Agronomy Journal 95:4-9 (2003)
© 2003 American Society of Agronomy
SYMPOSIUM PAPERS
Model Concepts to Express Genetic Differences in Maize Yield Components
Joe T. Ritchie* and
Gopal Alagarswamy
Dep. of Crop and Soil Sci., Michigan State Univ., East Lansing, MI 48824-1325
* Corresponding author (ritchie{at}msu.edu)
Received for publication May 1, 2001.
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ABSTRACT
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Maize (Zea mays L.) grain yield is closely related to kernel number per unit area. The quantification of genetic differences among maize cultivars to kernel number plant-1 (KNP) is critical for accurate yield simulation but remains one of the less accurate components of yield modeling. Our objective was to document the recently published KNP data and revise CERES Maize model (V3.5). The duration of a critical window for KNP simulation was 327°C days (227°C days before and 100°C days after silking—base temperature 8°C) when ears actively grew. The KNP was curvilinearly related to cumulative intercepted photosynthetically active radiation plant-1 (CIPAR) during the critical window. Potential kernel ear-1 and kernel produced per unit CIPAR were the genetic coefficients needed to simulate KNP. Apical ears produced maximum KNP at a plateau CIPAR of 64 MJ, and prolific hybrids produced secondary ears when CIPAR exceeded 64 MJ. The genetic differences in prolificacy in low plant density were expressed by another coefficient. Below a threshold CIPAR of 11 MJ, all plants were barren, and a barrenness coefficient expressed genetic differences among old and modern hybrids to produce KNP in high plant density. Sensitivity analysis with limited testing indicated that the revised model simulated yield reasonably well [root mean square error (RMSE) = 0.63 Mg ha-1] compared with the original model (RMSE = 1.25 Mg ha-1) across a wide range of plant densities. However, rigorous testing of the model will be required to gain greater confidence in the proposed concepts.
Abbreviations: AIPAR, average intercepted photosynthetically active radiation plant-1 day-1 • CIPAR, cumulative intercepted photosynthetically active radiation plant-1 • KN1, kernel number of apical ear • KN2, kernel number of the second ear • KNP, kernel number plant-1 • PGR, plant growth rate • RMSE, root mean square error
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INTRODUCTION
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MAIZE YIELDS in the USA have continually increased since 1930 due mainly to genetic improvement and improved management practices (Thompson, 1986). Besides tolerance to abiotic and biotic stresses, the likely cause for high yield in modern hybrids has been more ear-bearing plants per unit land area without reduction in kernels per ear (Duvik, 1997). Including these variable genetic features in crop simulation models is important when models are used for supporting strategic decision-making. Crop simulation models in general are strong in simulating the total biomass production through intercepted radiation approach but are weak in partitioning total biomass into different plant parts. Hence, the simulation of KNP is also weak even though it is an important yield determinant. Crop simulation models are still evolving and are continually being improved as a function of available new knowledge. Newer and fundamental relationships between light interception, ear development, and kernel set in maize were presented in a recent symposium entitled "Physiology and Modeling Kernel Set in Maize" (Westgate and Boote, 2000). In this symposium, Ritchie and Wei (2000) reviewed current knowledge on simulating KNP in maize and provided a synthesis of methods that may improve yield estimation of the maize simulation models.
Modern maize hybrids have greater yield potential compared with older hybrids (Russel, 1986). Comparing maize hybrids released between 1959 and 1988 in Ontario, Tollenaar et al. (1992) showed that higher yield in modern hybrids was associated with higher KNP and higher aboveground plant growth rates (PGRs, g plant-1 d-1) during 1 wk before silking to 3 wk postsilking. They also showed that higher prolificacy of modern hybrids was associated with lower barrenness at high plant density. Recently, Echarte et al. (2000) concluded that more KNP per unit PGR rather than greater PGR accounted for the genetic improvement of yield potential in modern Argentinean maize hybrids. When maize plants were grown in suboptimal populations, plants were prolific, and up to 50% of the total yield of the crop came from secondary and tiller ears (Du Toit and Prinsloo, 2000). Despite the existence of genetic differences in PGR, KNP, barrenness, and prolificacy among maize hybrids, the current maize simulation models do not have the capability to simulate prolificacy and barrenness. Hence, the models do not simulate KNP and yield correctly under wide range of plant densities. Quantifying genetic differences in barrenness, prolificacy, and KNP has received less research attention in the maize simulation models.
The objectives of this paper are to (i) document the new knowledge on KNP estimation, (ii) modify the CERES Maize (V3.5) model based on new knowledge, and (iii) test the sensitivity of the revised model to plant density variations. The genetic differences in KNP in simulation models are simulated with a view to be able to identify these differences in the future by using modern biotechnology techniques.
