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Spatial patterns in U.S. hard red winter wheat quality

Spatial patterns in U.S. hard red winter wheat quality AbbreviationsHRWWhard red winter wheatPGIPlains Grains, Inc.INTRODUCTIONHard red winter wheat (Triticum aestivum L; HRWW) can be used to make bread‐use flour and flour suitable for Asian noodles, hard rolls, and flatbreads. Information about wheat quality is valuable to wheat buyers; however, HRWW quality information is difficult for millers to acquire because elevators only conduct a limited number of quality tests due to the time and cost of testing (Regnier et al., 2004). Wheat quality characteristics can directly influence the quality of flour and end products. The characteristics of interest for most HRWW buyers include hardness, protein, test weight, kernel size, and damaged kernels. Protein, or gluten, in flour is the key factor that makes dough sticky (MacRitchie, 1987) and gives a smooth texture to bread. Test weight and percentage of large kernels can give millers an approximation of flour yield. Espinosa and Goodwin (1991) and Roberts (2020) have estimated hedonic models of wheat prices and selected wheat characteristics. Espinosa and Goodwin (1991) used Kansas wheat price and quality data and found that wheat buyers and end users use characteristics other than grading factors to price wheat. Roberts (2020) extended the previous work into the entire HRWW growing region.Plains Grains, Inc. (PGI) is a private, nonprofit wheat‐marketing organization dedicated to providing the link between HRWW producers, grain companies, and foreign and domestic flour millers to benefit all segments of the wheat industry. It was formed in 2004 with a mission to gather and deliver timely quality and production data; cultivate relationships between producers, elevators, grain handlers, and millers; and to effectively market the quality characteristics of annual HRRW to interested borrowers. The main objectives of this work were accomplished using PGI data to determine the spatial distribution of HRWW quality characteristics across the HRWW growing region of the United States and to determine if annual sampling provides new, valuable information to wheat buyers every year. The value of annual sampling is shown both by averages varying by year and the spatial correlation varying by year.MATERIALS AND METHODSDataWheat quality data were obtained from PGI and are considered unpublished data. Plains Grains, Inc. collects wheat samples, tests wheat qualities, and provides this information to wheat buyers every year. Sampling is focused on the Great Plains states of Texas, Oklahoma, Kansas, Nebraska, South Dakota, North Dakota, Colorado, Wyoming, and Montana and the Pacific Northwest states of Idaho, Oregon, and Washington. In the Great Plains states, PGI samples individual elevators. In the Pacific Northwest, the samples were from regional elevators and so represent a larger area. Local elevators typically sample each load of wheat, and after the sample is tested, the wheat is placed into a dump barrel. The PGI representative then takes a probe sample from the dump barrel. The samples were sent to the USDA‐ARS Hard Winter Wheat Quality Lab in Manhattan, Kansas (Plain Grains Inc., 2020) where they were tested for wheat quality. The grade of sampled wheat is officially declared by the Federal Grain Inspection Service office in Enid, Oklahoma.Plains Grains, Inc. breaks the selected wheat quality characteristics into three groups, including (a) wheat grading characteristics, (b) kernel quality characteristics, and (c) all other wheat characteristics. The grading characteristics include dockage, test weight, damaged kernels, shrunken and broken kernels, and foreign material (Plain Grains Inc., 2020). Kernel quality characteristics include total defects, kernel size, thousand kernel weight, and kernel diameter. All other wheat characteristics include protein, ash content, falling number, moisture, and kernel hardness. Plains Grains, Inc. also collects milling and baking data at a much more spatially aggregated scale, and such data were used by Roberts (2020). The milling and baking data were not used here since they are too aggregated to study spatial correlation.The original dataset had 4,032 observations. Unusable data included 239 observations of cultivars other than HRWW or missing values associated with wheat classification and 671 observations with missing latitude–longitude coordinates. Also, there were 159 locations sampled only once in eight years, so they were removed to avoid a perfect fit of regression. After removing all unusable observations, the dataset used in the analysis had 3,090 observations that covered 430 locations across eight years from 2012 to 2019. Note that some quality data were missing for some locations in certain years, so the observation number may differ according to the wheat quality characteristic. The dataset is also unbalanced within years and across years. In each year, the number of sampled elevators in each city differed, and some locations received repeated measures. For example, in 2012, 62 out of 305 sampled locations had more than one sampled elevator. The number of sampled locations