid seed production fields and then linked to CERES-Maize. The Modified CERES-Maize was calibrated against two years of field data involving three hybrids, eight population densities, and seven N levels. Integrating the capacity to simulate sink-limited kernel set with source-limited kernel set increased simulation accuracy dramatically, relative to original CERES-Maize. For 13 commercial fields tested, Modified CERES-Maize decreased simulation error for kernels per plant from 17.1 to 2.3%, improved r2 between measured and simulated values from 0.77 to 0.87, and decreased simulation error indicators mean error, root mean square error, and mean square deviation by 85, 40, and 64%, respectively. Modified CERES-Maize accounts for a much greater range of variability in the biological processes controlling kernel set.
Abbreviations: ASI, anthesis–silking interval • GDD, growing degree days • IPAR, intercepted photosynthetically active radiation
Simulating Source-Limited and Sink-Limited Kernel Set with CERES-Maize
J. I. Lizasoa,
A. E. Fonsecab and
M. E. Westgateb,*
a Dep. of Agronomy, Univ. of Florida, Gainesville, FL 32611-0500
b Dep. of Agronomy, Iowa State Univ., Ames, IA 50011
* Corresponding author (westgate{at}iastate.edu).
CERES-Maize simulates kernel set as a source-limited process based on average plant growth rate during the lag phase after flowering. Yet the number of kernels formed by maize (Zea mays L.) also depends on timely interaction between male and female flowers, which can limit formation of reproductive sinks under some conditions. Failure to account for sink-limited kernel set may contribute to simulation error observed under conditions that affect dynamics of pollen shed or silking, but do not alter crop growth rate. We developed algorithms for a Flowering Model to simulate sink-limited kernel set from flowering dynamics. This model was calibrated against kernel production in hybrid seed production fields and then linked to CERES-Maize. The Modified CERES-Maize was calibrated against two years of field data involving three hybrids, eight population densities, and seven N levels. Integrating the capacity to simulate sink-limited kernel set with source-limited kernel set increased simulation accuracy dramatically, relative to original CERES-Maize. For 13 commercial fields tested, Modified CERES-Maize decreased simulation error for kernels per plant from 17.1 to 2.3%, improved r2 between measured and simulated values from 0.77 to 0.87, and decreased simulation error indicators mean error, root mean square error, and mean square deviation by 85, 40, and 64%, respectively. Modified CERES-Maize accounts for a much greater range of variability in the biological processes controlling kernel set.
Abbreviations: ASI, anthesis–silking interval • GDD, growing degree days • IPAR, intercepted photosynthetically active radiation
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INTRODUCTION
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UNDER MOST CIRCUMSTANCES, kernel set in maize (Zea mays L.) is predominately a source-limited process. Edmeades and Daynard (1979) were the first to show a curvilinear relationship between photosynthetic activity at anthesis and the number of kernels formed on apical ears. Tollenaar et al. (1992) proposed a double curve to describe the relation between average shoot growth rate around flowering (1 wk before to 3 wk after silking) and the number of kernels set per plant in apical and subapical ears. Andrade et al. (1993) also reported a curvilinear relationship between the number of kernels set by apical ears and the mean intercepted photosynthetically active radiation (IPAR) accumulated during a 31-d period centered around silking. Andrade et al. (1999) reported a curvilinear relation between the shoot growth rate around flowering and the number of kernels set by apical ears.
Kiniry and Knievel (1995), Otegui (1997), and Kiniry et al. (2002), however, reported a linear relationship with a maximum plateau between average daily IPAR during a critical period around silking and kernel numbers in apical ears. However, Andrade et al. (2000) and Lizaso et al. (2001), who evaluated kernel set at plant population densities ranging from 2 to 17 plants m–2, observed that curvilinear models were more accurate for predicting kernel numbers per plant than were linear models across the biological range of IPAR values. Whether the relationship was established using photosynthetic rate directly, or a surrogate variable such as shoot growth rate or IPAR, all these studies indicate the amount of assimilates produced around flowering is critical in determining the number of kernels set by maize plants.