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NEW KNOWLEDGE AND MODEL CONCEPTS
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Critical Window of Time for Kernel Number Plant-1 Determination
As in other cereals, maize grain yield is closely related to kernel number m-2 at harvest. Crop models that simulate yield using KNP estimation either use PGR or intercepted radiation during a period around silking to simulate KNP because assimilate allocated to reproductive structures in general determines the yield. Tollenaar et al. (1992) used PGR during a period from 7 d before silking to 21 d after silking to estimate KNP. Andrade et al. (1993) used cumulative intercepted radiation during a 30-d period bracketing flowering while Kiniry and Knievel (1995) used the average intercepted radiation during a 7- to 10-d period after silking to estimate KNP. In these studies, the beginning and duration of the period for calculating factors that influence KNP estimation are not the same. Incorrect estimates of the beginning and duration of the critical period for KNP simulation could lead to substantial errors in yield simulation. Otegui and Bonhomme (1998) demonstrated that the actual period of ear expansion growth started at 227°C days (8°C as base temperature) before silking and continued until 100°C days after silking. During this window of time, approximately 40% of final ear length was reached at silking, and the remaining 60% was attained after silking. The 327°C day window was similar for several contrasting hybrids, but prevailing temperatures influenced both duration and biomass growth rates. The duration of this critical window of time is important because changes in environmental conditions associated with variations in sowing dates have influenced the rate of biomass production (Cirilo and Andrade, 1994). The deficiencies of water and nutrients during this critical window can also strongly reduce KNP. NeSmith and Ritchie (1992) found that a water deficit period of 37 d during tassel emergence and silking caused barrenness in 78% of plants. The KNP in ear-bearing plants was reduced by 75% compared with plants grown without any water deficits. The critical window bracketing silking (327°C days) offers a logical framework to simulate potential KNP in response to light interception and water and nutrient deficit factors.
Intercepted Radiation and Kernel Number Plant-1
Crop models that simulate KNP have used two approaches. One group of models uses rate of biomass production, and the other uses intercepted radiation to simulate KNP. Following the pioneering research of Edmeades and Daynard (1979), which related KNP to assimilation rate at anthesis, several researchers used modifications of this approach for KNP estimation (Tollenaar et al., 1992; Andrade et al., 1993, 1999). These studies used the PGR during periods bracketing silking to estimate KNP. Models for KNP simulation have also used the average intercepted photosynthetically active radiation plant-1 day-1 (AIPAR) during a 10-d period following silking (Kiniry and Knievel, 1995) or during the period of actual ear elongation (Otegui and Bonhomme, 1998). The use of CIPAR during the window instead of AIPAR should be more appropriate for estimating KNP because it is proportional to the total growth during that period. If the development period for the window of kernel determination is longer as a result of lower average temperatures, the plants have more time for growth at the average growth rate and should be able to set more kernels.
We chose to use simulated intercepted radiation to simulate KNP instead of simulated growth rate because it could be a more conservative approach. Most functional crop models use radiation use efficiency to convert intercepted radiation to biomass production and then partition the biomass into plant parts. Various models may use differing values of radiation use efficiency as well as the partitioning coefficients in estimating the daily production of aboveground biomass, but they would likely be in more agreement in the estimation of AIPAR or CIPAR. The measurement of plant growth around the time of silking relies on the destructive sampling of plants at the beginning and end of the period of interest. On the other hand, the measurement of radiation interception does not require destructive sampling and thus should have less experimental error when evaluating the genetic coefficients for use in models. A problem with both approaches is the quantification of deficits of water or nutrients during the time of PGR, AIPAR, or CIPAR evaluation. If such deficits cause the PGR to decrease, the grain number would be decreased, whereas the light interception might not be influenced by the deficits unless the deficit is too severe to cause leaf rolling. Both approaches, when used in models, require the quantification of these deficits and their appropriate use in modifying the KNP estimations. Thus, the use of CIPAR for estimating potential kernel numbers should be more reproducible and conservative for measuring or modeling purposes than the use of measured or modeled PGR.