also differed across years, and the sampled locations changed by year.Core IdeasWheat buyers benefit from knowing which elevators have desired grain qualities.Wheat quality characteristics had strong spatial correlation within a year and across years.Geospatial maps show how wheat qualities vary across the wheat‐producing region.Latitude–longitude coordinates were extracted on a city‐level following the World Geodetic System 1984 (WGS84). The Single Kernel Characterization System was used to measure kernel hardness and diameters. Other wheat characteristics were dockage, test weight, damaged kernels, shrunken and broken kernels, foreign material, total defects, kernel size (large, medium, and small), thousand kernel weight, protein, individual wheat ash, falling number, and moisture content. Protein and individual wheat ash measurements were on a 12% moisture basis. Descriptive statistics for the data are presented in Table 1.1TABLESummary statistics of U.S. hard red winter wheat quality characteristicsCharacteristicCountMeanSDMinMaxGrading characteristicsDockage, %3,1320.550.520.007.00Test weight, kg hl−13,13360.351.7652.1065.40Damage kernel, %3,1290.270.500.0010.60Shrunken and broken kernel, %3,1341.110.800.0013.20Foreign material, %3,1310.150.280.006.70Total defects, %3,1221.520.950.1013.40Kernel characteristicsKernel size large, %3,07259.8916.170.3598.10Kernel size medium, %3,07238.7115.361.8596.35Kernel size small, %3,0721.411.190.0011.10Thousand kernel weights, g3,13629.883.4419.6747.64SKCS average diameters, mm3,1362.580.122.243.21Other characteristicsProtein, 12% mb3,13712.171.407.6017.50Individual wheat ash, 12% mb3,1351.560.130.002.10Falling number, s3,133391.7642.1098.00598.00Moisture, %3,13711.291.401.2319.20SKCS average hardness3,07263.629.8927.3394.71Note. Single Kernel Characterization System (SKCS) hardness is an index. Below 50 is soft grain, and above 50 is hard grain. The data were collected by Plains Grains, Inc., from 2012 to 2019.Mixed‐effects model and geospatial mappingStudies have used various methods to examine the factors affecting wheat quality. Factors that can determine wheat quality include wheat cultivar (Barkley & Porter, 1996; Lambert & Wilson, 2003); weather and soil conditions (Gooding et al., 2003; Johansson et al., 2008; Lee et al., 2013); and the level of nitrogen (N) applied on the field (Bongiovanni et al., 2007; Erekul & Köhn, 2006; Meyer‐Aurich et al., 2010; Zecevic et al., 2010). Since the data involved both spatial and time effects, spatial autocorrelation could come from local values and residuals. Lee et al. (2013) utilized a spatial lag model to study the influence of temperature and rainfall on wheat protein and test weight. Meyer‐Aurich et al. (2010) applied a spatial error model to estimate the wheat yield and protein response to nitrogen applied. Spatial error and spatial lag models do not allow coefficients to vary across space, which differs from the spatially varying coefficients model used here.For this study, a mixed‐effects regression model was used to find the mean value of wheat characteristics for each location. The data were unbalanced with more observations in some years than others, and the mixed‐effects model was used to remove the year effects. Dummy location variables were considered fixed effects, while year was treated as a random effect so the random influence in each year could be averaged out. The long‐term means of each location could be useful to wheat buyers who are contracting purchases in advance of harvest or early in the harvest while quality information is limited. It may also provide evidence that would support PGI's surveying work every year. The mixed‐effects regression model used to estimate the mean of wheat quality for each location is represented mathematically as:1yit=β1+∑j=2LβjIlocationit=locationIDj+γt+uit\begin{equation}\ {y_{it}} = \ {{{\beta}}_1} + \mathop \sum \limits_{j\ = \ 2}^L {{{\beta}}_j}I\left( {{\rm{locatio}}{{\rm{n}}_{it}} = \ {\rm{locationI}}{{\rm{D}}_j}} \right) + {{{\gamma}}_t} + {u_{it}}\end{equation}Where yit is the ith observation in year t of a wheat characteristic, βs are regression coefficients, I(locationit = locationIDj) is an indicator function that equals 1 if the location of the ith observation in year t is equal to the jth$\ $locationID and 0 otherwise, locationID is an alphabetically sorted list of cities, γt∼N(0,σγ2)${{{\gamma}}_t}\sim N( {0,{{\sigma}}_{{\gamma}}^2} )$ is the random year effect in year t, and uit∼N(0,σu2)${{\rm{u}}_{it}}\sim N( {0,{{\sigma}}_{\rm{u}}^2} )$ is the error term. The mixed model in Equation 1 was estimated using restricted maximum likelihood with the lme() option in the nlme package in R (Pinheiro et al., 2021). The gstate package in R was used to create geospatial maps for each quality characteristic. These are maps of the estimated values of β1 + βj. Geospatial mapping was chosen because it is less restrictive than other methods such as cluster analysis (Bivand et al., 2013).Semi‐variograms were estimated both for the local means and for the residuals of each year. A variogram (or semi‐variogram) measures similarity based on distances (Isaaks & Srivastava, 1989). The function that describes the empirical