The length and timing of the critical period for assessing this source limitation have varied from 15 d after silking (Kiniry and Knievel, 1995) to the 30-d period centered around silking Otegui (1997). The uncertainty in defining the critical period for kernel set likely reflects the empirical nature of these relationships and the environmental variability across sites and years. Otegui and Bonhomme (1998), however, observed a nearly constant thermal time duration of ear growth for a wide range of hybrids and conditions when growth was normalized relative to maximum ear length. They also reported that kernel number per ear was related closely to IPAR accumulated during ear growth from 227 degree days (°C d) before silking to 100°C d after silking. Lizaso et al. (2001) also used this range of degree days to define the curvilinear relationship between average IPAR per plant and kernel number per plant.
The common underlying assumption in these studies is that kernel set in maize is always source-limited. Also common to these studies is that crop management was established to prevent any significant plant stresses. Under source-limited kernel set, plants presumably produce an excess of fertilized ovaries and the current flow of assimilates determines how many of these continue to develop. Under certain field conditions, such as limited pollen supply or stresses that disrupt synchrony between anthesis and silking, however, a limited number of fertilized ovaries are produced. That is, kernel set becomes sink-limited. The correct simulation of kernel numbers under these circumstances can be achieved, however, provided accurate descriptions of pollen shed and silking dynamics are available (Lizaso et al., 2003c). Currently, CERES-Maize (Jones and Kiniry, 1986) estimates kernel numbers under these conditions by calculating a source-limited kernel number per plant, then "correcting" this value with stress factors. There is no mechanistic basis for simulating sink-limited kernel set in this way. The purpose of this work is to develop the algorithms required to simulate sink-limited kernel set in maize based on quantitative interactions between male and female flowering dynamics (Westgate et al., 2003). A second objective is to link these algorithms into CERES-Maize and test the accuracy of the resulting model when simulating kernel numbers under both source- and sink-limited conditions. To accomplish our first objective, we developed a stand-alone Flowering Model to simulate sink-limited kernel set based on flowering processes. Once we established the Flowering Model was working properly, we linked it into CERES-Maize to meet our second objective.
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MATERIALS AND METHODS
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Procedures and new algorithms simulating both source-limited and sink-limited kernel set were incorporated into an experimental version of CERES-Maize that uses source code of Generic CERES version 3.1 (dated 31 Dec. 1996) distributed with DSSAT version 3.1 (Hoogenboom et al., 1994). Our experimental version included additional procedures to improve the simulation of daily light capture by the canopy (Lizaso et al., 2003b) and leaf area (Lizaso et al., 2003a), thus improving the simulation of daily IPAR (Lizaso et al., 2003b). This experimental version will be referred to as Modified CERES and distinguished from the Original CERES that will be used to refer to the Generic CERES as distributed with version 3.1 of DSSAT. We also developed a stand-alone model to test the procedures of sink-limited kernel set. This stand-alone model will be referred to as the Flowering Model.
Development of the Flowering Model
The simulation of sink-limited kernel set follows the procedures described by Lizaso et al. (2003c). The progression of the population reaching anthesis (P, %) is described with a sigmoidal function:
 | [1] |
where Px is the maximum percentage of the plants shedding pollen, parameter k controls the slope, and tm is the time (day of the year) when 50% of the plants have reached anthesis. Pollen shed from each tassel is simulated using a Gauss function:
 | [2] |
Pr is the daily pollen rate in grains per plant per day, Pt is the total pollen produced per tassel (grains plant–1), w is the width of the pollen shed curve (days), measured at half the maximum pollen shed rate, and tx is the time (days after the beginning of shedding) when pollen rate peaks. Parameters w and tx are associated with the average duration of pollen shed (Pdur, days) observed on individual tassels as:
 | [3] |
 | [4] |
The Flowering Model can accommodate two male subpopulations if present, using Eq. [1] and [2] with different inputs, and then calculating a daily pollen rate with the contributions of both subpopulations.