The linear approach of relating AIPAR or CIPAR to KNP usually results in a positive intercept leading to estimation of some kernels when extrapolated to zero AIPAR or CIPAR (Andrade et al., 1993, Kiniry and Knievel, 1995; Otegui and Bonhomme, 1998). This linear approach worked well in normal plant densities but resulted in inaccurate simulation of yield in suboptimal plant densities (Du Toit et al., 1994). Andrade et al. (2000) proposed a curvilinear model instead of linear approach, relating daily AIPAR during a critical period (silking minus 10 d to silking plus 20-d period) to KNP. Their curvilinear model defined a plateau AIPAR of 1.75 MJ plant-1 when 95% of maximum KNP was reached and also introduced a concept of threshold AIPAR of 0.34 MJ plant-1 below which all plants were barren. This logical curvilinear approach is necessary for more accurate simulation of yields over a broad range of plant densities.
Prolificacy
Maize plants usually produce a single apical ear when planted in favorable conditions at plant densities required for high yields. However, when planted at low densities (<2 plants m-2), as practiced in semiarid regions to avoid water deficit, maize plants are usually prolific and produce secondary ears. Prolificacy in maize is controlled by a single major gene and is amenable to genetic manipulation creating genetic differences in prolificacy among maize hybrids (Motto and Moll, 1983). The grain yield from secondary ears can account for up to 50% of total yield (Du Toit and Prinsloo, 2000). Tollenaar et al. (1992) and Andrade et al. (1999) reported details of KNP measurements (separating apical ear kernels from secondary ears) and PGR during the period bracketing silking. The results from both experiments indicate that in prolific hybrids, secondary ears developed when the PGR was about 6.0 g or more during period bracketing silking. Nonprolific hybrids made no secondary ears even at plant densities as low as 2 plants m-2 (Tollenaar et al., 1992). Andrade et al. (1999) showed that at PGRs greater than 4.0, any further increase in PGR did not increase kernel ear-1 beyond 500 in nonprolific plants and in uppermost ears in prolific plants. However, prolific plants produced secondary ears at PGRs greater than 6.0 g (Tollenaar et al., 1992; Andrade et al., 1999).
Intercepted Radiation and Barrenness
High maize yields are obtained at plant densities ranging from 7 to 10 plants m-2, but barrenness occurs more frequently when plant densities exceed 10 plants m-2. Plant densities influence both PGR and barrenness. At high densities, maize plants have low PGR and are barren while at low densities, plants have higher PGR and are prolific. Relating barrenness to PGR, Tollenaar et al. (1992) and Andrade et al. (1999) found that maize plants were barren when PGR averaged about 1.0 g during the 30-d period bracketing silking. Maize genotypes appear to have major genetic differences in barrenness. Tollenaar et al. (1992) found that lower barrenness in modern maize hybrids compared with older hybrids at higher plant densities was associated with higher PGR from 1 wk presilking to 3 wk postsilking. Instead of relating PGR to barrenness, Andrade et al. (2000) related AIPAR to barrenness and found a threshold AIPAR of 0.34 MJ plant-1 d-1 during ear development stage was necessary to avoid barrenness. There was a variation of 0 and 200 kernels ear-1 among plants at this threshold AIPAR, indicating the level of uncertainty in the assessment of barrenness. Some of this variation could have been caused by variation in light interception between individual plants within the same plant density. Several factors such as small differences in plant spacing, skips in the plant stand, differences in leaf orientation between rows, and differences in the time of seedling emergence can cause variation in radiation interception for individual plants within a canopy, resulting in KNP variations. The existence of threshold AIPAR or CIPAR when plants become barren and the percentage of barren plants at this threshold need further focused research. These findings indicate that simulation models that attempt to account for genotypic differences in maize will require at least one additional genetic coefficient to improve accuracy in simulating KNP at higher plant densities and to account for genetic differences in barrenness.
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SIMULATION OF GENETIC DIFFERENCES IN KERNEL NUMBER PLANT-1
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Kernel Number of Apical Ear
The original CERES Maize model simulates the number of grains per plant (GPP) using the equation:
where G2 = potential kernel number per plant and PSKER = average rate of biomass produced during 170°C days after silking.