semi‐variogram based on the data{ŷj,i…,L}$\{ {{{\hat{y}}_j},i\ldots,L} \}$ is2γh=12nh∑i,j:hij=hŷi−ŷj2\begin{equation}{{\gamma}}\ \left( h \right) = \frac{1}{{2n\left( h \right)}}\ \mathop \sum \limits_{\left( {i,j} \right):\ {h_{ij}} = \ h} {\left( {{{\hat{y}}_i} - {{\hat{y}}_j}} \right)^2}\end{equation}where γ(h) is the estimated semi‐variogram at distance h, n(h) is the number of point pairs with distance h, and ŷi${\hat{y}_i}$ and ŷj${\hat{y}_j}$ are a pair of points at location i and j with distance h. If hij is small, which means distance is close, then points should be similar to each other, and the semi‐variogram should be small. The variogram function with default settings from the gstat package in R (Pebesma, 2004) was used to obtain the number of point pairs, distance, and estimated semi‐variogram by distance, which were then used to estimate a parametric model for the variogram.Theoretically, a semi‐variogram will keep increasing as distance increases. When distance reaches a specific point, differences between points reach a maximum, and the semi‐variogram will reach a plateau and stay there. The exponential variogram model was fitted for wheat dockage, foreign material, and protein.The empirical variogram for the other wheat characteristics never reached the plateau before 1,000 km, and the scatterplot for those characteristics suggested that a linear variogram model was a good fit. Therefore, we imposed that the plateau of the linear models was 1,000 km and did not estimate the plateau parameter.Wheat dockage, foreign material, and protein variograms were estimated using the fit.variogram() option in the gstat function in R. Note that fit.variogram() option only allowed 200 iterations per execution, so an iteration procedure was used by repeating the procedure using the previous estimation of parameters in order to obtain our results. For all the other wheat characteristics, a linear variogram model was estimated using the lm() function in the stats procedure in R. The estimated regressions had the semi‐variogram values as the dependent variable, distance as the independent variable, the number of point pairs as the weight, and the partial sill effect calculated as 1,000c1. The variograms for residuals of each wheat characteristic in each year were estimated using the exponential model.RESULTS AND DISCUSSIONThe mean for protein, test weight, kernel size, kernel hardness, shrunken and broken kernels, and damaged kernel quality characteristics by elevator are mapped in Figures 1–6. Figure 1 shows protein by elevator, which is a key quality characteristic for buyers. An area of high protein is shown in the Texas Panhandle up to southwestern Kansas. These areas are often dry, and this could explain the higher protein. There is an area of low protein in North Dakota. The northern areas show more variation due to these locations having fewer years of data for some elevators.1FIGUREMap of hard red winter wheat protein (%) content by elevator. The data are averages over 2012–2019. No adjustment is made for missing data2FIGUREMap of hard red winter wheat test weight (kg hl‐1) by elevator3FIGUREMap of percentage of hard red winter wheat kernels of size large by elevator4FIGUREMap of Single Characterization System average kernel hardness of hard red winter wheat5FIGUREMap of hard red winter wheat shrunken and broken kernels (%) by elevator6FIGUREMap of hard red winter wheat damaged kernel (%) by elevatorTest weight (Figure 2) also shows a strong spatial pattern. Northern areas consistently deliver higher test weights than southern areas. Heat and drought stress decrease test weight as can stress from diseases and insects.Larger kernels provide higher milling yield. Figure 3 shows that the areas with the largest kernels are in the north. Southern Plains states (i.e., Texas and Oklahoma) provide few areas with the largest kernels. Drought and high temperatures during kernel filling can reduce kernel weight (Wardlaw, 2002) and these weather conditions are more prevalent in the South.Kernel hardness (Figure 4) also shows a clear spatial pattern. The area with the hardest kernels is Montana. Northern Kansas shows less kernel hardness than areas south of it. Stress environments, such as heat combined with drought (Elhadi et al., 2021), can create kernel hardness, so the high hardness in the Texas Panhandle and western Kansas is expected.Shrunken and broken kernels are more prevalent in southern and western areas of the wheat‐growing region (Figure 5). High temperatures during grain filling can create shrunken and broken kernels (Wu et al., 2016). Damaged kernels are low in Montana and high in eastern North Dakota (Figure 6). The high damaged kernels in a swath of North Dakota resulted from extreme weather in one or two years and may not be typical.The means of quality characteristics for combinations of states are shown in Table 2. These means support the conclusions from the figures. Heat and drought in southern areas lead to quality being lower for many factors (i.e., more dockage, lower test weight, more shrunken and broken kernels, more foreign material, more total defects, and smaller kernels) in southern areas. The southern areas do have higher protein and greater