The progression of the population reaching silking also follows a sigmoidal function similar to Eq. [1], with tm being the time (day of the year) when 50% of the plants reach silking. The exsertion of silks on individual ears follows a monomolecular function:
 | [5] |
Sn is the number of visible silks, St is the total number of silks on each ear, t0 is the theoretical time (days after beginning of silk exsertion) when the first silk emerges from the husks, and a is a shape parameter controlling the slope of the curve. For practical purposes, t0 is set to zero and parameter a is estimated from the average duration of silk exsertion (Sdur, days) observed on individual ears:
 | [6] |
Equations [1–6]
are used along with female and male plant densities to calculate the number of receptive silks exposed and the corresponding pollen shed rate per unit land area on a daily basis. The relationship published by Bassetti and Westgate (1994) was used to estimate the percentage of receptive female flowers (exposed silks) that set kernels (ks, %) from the daily pollen shed rate according to
 | [7] |
where PSR is the daily pollen shed rate (grains cm–2 d–1). The model also adjusts kernel set for the negative effect of asynchronous pollination within an ear (Cárcova et al., 2000) and the delay of silk emergence on subapical ears causing asynchronous pollination between ears (Lizaso et al., 2003c).
Development of Modified CERES-Maize
Modified CERES was developed to simulate both source-limited and sink-limited kernel set. To simulate sink-limited kernel set with CERES, we incorporated the procedures developed for the stand-alone Flowering Model with a few modifications. First, the time scale for the male and female populations reaching anthesis or silking (Eq. [1]) was changed from a daily time step to a thermal time scale based on growing degree days (GDD8, base temperature 8°C) as used in CERES. Second, the slope parameter, k, in Eq. [1] was calculated from field observations of the duration of flowering. We defined the duration of anthesis (Mdur, days) as the time interval between 10 and 90% of the male population beginning to shed pollen. Similarly, the duration of silking (Fdur, days) is defined as the time between 10 and 90% of the female population reaching silking. Thus, parameter k in Eq. [1] is given by:
 | [8] |
Equation [8] also was used to calculate the corresponding parameter k for the female population, using Fdur instead of Mdur. The Flowering Model requires as input the average number of ears per plant to simulate the effects of barrenness or prolificacy. The third modification added was a prolificacy code identification (0 = nonprolific; 1 = prolific) to differentiate the simulation of prolific and nonprolific cultivars in Modified CERES. Table 1
shows the required inputs to simulate sink-limited kernel set with Modified CERES. Details on standard procedures to collect these inputs are provided elsewhere (Fonseca et al., 2002, 2004). Some of these inputs may be difficult to obtain, such as total production of pollen and silks (Pt, St) or duration of pollen shed and silk exsertion (Pdur, Sdur). For the convenience of model users, Table 2
provides some approximate values for these inputs.
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Table 1. Additional inputs required by Modified CERES-Maize to simulate sink-limited kernel set in hybrid seed production. Typical values (in parentheses) may be suitable for relative comparisons, if measured values are not available. The model converts inputs commonly recorded in days to thermal units.
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Table 2. Categorical descriptions for selected inputs required by Modified CERES-Maize. Values listed for each category are approximate ranges and intended only for relative comparisons.
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To simulate source-limited kernel set, we followed the approach developed by Lizaso et al. (2001). Briefly, the model averages IPAR (MJ plant–1 d–1) during a thermal time window defined by Otegui and Bonhomme (1998) as the critical period for kernel set. The thermal time window brackets 250 GDD8 before silking to 100 GDD8 after silking. Kernel numbers calculated from IPAR are reduced using stress indices as in the original CERES-Maize. Average IPAR during this critical period provides an estimate of the amount of assimilate available for kernel set, thus establishing the potential for a source constraint on kernel set. When the supply of assimilate per plant is large around flowering (e.g., at low population density), prolific genotypes set kernels on a second ear. When assimilate per plant is limited (e.g., at high population density), some plants do not set kernels and exhibit barrenness. We adopted the approach proposed by Ritchie and Alagarswamy (2003) and used average IPAR around silking to calculate either prolificacy or barrenness. Monomolecular functions such as those presented by Tollenaar et al. (1992) were used to simulate both ears per plant and kernels per plant as a function of IPAR:
 | [9] |
where A is the asymptote of the function, S the parameter controlling the steepness of the slope, and X0 (MJ plant–1 d–1) is the threshold IPAR required to start setting kernels in the apical ear. For the calculation of ears per plant, A has a value of 1.0 for the first ear and 2.0 for the second ear. For kernels per plant the genetic input G2, which we define as the potential number of grains on the apical ear, corresponds to A for the first ear, and 2 x G2 for the second ear, which implies an equal potential for kernel set.