In the model revision, we modified the GPP simulation. A curvilinear model relating CIPAR during the time window around silking to kernel number of apical ear (KN1) best described the results of Tollenaar et al. (1992) and Andrade et al. (2000). The time window [-227°C days (8°C as base temperature) before silking and continued until 100°C days after silking] used in the model revision is based on the findings of Otegui and Bonhomme (1998). There are obvious genetic differences among maize hybrids in the maximum KN1 and in the production of kernels on a second ear (KN2) (Tollenaar et al., 1992). A constant threshold value of 11 MJ of CIPAR, below which no grains are produced, fits the available data for a range of genotypes (Fig. 1)
. Two coefficients describing genetic variability are used in the revision to simulate KN1. One coefficient is the potential kernels per plant (GK). This is similar to the coefficient G2 used in the original CERES Maize model (Ritchie et al., 1986), except our definition is limited to KN1. A second coefficient (GE) represents the nonlinear kernel-setting efficiency per unit of CIPAR. The KN1 is simulated using the equations:
 | [1] |
 | [2] |
The coefficients derived for the various hybrids are shown in Table 1. The source of data for ‘Pioneer 34G82’ was from measured data taken from an award-winning farm in Iowa with unusually high yields and from published data of the same farm (Murrell and Childs, 2000). The source for the other hybrids was from Tollenaar et al. (1992). The derived genetic coefficients show that for maximum kernel numbers, the ears should have large GK and GE. Results from Tollenaar et al. (1992) indicated that the modern hybrid ‘Pioneer 3851’ had a GK of 550 while the older hybrid ‘Pride 5’ had a GK of 700. Comparing maize hybrids released between 1965 and 1993, Echarte et al. (2000) showed that the modern hybrids had higher KNP per unit PGR compared with the older hybrids. The larger kernel-setting efficiency coefficient GE for the more recently released hybrid reported in our study (Table 1) supports this finding.
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Table 1. Genetic coefficients for potential kernel number, kernel setting efficiency, barrenness, and prolificacy for selected maize hybrids
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Data of Otegui and Bonhomme (1998) in Fig. 1 contain results from hybrids with an apparent large contrast in GK coefficients. The results from all of these hybrids fit within the boundaries of 1980s hybrids for Ontario (Tollenaar et al., 1992) and the most recently released hybrid Pioneer 34G82 in Iowa. The data of Tollenaar et al. (1992) clearly demonstrated that modern hybrids produced more kernels per ear in the competitive environments caused by use of high plant density due primarily to higher PGR during silking and a greater tendency to prolificacy.
Prolificacy
Although hybrid differences in prolificacy are difficult to quantify, we used a simple and qualitative yes–no type designation as a genetic coefficient to express prolificacy. A value of 1 was used for prolific and 0 for nonprolific hybrids. We used KNP and PGR data of Tollenaar et al. (1992) and Andrade et al. (1999) in the determination of the prolificacy relationships. We obtained temperature data from Ellora, Canada, and Balcarce, Argentina, where these two studies were conducted, and using simulated leaf area index data, we derived CIPAR during the critical window of time. These derived CIPAR data, along with the reported KNP, indicated that approximately 10 MJ of calculated CIPAR compared closely to 1 g of measured PGR. In prolific hybrids, maize plants produced two ears when CIPAR exceeded 64 MJ. This value was equivalent to a PGR of approximately 6.4 g plant-1 d-1 as reported by Tollenaar et al. (1992) and Andrade et al. (1999). The KN2 was estimated using Eq. [3] with a threshold CIPAR of 64 MJ.
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where GP = prolificacy coefficient.
The KNP model using these equations is depicted in Fig. 2
. This relationship assumes that the potential KN2 can be as large as KN1 if CIPAR is high enough. The KN1 is usually around its maximum value when the second ear develops kernels as presented in studies of Bauman (1960). With prolific hybrids, the total kernel plant-1 is the sum of KN1 and KN2.
Barrenness
Quantitative data regarding barrenness from Tollenaar et al. (1992), Pommel and Bonhomme (1998), and Andrade et al. (1999) were used to determine the relationship between barrenness and CIPAR. Similar to the KN functions of Eq. [1], a threshold CIPAR of about 11 MJ existed, below which all plants were barren. The fraction of ear-bearing plants (Fe) representing barrenness is simulated using the equations:
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where GB = genetic coefficient accounting for differences among hybrids in tolerating plant densities without barrenness.
The observed data and model response for barrenness using Eq. [5] and [6] are presented in Fig. 3
. There was greater barrenness per unit CIPAR in hybrids released in the 1960s, with barrenness occurring for CIPAR values up to about 45 MJ, compared with hybrids released in later years having little barrenness above 25 MJ. When the CIPAR value was lower than the ceiling, the fraction of plants bearing ears decreased rapidly, and the rate of decline was quite closely related to the year of hybrid release. The barrenness coefficient (GB) values fitted to the available data were found to increase with the decade of hybrid release (Table 1).
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Fig. 3. Relationship between fraction of ear-bearing plants and cumulative intercepted photosynthetically active radiation (CIPAR) during the period bracketing silking (327°C days). Symbols indicate observed data, and lines indicate modeled response using Eq. [5].