kernel hardness. Falling number, moisture, and ash content do not show a consistent geographical pattern.2TABLEMean hard red winter wheat quality characteristics by U.S. state or regionCharacteristicsTX & OKKS & CONE, SD & NDPNWGrading characteristicsDockage, %0.630.480.560.49Test weight, kg hl−178.7579.0779.7780.42Damage kernel, %0.290.300.330.00Shrunken and broken kernel, %1.311.080.941.02Foreign material, %0.220.130.140.10Total defects, %1.811.501.401.15Kernel characteristicsKernel size large, %54.6860.2267.7463.47Kernel size medium, %43.5838.4131.2835.39Kernel size small, %1.791.340.981.14Thousand kernel weights, g28.9229.6230.9231.41SKCS average diameters, mm2.562.572.612.61Other characteristicsProtein, 12% mb12.3212.2411.9311.78Individual wheat ash, 12% mb1.561.561.591.44Falling number, s388.28395.50386.64390.80Moisture, %11.5711.3011.7610.38SKCS average hardness67.0462.0959.5267.82Note. Single Kernel Characterization System (SKCS) hardness is an index. Below 50 is soft grain, and above 50 is hard grain.PNW, Pacific Northwest.The estimated spatial parameters (i.e., nugget, partial sill, and range) of the exponential variogram for dockage, foreign material, and protein content qualities are reported in Table 3. The variograms use each location's mean value across years, which is the same statistic that is shown in Figures 1–6. The strength of spatial relationships can be measured through variograms. Range is the distance that it takes for the fitted variogram to reach the plateau. It measures if spatial correlation is in a small region or a relatively large area. For dockage, foreign material, and protein, the estimated range parameters are all below 1,000 km (Table 3). The fitted variogram for foreign material and protein increased up to 600 km, but the variogram for dockage reached the sill at 175 km. This implies that spatial correlation in dockage decays quickly as distance increases. What is important about the information in Table 3 is that it verifies the visual information and shows that there is a strong spatial pattern to the wheat quality characteristics.3TABLEEstimated spatial parameters of U.S. hard red winter wheat characteristics using an exponential model for the semi‐variogram CharacteristicNuggetPartial sillRangeDockage0.030.05175.39Foreign material0.020.01497.68Protein0.190.48531.13Note. The data used were the least squares means for each location that were obtained from estimating Equation (1). Unit of range is km. Nugget and partial sill are similar to variance. Its unit depends on the unit of parameters. Squaring the corresponding unit in Table 1 will give the unit of nugget and partial sill. For example, the unit for nugget and partial sill of dockage is %2${\% ^2}$. Range measures the maximum distance at which two points are still spatially correlated. Nugget and partial sill together measure the spatial correlation behavior. The variograms of the above three wheat characteristics show plateau before 1,000 km, so an exponential model is fitted.Estimated spatial parameters (i.e., nugget and partial sill) of the linear variogram representing quality characteristics for test weight, damaged kernels, shrunken and broken kernels, total defects, kernel size, kernel test weight, kernel size, wheat ash, falling number, moisture, and hardness are reported in Table 4. Foreign material, test weight, shrunken and broken kernels, total defects, and the estimated nugget effects are bigger than the partial sill effects (Tables 3 and 4). A relatively large nugget implies that these measures are less repeatable (within a season and across nearby elevators). For example, test weight has a large nugget. Test weight can be high early in the harvest season and then can fall after a rain. Plains Grains, Inc. takes samples over a short period of time to reduce this noise, but it is still present in the data.4TABLEEstimated spatial parameters of U.S. hard red winter wheat characteristics using a linear model for the semi‐variogramCharacteristicNuggetPartial sillTest weight1.241.14Damaged kernels0.0200.066Shrunken & broken kernel0.120.04Total defects0.160.13Kernel size large22.992.1Kernel size medium20.583.0Kernel size small0.200.28Thousand kernel weights0.503.76SKCS average diameters0.00100.0032Individual wheat ash0.00220.0062Falling number233.3415.9Moisture0.231.06SKCS average hardness12.227.9Note. The data used were the least squares means for each location that were obtained from estimating Equation (1). The variogram of these wheat characteristics does not have a plateau before 1,000 km. Thus, the range is fixed at 1,000 km, and partial sill is calculated based on that. SKCS, Single Kernel Characterization System.For each wheat characteristic, variograms of residuals were estimated by year. Examples of these variograms are provided in Figure 7. Each curve in the plot is a fitted variogram. The distance at which the fitted variogram line reaches the plateau is the maximum distance at which the residuals are still correlated.7FIGUREVariograms of residuals from models of wheat quality characteristics. The residuals are the estimated uit from Equation 1Test weight residuals is an example of a characteristic that does not have much spatial correlation