Original CERES assumes silking is the cardinal event for flowering. The model simulates silking date as the day when the expansion of the flag leaf is completed. In Modified CERES, however, the cardinal event for flowering is anthesis; therefore, pollen shed begins when the flag leaf completes expansion. A cultivar-specific input, anthesis–silking interval (ASI, GDD8), controls the timing of silking relative to anthesis. Anthesis–silking interval is defined as the thermal time interval (GDD8) elapsed between 50% silking and 50% anthesis. Early studies on the ASI focused only on treatments that delayed silking relative to pollen shed (protandry), and consistently observed a strong negative correlation between ASI and grain yield (Du Plessis and Dijkhuis, 1967; Bolaños and Edmeades, 1993, 1996). Curiously, ASIs in these studies were calculated as silking–anthesis intervals (i.e., 50% silking date–50% anthesis date). As such, protandrous treatments which only had negative impacts on kernel set were assigned positive ASI values. Modern maize hybrids, however, often begin to exsert silks before shedding pollen (protogyny) under favorable conditions. Likewise, floral synchrony between male and female inbreds in hybrid seed production can be manipulated to be protogynous or protandrous. Our studies relating flowering dynamics to kernel set indicate protogynous synchrony (silking before pollen shed) has a positive impact on kernel set in hybrid seed production, as well as in hybrid monoculture (Lizaso et al., 2003c; Fonseca et al., 2004), while protandry (silking after pollen shed) is negative as reported earlier. To ensure Modified CERES was coded appropriately for the response of kernel set to a broad range of floral synchronies, we logically assigned positive ASI values to protogynous flowering dynamics, and negative ASI values to protandrous flowering dynamics.
Modified CERES simulates expansion and senescence of individual leaves (Lizaso et al., 2003a). This enabled the simulation of detasseling and male removal to represent the changes in canopy light interception in seed production fields. On the day of detasseling, the model subtracts the input surface area of the leaves and/or leaf sections removed (Table 1). Leaves partially removed before completing expansion will continue growing. On the same date, leaf weight is reduced by 10.5% and stem weight by 5.0% (Rasse et al., 2000). On the day of male plant removal, the remaining plant population density is reduced according to the loss of male plants and the initial proportion of male and female plants in the field (Table 1).
Model Calibration
The algorithms incorporated into Modified CERES to simulate sink-limited kernel set were calibrated previously (Lizaso et al., 2003c). The methods to simulate source-limited kernel set have been evaluated as well (Lizaso et al., 2001). For this study, there was only need to calibrate the parameters of Eq. [9] to represent field responses of prolific and nonprolific cultivars under favorable growing conditions. We used field measurements of kernel numbers and IPAR collected in two experiments. The first experiment was planted in Nashua, IA (43° N, 92° W) on 26 May 1999. Treatments included three hybrids (Asgrow 740, Dekalb 611, and LH198 x LH185), four population densities (2, 5, 8, and 15 plants m–2), and four N rates (0, 56, 112, and 225 kg N ha–1). Asgrow 740 and Dekalb 611 were typically prolific and LH198 x LH185 was nonprolific. Percent IPAR was measured around solar noon with a line quantum sensor (LI-191SA, LI-COR, Lincoln, NE), 1 to 2 wk before and after silking, and at silking. At harvest, all ears were collected from 10 m2 in two contiguous rows, and plants were counted. Kernels on each ear were counted (Syntron, Model EB00-D, Homer City, PA), differentiating kernel numbers in apical and subapical ears.
The second experiment was planted in Ames, IA, (42° N, 92° W) on 4 May 2000. Treatments included two hybrids (Asgrow 740, and LH198 x LH185), four population densities (1, 4, 8, and 18 plants m–2), and three N rates (56, 168, and 337 kg N ha–1). Light intercepted around flowering and ears per plant and kernels per ear at harvest were evaluated as in the previous experiment.