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SENSITIVITY OF REVISED CERES MAIZE MODEL TO PLANT DENSITY VARIATIONS
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Plant density variations provide an opportunity for expressing genetic differences in kernel-setting efficiency, prolificacy, and barrenness. For KNP determination, simulation of prolificacy is important at low plant density while simulation of barrenness is important at high plant densities (Du Toit and Prinsloo, 2000; Ritchie and Wei, 2000). The CERES Maize model (V 3.5) was revised using the KNP, prolificacy, and barrenness coefficients described in the previous sections. The plant density effects on maize yield were simulated for sites in Iowa and Ontario where data on weather, soil characteristics, and measured yield components were available.
The northeastern Iowa site was one where a farmer frequently wins both state and national maize yield contests (NCGA, 2000). Grain yield at the 1999 contest was 20.9 Mg ha-1 (at 0% moisture), possibly a world record. Simulation results using the revised and original CERES Maize model and 1999 weather data from Manchester, IA, are presented in Fig. 4
along with the reported contest yields from 1990 to 1998. The contest yields from this Iowa farm in the past decade have increased substantially from 11.7 to 20.9 Mg ha-1 (at 0% moisture). Presumably, the increase in contest yield over the years was through the combined use of the modern hybrids, improved management practices, and increased plant density from 6.9 plants m-2 in 1990 to 10.9 plants m-2 in 1999. Simulated yields (using 1999 weather) increased almost linearly between 0.5 and 8 plants m-2 and declined when the plant density exceeded 12 plants m-2 for the Iowa site. When the original CERES Maize model was used, the simulated yields continued to increase slightly at populations >8 plants m-2.
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Fig. 4. Relationship between plant density and simulated yield by original (broken line) and revised (solid line) CERES Maize model. The top two curves are for simulated yield for the Iowa site in 1999, and the bottom two curves are for the hybrid Pride 5 from Ontario site in 1989. The symbols represent observed yield. The closed symbols are for the Iowa maize yield contest (the year of contest in parenthesis), and open symbols are for Pride 5 in Ontario, Canada (Tollenaar, 1992).
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For the Ontario site, simulated results for a low-yielding, nonprolific hybrid, Pride 5 (released in 1959), using original and revised CERES Maize model using weather data from near the experimental site are provided in Fig. 4. The observed yield data were obtained from Tollenaar (1992), and the genetic coefficients for the hybrid Pride 5 were developed from independent data (Tollenaar et al., 1992). The simulated yields by the original model increased asymptotically above 2 plants m-2 and showed no reduction in yield, even at 24 plants m-2. On the contrary, simulated yield by the revised model decreased when plant density increased beyond 12 plants m-2. The revised model simulated the plant density response reasonably well (RMSE = 0.63 Mg ha-1) compared with the original model response (RMSE = 1.25 Mg ha-1). In an independent study at Florence, SC, using the original CERES Maize model, Sadler et al. (2000) simulated an essentially flat yield response when plant densities varied from 3 to 15 plants m-2.
The simulated yields by the original CERES Maize model at the Ontario, northern Iowa, and Florence sites showed a lack of sensitivity to unusually high plant density because the model did not simulate barrenness correctly. These results demonstrate that to accurately simulate yield response to variations in plant density, the effects of competition for resources on KNP need to be included in maize simulation models. The simulated yields started to decline beyond 12 plants m-2 at both Iowa and Ontario sites as a result of including barrenness and a nonlinear model for KNP simulation in the revised CERES Maize model.
Few independent data sets are available to test the revised model for maize yields and barrenness at very high plant densities. Evaluating the relationship between individual PGR and barrenness, Andrade et al. (1999) indicated that some plants were barren when the PGR was 2 g d-1 during 30-d period bracketing silking. However, in the same study, there were plants with PGR of 2 g d-1 that produced 100 to 400 kernels. Such variation in barrenness among maize plants at the same PGR indicates the difficulties and emphasizes the general problems in assessing the barrenness. Effects of high plant density on plant barrenness therefore needs specifically focused experiments to examine the effects of individual plant variations in space and development stage as they influence PGR, CIPAR, and KNP of the plants within a somewhat heterogeneous canopy. Results from such studies will help to test and improve further the revised CERES Maize model performance to simulate KNP more accurately over a wide range of plant densities.
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ACKNOWLEDGMENTS
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We are grateful to Professors L.A. Hunt of University of Guelph and F.H. Andrade of Unidad Integrada INTA, Balcarce, for providing weather data for the location Ellora, Canada, and Balcarce, Argentina. The comments by Dr. A.J. Hall and A. Weiss and by the anonymous reviewers on the manuscript are gratefully acknowledged.
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ABSTRACT
INTRODUCTION
are from 
for Pioneer 3902 from