for most years. In one year, the test weight fitted variogram went from a low level to a plateau, which means test weight residuals showed strong spatial correlation only once out of eight sampling years. This means that although the spatial correlation exists, it is limited in a small region. For the rest of the fitted variogram, they are almost horizontal and at a low level, implying little spatial correlation.Since the variograms (Figure 7) of protein, kernel size large, and hardness are not horizontal lines from the beginning, this shows that there is still some remaining spatial correlation in the residuals, especially for protein and kernel hardness. There are some increasing straight lines in protein and hardness residuals, and they are still increasing around 1,000 km. It implies that protein and hardness residuals have strong spatial correlation in some years. Even if fitted variograms of residuals, like hardness, share the same pattern across years (i.e., increase followed by a plateau) , the maximum plateau varies across years. This means the variability of wheat characteristics changes across years. It implies that PGI is collecting useful and unique information of wheat characteristics every year for wheat buyers.Table 5 is used to even more directly address the question of whether sampling is needed every year. Of particular interest in Table 5 is the column with the residual standard deviation. While the year effects are substantial, they could be determined with a much smaller sample. Most residual standard deviations are larger than the standard deviation of year effects. Key measures like test weight, kernel size, protein, and kernel hardness all show substantial residual variation. For example, the residual standard deviation for protein is a little over one, meaning that a 95% confidence interval for a location that averages 12% protein would vary from about 10% protein to 14% protein. Thus, Table 5 shows that there is considerable value in conducting the survey every year.5TABLEStandard deviations (SD) of nonspatial effects on U.S. hard red winter wheat quality characteristicsSDCategoryYearResidualGrading characteristicsDockage, %0.110.5Test weight, kg hl−10.944.08Damage kernel, %0.150.46Shrunken and broken kernel, %0.280.72Foreign material, %0.010.27Total defects, %0.260.86Kernel characteristicsKernel size large, %9.812.55Kernel size medium, %9.4211.88Kernel size small, %0.491.06Thousand kernel weights, g2.232.51SKCS average diameters, mm0.060.1Other characteristicsProtein, 12% mb0.841.08Individual wheat ash, 12% mb0.050.11Falling number, s18.9536.3Moisture, %0.421.1SKCS average hardness6.427.21Note. The standard deviations were obtained by estimating Equation (1) and specifying year as a random effect. The null hypothesis of no year effect was rejected in all cases (P < .05). SKCS, Single Kernel Characterization System.CONCLUSIONSWheat buyers such as bakers and noodle‐makers target different niche food markets and are very specific about certain quality levels of the HRWW that they purchase. Hard red winter wheat quality characteristics showed spatial patterns with some areas consistently producing higher values of quality factors than other locations. The importance of spatial variation was shown by mean wheat quality characteristics and residuals having strong spatial correlation. The measures at each location vary considerably by year, which indicates there is value in conducting the sample every year.ACKNOWLEDGMENTSFunding for this research was provided by the Oklahoma Agricultural Experiment Station and National Institute of Food and Agriculture Hatch Project OKL03170 as well as the A.J. and Susan Jacques chair. We express gratitude to Plains Grains, Inc. and Mark Hodges for making the data available to us. The data for the research could not have been collected without the participation of numerous elevators, initial support from the Oklahoma Wheat Commission, and many others. Considerable editorial assistance from Jon Biermacher is gratefully acknowledged.AUTHOR CONTRIBUTIONSYikuan Chen: Formal analysis; Investigation; Methodology; Resources; Software; Validation; Visualization; Writing – original draft; Writing – review & editing. B. Wade Brorsen: Conceptualization; Data curation; Funding acquisition; Investigation; Methodology; Project administration; Resources; Software; Supervision; Validation; Visualization; Writing – review & editing.CONFLICT OF INTERESTThe authors declare no conflict of interest.REFERENCESBarkley, A. P., & Porter, L. L. (1996). The determinants of wheat variety selection in Kansas, 1974 to 1993. American Journal of Agricultural Economics, 78, 202–211. https://doi.org/10.2307/1243791Bongiovanni, R. G., Robledo, C. W., & Lambert, D. M. (2007). 