Model Evaluation
The ability of Modified CERES to simulate kernel numbers correctly under both source-limited or under sink-limited conditions was tested using data from three experiments planted with commercial hybrids in Iowa in 1999 and 2001 (source-limited) and from data collected in seed production fields in 2002 and 2003 (sink-limited). The source-limited experiments were planted near Ames, IA, on 24 and 27 May in 1999, and on 8 May 2001. In the 1999 experiments, treatments were three hybrids (Asgrow 740, Dekalb 611, and LH198 x LH185), four population densities (2, 5, 8, and 15 plants m–2), and four N rates (0, 56, 112, and 225 kg N ha–1). In the 2001 experiment treatments were two hybrids (Dekalb 611 and LH198 x LH185), three population densities (1, 8, and 18 plants m–2), and three N rates (56, 168, and 336 kg N ha–1). Inputs listed in Table 1 were measured in 2001. Inputs for Asgrow 740 were measured in a similar experiment in 2000. These measured inputs were used in the simulations of 1999 and 2001, although the model determined that kernel set was source-limited in all cases. Procedures to determine ears per plant and kernels per ear were similar to those described in the previous section.
The sink-limited data were collected in 13 seed production fields managed by Syngenta Seeds Inc. in Washington County, Iowa, during 2002 and 2003. Female to male planting patterns included four female rows per one or two male rows. Male and female flowering dynamics were evaluated in a sampling area chosen 2 wk before anthesis to be at least 25 m from the field border and represent the typical development of inbreds. All inputs enumerated in Table 1 were measured in these 13 fields. Seeds from 1.3 ha of female inbred were harvested and weighed. Kernel numbers were estimated from the number of seeds in a subsample of 454 g. Additional details about this data set are provided in Fonseca et al. (2004).
Simulated and measured data were compared using various statistical indices. The mean error (ME) and root mean square error (RMSE) were calculated as:
 | [10] |
 | [11] |
where Si and Oi are the number of kernels simulated and observed, and n is the number of observations. Mean square deviation (MSD) was calculated according to Kobayashi and Salam (2000). Mean square deviation was partitioned into three components, squared bias (SB), nonunity slope (NU), and lack of correlation (LC) following Gauch et al. (2003):
 | [12] |
 | [13] |
 | [14] |
where b is the slope of the regression of measured on simulated kernel numbers, and r2 is the coefficient of determination of the regression.
Sensitivity Analysis
The sensitivity of the simulated seed production to systematic changes in selected inputs was tested. We report the simulations obtained when changing the following inputs in Modified CERES:
- ASI (GDD8)
- Time interval between two male subpopulations (GDD8)
- Fraction of land with female plants
- Fraction of male plants in first subpopulation
- Silk production (silks per ear)
- Pollen production (million grains per tassel)
- Duration of silk exsertion (d)
- Duration of pollen shed (d)
One of the seed fields planted in 2003 was used as the baseline for the inputs. Then, each input was changed, one at a time, above and below the baseline to cover the variation typically encountered for that parameter. For instance, pollen production on male plants was 2.5 million grains per tassel. We simulated the responses to pollen production within the range of 0.5 to 5.5 million grains per tassel.
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RESULTS AND DISCUSSION
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The calibration data included plant population densities ranging from 0.9 to 17.6 plants m–2. Average IPAR around flowering varied from 0.49 to 3.47 MJ plant–1 d–1. Harvested grain numbers ranged from 110 to 1405 grains plant–1, and ears plant–1 varied from 0.6 to 2.0 (Fig. 1
). A few plants grown at very low population density set a third kernel-bearing ear, but we did not include these ears in our analysis. Our data indicated an average IPAR threshold to set kernels in the apical ear of 0.33 MJ plant–1 d–1, which is within the range of 0.31 to 0.37 MJ plant–1 d–1 reported by Andrade et al. (2000). This threshold for kernel set on apical ears was independent of prolificacy. The nonprolific hybrid (LH198 x LH185) set kernels on subapical ears, but required twice as much intercepted light per plant compared to the prolific hybrids to do so (Fig. 1).
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Figure 1. Relationships between average daily intercepted photosynthetically active radiation (IPAR) and number of ears per plant (upper panel) and number of kernels per plant (mid panel) for prolific and nonprolific hybrids. IPAR was averaged over a thermal time period from 250 degree days (°C d) before silking to 100°C d after silking. Each point is the mean of three replications. Lower panel depicts modeled relationships with IPAR thresholds to set kernels on apical and subapical ears.