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Computers and Electronics in Agriculture, 74, 73–79. https://doi.org/10.1016/j.compag.2010.06.007Pebesma, E. J. (2004). Multivariable geostatistics in S: The gstat package. Computers & Geosciences, 30, 683–691. https://doi.org/10.1016/j.cageo.2004.03.012Pinheiro, J., Bates, D., DebRoy, S., & Sarkar, D., & R Core Team. (2021). nlme: Linear and nonlinear mixed effects models (R package version 3, pp. 1–152). https://CRAN.R‐project.org/package=nlmePlains Grains, Inc. (2020). Hard red winter wheat 2020 regional quality survey. https://www.plainsgrains.org/wp‐content/uploads/2020/12/Plains_Grains‐2020_Winter_Wheat_Report.pdfRegnier, S., Holcomb, R., & Rayas‐Duarte, P. (2004). Relating wheat quality to end‐product quality (FAPC‐129). Oklahoma State University. https://shareok.org/bitstream/handle/11244/50192/oksd_fapc_129_2010‐07.pdf?sequence=1Roberts, S. J. (2020). The role of quality characteristics in pricing hard red winter wheat [Master's thesis, University of Nebraska‐Lincoln]. DigitalCommons@University of Nebraska. https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1065&context=agecondissWardlaw, I. F. (2002). Interaction between drought and chronic high temperature during kernel filling in wheat in a controlled environment. Annals of Botany, 90, 469–476. https://doi.org/10.1093/aob/mcf219Wu, Y.‐C., Chang, S.‐J., & Lur, H.‐S. (2016). Effects of field high temperature on grain yield and quality of a subtropical type japonica rice —Pon‐Lai rice. Plant Production Science, 19, 145–153. https://doi.org/10.1080/1343943X.2015.1128091Zecevic, V., Knezevic, D., Boskovic, J., Micanovic, D., & Dozet, G. (2010). Effect of nitrogen fertilization on winter wheat quality. Cereal Research Communications, 38, 243–249. https://doi.org/10.1556/crc.38.2010.2.10 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Agrosystems, Geosciences & Environment" Wiley

Spatial patterns in U.S. hard red winter wheat quality

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Abstract

AbbreviationsHRWWhard red winter wheatPGIPlains Grains, Inc.INTRODUCTIONHard red winter wheat (Triticum aestivum L; HRWW) can be used to make bread‐use flour and flour suitable for Asian noodles, hard rolls, and flatbreads. Information about wheat quality is valuable to wheat buyers; however, HRWW quality information is difficult for millers to acquire because elevators only conduct a limited number of quality tests due to the time and cost of testing (Regnier et al., 2004). Wheat quality characteristics can directly influence the quality of flour and end products. The characteristics of interest for most HRWW buyers include hardness, protein, test weight, kernel size, and damaged kernels. Protein, or gluten, in flour is the key factor that makes dough sticky (MacRitchie, 1987) and gives a smooth texture to bread. Test weight and percentage of large kernels can give millers an approximation of flour yield. Espinosa and Goodwin (1991) and Roberts (2020) have estimated hedonic models of wheat prices and selected wheat characteristics. Espinosa and Goodwin (1991) used Kansas wheat price and quality data and found that wheat buyers and end users use characteristics other than grading factors to price wheat. Roberts (2020) extended the previous work into the entire HRWW growing region.Plains Grains, Inc. (PGI) is a private, nonprofit wheat‐marketing organization dedicated to providing the link between HRWW producers, grain companies, and foreign and domestic flour millers to benefit all segments of the wheat industry. It was formed in 2004 with a mission to gather and deliver timely quality and production data; cultivate relationships between producers, elevators, grain handlers, and millers; and to effectively market the quality characteristics of annual HRRW to interested borrowers. The main objectives of this work were accomplished using PGI data to determine the spatial distribution of HRWW quality characteristics across the HRWW growing region of the United States and to determine if annual sampling provides new, valuable information to wheat buyers every year. The value of annual sampling is shown both by averages varying by year and the spatial correlation varying by year.MATERIALS AND METHODSDataWheat quality data were obtained from PGI and are considered unpublished data. Plains Grains, Inc. collects wheat samples, tests wheat qualities, and provides this information to wheat buyers every year. Sampling is focused on the Great Plains states of Texas, Oklahoma, Kansas, Nebraska, South Dakota, North Dakota, Colorado, Wyoming, and Montana and the Pacific Northwest states of Idaho, Oregon, and Washington. In the Great Plains states, PGI samples individual elevators. In the Pacific Northwest, the samples were from regional elevators and so represent a larger area. Local elevators typically sample each load of wheat, and after the sample is tested, the wheat is placed into a dump barrel. The PGI representative then takes a probe sample from the dump barrel. The samples were sent to the USDA‐ARS Hard Winter Wheat Quality Lab in Manhattan, Kansas (Plain Grains Inc., 2020) where they were tested for wheat quality. The grade of sampled wheat is officially declared by the Federal Grain Inspection Service office in Enid, Oklahoma.Plains Grains, Inc. breaks the selected wheat quality characteristics into three groups, including (a) wheat grading characteristics, (b) kernel quality characteristics, and (c) all other wheat characteristics. The grading characteristics include dockage, test weight, damaged kernels, shrunken and broken kernels, and foreign material (Plain Grains Inc., 2020). Kernel quality characteristics include total defects, kernel size, thousand kernel weight, and kernel diameter. All other wheat characteristics include protein, ash content, falling number, moisture, and kernel hardness. Plains Grains, Inc. also collects milling and baking data at a much more spatially aggregated scale, and such data were used by Roberts (2020). The milling and baking data were not used here since they are too aggregated to study spatial correlation.The original dataset had 4,032 observations. Unusable data included 239 observations of cultivars other than HRWW or missing values associated with wheat classification and 671 observations with missing latitude–longitude coordinates. Also, there were 159 locations sampled only once in eight years, so they were removed to avoid a perfect fit of regression. After removing all unusable observations, the dataset used in the analysis had 3,090 observations that covered 430 locations across eight years from 2012 to 2019. Note that some quality data were missing for some locations in certain years, so the observation number may differ according to the wheat quality characteristic. The dataset is also unbalanced within years and across years. In each year, the number of sampled elevators in each city differed, and some locations received repeated measures. For example, in 2012, 62 out of 305 sampled locations had more than one sampled elevator. The number of sampled locations also differed across years, and the sampled locations changed by year.Core IdeasWheat buyers benefit from knowing which elevators have desired grain qualities.Wheat quality characteristics had strong spatial correlation within a year and across years.Geospatial maps show how wheat qualities vary across the wheat‐producing region.Latitude–longitude coordinates were extracted on a city‐level following the World Geodetic System 1984 (WGS84). The Single Kernel Characterization System was used to measure kernel hardness and diameters. Other wheat characteristics were dockage, test weight, damaged kernels, shrunken and broken kernels, foreign material, total defects, kernel size (large, medium, and small), thousand kernel weight, protein, individual wheat ash, falling number, and moisture content. Protein and individual wheat ash measurements were on a 12% moisture basis. Descriptive statistics for the data are presented in Table 1.1TABLESummary statistics of U.S. hard red winter wheat quality characteristicsCharacteristicCountMeanSDMinMaxGrading characteristicsDockage, %3,1320.550.520.007.00Test weight, kg hl−13,13360.351.7652.1065.40Damage kernel, %3,1290.270.500.0010.60Shrunken and broken kernel, %3,1341.110.800.0013.20Foreign material, %3,1310.150.280.006.70Total defects, %3,1221.520.950.1013.40Kernel characteristicsKernel size large, %3,07259.8916.170.3598.10Kernel size medium, %3,07238.7115.361.8596.35Kernel size small, %3,0721.411.190.0011.10Thousand kernel weights, g3,13629.883.4419.6747.64SKCS average diameters, mm3,1362.580.122.243.21Other characteristicsProtein, 12% mb3,13712.171.407.6017.50Individual wheat ash, 12% mb3,1351.560.130.002.10Falling number, s3,133391.7642.1098.00598.00Moisture, %3,13711.291.401.2319.20SKCS average hardness3,07263.629.8927.3394.71Note. Single Kernel Characterization System (SKCS) hardness is an index. Below 50 is soft grain, and above 50 is hard grain. The data were collected by Plains Grains, Inc., from 2012 to 2019.Mixed‐effects model and geospatial mappingStudies have used various methods to examine the factors affecting wheat quality. Factors that can determine wheat quality include wheat cultivar (Barkley & Porter, 1996; Lambert & Wilson, 2003); weather and soil conditions (Gooding et al., 2003; Johansson et al., 2008; Lee et al., 2013); and the level of nitrogen (N) applied on the field (Bongiovanni et al., 2007; Erekul & Köhn, 2006; Meyer‐Aurich et al., 2010; Zecevic et al., 2010). Since the data involved both spatial and time effects, spatial autocorrelation could come from local values and residuals. Lee et al. (2013) utilized a spatial lag model to study the influence of temperature and rainfall on wheat protein and test weight. Meyer‐Aurich et al. (2010) applied a spatial error model to estimate the wheat yield and protein response to nitrogen applied. Spatial error and spatial lag models do not allow coefficients to vary across space, which differs from the spatially varying coefficients model used here.For this study, a mixed‐effects regression model was used to find the mean value of wheat characteristics for each location. The data were unbalanced with more observations in some years than others, and the mixed‐effects model was used to remove the year effects. Dummy location variables were considered fixed effects, while year was treated as a random effect so the random influence in each year could be averaged out. The long‐term means of each location could be useful to wheat buyers who are contracting purchases in advance of harvest or early in the harvest while quality information is limited. It may also provide evidence that would support PGI's surveying work every year. The mixed‐effects regression model used to estimate the mean of wheat quality for each location is represented mathematically