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Modified CERES calculated the potential number of kernels per unit area from the simulated daily dynamics of silk exsertion and pollen shed, assuming two ears are setting kernels per plant. Potential kernel number represents the sink-constraint on kernel set. The model also computed the average IPAR per plant during the critical thermal time period for kernel set (250 GDD8 before to 100 GDD8 after silking; Otegui and Bonhomme, 1998). The average IPAR represents the source-constraint to kernel set. At the end of the lag phase for kernel growth, the model estimates ears per plant and kernels per plant using the average IPAR and the calibrated equations (Eq. [9], Fig. 1). At this point, both the sink-limited number of kernels calculated from pollen and silks dynamics, and the source-limited number of kernels calculated from average IPAR are restricted by barrenness or prolificacy (i.e., ears per plant). When source-limited conditions were simulated (Fig. 2
), the progression of the sink-limited kernel set calculated for two ears increased until the end of the lag phase. On Day 230 (1200 GDD8), the end of the lag phase, the model estimated 1.02 ears plant–1 based on average IPAR around flowering. It calculated 550 kernels plant–1 would develop based on average IPAR (source-limited kernel set). In addition, the model calculated the potential kernel number at 635 kernels plant–1 according to the sink-limited kernel set algorithms assuming 2% of the female plants would support subapical ears. Modified CERES selects the lesser value (i.e., 550 kernels per plant) indicating kernel set limited primary by source capacity, which compares favorably with the measured value of 475 kernels per plant. In this example, pollen production per tassel was measured at 2 million grains, and pollen shed continued for 11 d including 5 d with pollen rates above 100 grains cm–2, sufficient to maximize daily kernel set (Bassetti and Westgate, 1994).
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Figure 2. Upper panel, simulation of source-limited and sink-limited kernel set by Modified CERES-Maize under source-limited conditions. Lower panel, associated simulations showing field dynamics of male and female flowering and sink-limited kernel set. GDD8 is growing degree days calculated with a base temperature of 8°C.
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Sink-limited kernel set was simulated for a hybrid seed production field, which was limited by pollen amount (Fig. 3
). The field was planted at 7.0 plants m–2 for both male and female inbreds, in a ratio of four female rows per male row. The male inbred produced 2.5 million grains per tassel, but the limited number of male plants determined pollen rates that peaked at 62 grains cm–2, which was not sufficient for maximum daily kernel set. Under these conditions, the number of kernels estimated using IPAR (source-limited) was 409 kernels per plant, well above the measured number of 300 kernels per plant. The sink-limited algorithms of Modified CERES simulated kernel set at 319 kernels per plant, confirming that limited pollen production constrained kernel number well below that potentially supported by assimilate availability. Modified CERES selects the lesser value (i.e., 319 kernels plant–1) reflecting the primary limitation for kernel set, which again compares favorably with the measured value.
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Figure 3. Upper panel, simulation of source-limited and sink-limited kernel set by Modified CERES-Maize under sink-limited conditions. Lower panel, associated simulations showing field dynamics of male and female flowering and sink-limited kernel set. GDD8 is growing degree days calculated with a base temperature of 8°C.
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Simulating Sink-Limited Kernel Set
Under sink-limited conditions, such as those depicted in Fig. 3, Original CERES-Maize typically overpredicts kernel number per plant at the low range and underpredicts this yield component at the high end. The reason for this is that the model does not actually simulate processes limiting kernel set. Simulated kernel numbers for 13 commercial seed production fields varied dramatically depending on the model used (Fig. 4
). The Flowering Model was the most accurate at simulating kernel set across the entire range of yield levels encountered (r2 = 0.84; MSD = 2129). This result confirmed that the flowering algorithms developed for this model correctly simulated kernel set under sink-limited conditions. Simulation of kernel set per plant by the original CERES-Maize exhibited large deviations from the measured values (MSD = 15,084). There was apparently a negative relation between measured and simulated kernels per plant (slope = –0.32), and the regression model explained only 17% of the measured variability in kernel numbers (r2 = 0.17). Adapting and linking the algorithms in the Flowering Model into CERES-Maize improved simulation accuracy for kernel numbers per plant dramatically. Modified CERES, now with the capacity to simulate sink-limited kernel set, decreased simulation error by 56% (MSD = 6664) and explained over 70% of the variation in measured kernel numbers per plant in these 13 fields (r2 = 0.73).
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Figure 4. Comparison of measured and simulated kernel number per plant under sink-limited conditions. Simulated values were obtained using the Original CERES-Maize (O), with a stand-alone Flowering Model (F), and with a Modified CERES-Maize (M) incorporating algorithms to simulate source- and sink-limited kernel set. The Flowering Model simulates only sink-limited kernel set.
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Simulating Source-Limited and Sink-Limited Kernel Set
Simulating kernel set under sink-limiting conditions is a unique feature of the Modified CERES-Maize model. Importantly, this feature was added without sacrificing accuracy under source-limited conditions. Original CERES and Modified CERES simulations were compared across a range of source-limited and sink-limited conditions (Fig. 5
). Original CERES generally underestimated kernel numbers (ME = –82.37). This problem was clearly evident at low population densities when plants produce a large number of kernels per ear. Modified CERES generated much more accurate estimates of kernel numbers throughout the range of population densities tested, greatly reducing bias in the simulation (ME = 12.75). Modified CERES clearly was superior to the Original CERES in simulating kernel numbers across the environments tested as indicated by a significant reduction in MSD and its three components measuring bias (SB), nonunity in regression slope (NU), and lack of correlation (LC) (Table 3
).
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Figure 5. Comparison of measured and simulated kernel numbers per plant under a range of source- and sink-limited conditions. Simulations were obtained with the Original CERES-Maize (O), and with a modified version of CERES-Maize (M) incorporating algorithms to simulate source- and sink-limited kernel set. All evaluation data sets were included. Each data point is the average of replicated measurements; n = 127.
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Table 3. Statistics analysis of kernel number simulation by the Original CERES and Modified CERES. Measured and simulated kernel numbers per plant were derived from a broad range of source- and sink-limited conditions typical of grain and hybrid seed production (n = 127).
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Sensitivity Analysis
The sensitivity of Modified CERES to changes in model inputs was examined systematically for the ASI, thermal time between anthesis of split male populations, fraction of land with female plants, fraction of male plants in first subpopulation, silk production, pollen production, duration of silk exsertion, and duration of pollen shed (Fig. 6
). We used the same parameters for the hybrid seed production field simulated in Fig. 3 as a baseline for this analysis. Kernel set in this field was sink-limited. The ASI (Fig. 6a) reflects the synchrony between male and female flowering. A value of zero indicates perfect synchrony ("nick") between both processes. In agreement with field observations, greater kernel set would be achieved when silking preceded anthesis (positive ASI values). For this particular field and combination of inbreds, the maximum kernel set would occur at ASI = 22 GDD8. Of the model inputs tested, Modified-CERES proved to be most responsive to changes in the ASI. This result underscores the potential for simulation as a tool to achieve optimum female–male inbred synchrony in seed production.
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Figure 6. Simulated seed production in response to changes in selected model inputs; (a) anthesis–silking interval (GDD8); (b) thermal time interval between two male subpopulations (GDD8); (c) fraction of land occupied with female plants; (d) fraction of male plants in first pollen shedding subpopulation (P1); (e) number of silks on apical ears (St, Eq. [5], silks per ear); (f) number of pollen grains on individual tassels (Pt, Eq. [2], million grains per tassel); (g) duration of silk exsertion from apical ears (Sdur, Eq. [6], days); (h) duration of pollen shed from individual tassels (Pdur, Eq. [3] and [4], days). GDD8 is growing degree days calculated with a base temperature of 8°C.
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Seed production managers often attempt to spread the duration of pollen shed with split plantings or other mechanical means. Sensitivity analysis indicated that increasing the thermal time between two pollen shedding populations indeed distributes pollen shed over a longer time period and increases kernel set per plant (Fig. 6b). It also shows that optimum seed production would be achieved if anthesis for the two male populations was separated by about 100 GDD8.
An important management decision in hybrid seed production is choosing the optimum ratio of male to female rows. The objective is to maximize the number of productive female plants while assuring adequate pollen rates from male plants. Our baseline seed field used the common pattern of four female rows for every male row. In this case, the female plants occupy 0.8 (i.e., 80%) of the land area. Increasing the proportion of land allocated to female plants in this field would have decreased kernel production sharply (Fig. 6c). This result implicates low pollen production by the male inbred as a primary limitation for kernel set. In most cases, field managers would attempt to compensate for this limitation by increasing male plant density. The sensitivity analysis, however, suggests that greater seed production from the field would have been obtained by allocating less area to the female inbred. A female to male ratio of 3:1 yielded 28.4 million seeds ha–1 compared to the 27.4 million seeds ha–1 calculated for the 4:1 ratio. This approach enables other nonconventional planting patterns to be evaluated as well.
Pollen uniformity can be managed in the field by assigning various proportions to each male subpopulation. Simulation of this parameter indicated that reducing the proportion of plants in the first subpopulation (relative to the second) would likely increase seed production (Fig. 6d). Flowering dynamics in this field (Fig. 3) indicate that pollen shed occurred too early to pollinate late emerging silks effectively. Under these circumstances, greater pollen production by the second population of male plants would have been highly beneficial. Taking full advantage of this knowledge, however, requires additional information about the silking characteristics of the female inbred. Female inbreds with large ears that are slow to exsert silks or are not uniform in development would be good candidates for this management option.
As expected, increasing silk numbers and pollen density per unit area resulted in increased seed production (Fig. 6e, 6f). This analysis assumes no change in duration of silking or pollen shed for the population, which might occur as plant population is manipulated. Nonetheless, the results show that the system will become saturated with pollen at some point in accord with field observations (Westgate et al., 2003). The saturation value for a given field will depend on the potential number of receptive silks, their synchrony with pollen shed, and source capacity of the female plants.
Inbreds vary considerably in the length of time required to exsert all the silks on the ear and for days pollen is shed from the tassel (Table 2). Sensitivity of kernel set to silking indicated a negative relationship between the duration of silk exsertion and potential for seed production (Fig. 6g). The female inbred in our test field required 8 d to expose silks from each ear completely. Female inbreds exposing their silks more rapidly would have an intrinsic advantage for producing more seed, all other things being equal within the seed production field. In contrast, extending the duration of pollen shed from individual tassels resulted in a greater number of receptive silks being pollinated (Fig. 6h). As was the case for increasing the interval between anthesis for male subpopulations and increasing the proportion of pollen shed by the second male population, the advantage results from pollinating a greater number of late-emerging silks.
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CONCLUSIONS
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We have developed a modified version of CERES-Maize that includes algorithms to simulate kernel set under source-limited and sink-limited conditions. The source-limited process is simulated with a double curve for apical and subapical ears where kernel numbers are calculated as a function of the average plant intercepted light during a critical period around flowering (–250 to +100 GGD after silking). The sink-limited kernel numbers are estimated from the simulated field dynamics of pollen shed and silk exsertion. The model calculates kernel set for both source- and sink-limited conditions and selects the more limiting process to define final kernel number per plant. Prolificacy and/or barrenness are also computed from the average IPAR during the same period. Modified CERES was tested using data from commercial seed fields where measured pollen rates indicated a sink-limited process and using data from experimental production fields yielding accurate simulations and closer to measured values than the Original CERES. The sensitivity analysis did not reveal any model instabilities and showed very dynamic responses to changes in model inputs. Manipulating the ASI between male and female inbreds showed the greatest potential for increasing seed production.
A limitation in Modified CERES for application to hybrid seed production is that it does not simulate growth and development of the male and female inbreds separately. The model simulates the growth of the female inbred (i.e., leaf area inputs), but the phenology is calibrated to simulate anthesis according to the male inbred. The onset of silking for the female population, however, can be simulated adequately from anthesis and the ASI. Future refinements will include separate simulation of growth and development for both male and female inbreds within the same hybrid seed production field.
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NOTES
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All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher. Permission for printing and for reprinting the material contained herein has been obtained by the publisher.
Received for publication August 19, 2006.
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ABSTRACT
INTRODUCTION