as:1yit=β1+∑j=2LβjIlocationit=locationIDj+γt+uit\begin{equation}\ {y_{it}} = \ {{{\beta}}_1} + \mathop \sum \limits_{j\ = \ 2}^L {{{\beta}}_j}I\left( {{\rm{locatio}}{{\rm{n}}_{it}} = \ {\rm{locationI}}{{\rm{D}}_j}} \right) + {{{\gamma}}_t} + {u_{it}}\end{equation}Where yit is the ith observation in year t of a wheat characteristic, βs are regression coefficients, I(locationit = locationIDj) is an indicator function that equals 1 if the location of the ith observation in year t is equal to the jth$\ $locationID and 0 otherwise, locationID is an alphabetically sorted list of cities, γt∼N(0,σγ2)${{{\gamma}}_t}\sim N( {0,{{\sigma}}_{{\gamma}}^2} )$ is the random year effect in year t, and uit∼N(0,σu2)${{\rm{u}}_{it}}\sim N( {0,{{\sigma}}_{\rm{u}}^2} )$ is the error term. The mixed model in Equation 1 was estimated using restricted maximum likelihood with the lme() option in the nlme package in R (Pinheiro et al., 2021). The gstate package in R was used to create geospatial maps for each quality characteristic. These are maps of the estimated values of β1 + βj. Geospatial mapping was chosen because it is less restrictive than other methods such as cluster analysis (Bivand et al., 2013).Semi‐variograms were estimated both for the local means and for the residuals of each year. A variogram (or semi‐variogram) measures similarity based on distances (Isaaks & Srivastava, 1989). The function that describes the empirical semi‐variogram based on the data{ŷj,i…,L}$\{ {{{\hat{y}}_j},i\ldots,L} \}$ is2γh=12nh∑i,j:hij=hŷi−ŷj2\begin{equation}{{\gamma}}\ \left( h \right) = \frac{1}{{2n\left( h \right)}}\ \mathop \sum \limits_{\left( {i,j} \right):\ {h_{ij}} = \ h} {\left( {{{\hat{y}}_i} - {{\hat{y}}_j}} \right)^2}\end{equation}where γ(h) is the estimated semi‐variogram at distance h, n(h) is the number of point pairs with distance h, and ŷi${\hat{y}_i}$ and ŷj${\hat{y}_j}$ are a pair of points at location i and j with distance h. If hij is small, which means distance is close, then points should be similar to each other, and the semi‐variogram should be small. The variogram function with default settings from the gstat package in R (Pebesma, 2004) was used to obtain the number of point pairs, distance, and estimated semi‐variogram by distance, which were then used to estimate a parametric model for the variogram.Theoretically, a semi‐variogram will keep increasing as distance increases. When distance reaches a specific point, differences between points reach a maximum, and the semi‐variogram will reach a plateau and stay there. The exponential variogram model was fitted for wheat dockage, foreign material, and protein.The empirical variogram for the other wheat characteristics never reached the plateau before 1,000 km, and the scatterplot for those characteristics suggested that a linear variogram model was a good fit. Therefore, we imposed that the plateau of the linear models was 1,000 km and did not estimate the plateau parameter.Wheat dockage, foreign material, and protein variograms were estimated using the fit.variogram() option in the gstat function in R. Note that fit.variogram() option only allowed 200 iterations per execution, so an iteration procedure was used by repeating the procedure using the previous estimation of parameters in order to obtain our results. For all the other wheat characteristics, a linear variogram model was estimated using the lm() function in the stats procedure in R. The estimated regressions had the semi‐variogram values as the dependent variable, distance as the independent variable, the number of point pairs as the weight, and the partial sill effect calculated as 1,000c1. The variograms for residuals of each wheat characteristic in each year were estimated using the exponential model.RESULTS AND DISCUSSIONThe mean for protein, test weight, kernel size, kernel hardness, shrunken and broken kernels, and damaged kernel quality characteristics by elevator are mapped in Figures 1–6. Figure 1 shows protein by elevator, which is a key quality characteristic for buyers. An area of high protein is shown in the Texas Panhandle up to southwestern Kansas. These areas are often dry, and this could explain the higher protein. There is an area of low protein in North Dakota. The northern areas show more variation due to these locations having fewer years of data for some elevators.1FIGUREMap of hard red winter wheat protein (%) content by elevator. The data are averages over 2012–2019. No adjustment is made for missing data2FIGUREMap of hard red winter wheat test weight (kg hl‐1) by elevator3FIGUREMap of percentage of hard red winter wheat kernels of size large by elevator4FIGUREMap of Single Characterization System average kernel hardness of hard red winter wheat5FIGUREMap of hard red winter wheat shrunken and broken kernels (%) by elevator6FIGUREMap of hard red winter wheat damaged kernel (%) by elevatorTest weight (Figure 2) also shows a strong spatial pattern. Northern areas consistently deliver higher test weights than southern areas. Heat and drought stress decrease test weight as can stress from diseases and insects.Larger kernels provide higher milling yield. Figure 3 shows that the areas with the largest kernels are in the north. Southern Plains states (i.e., Texas and Oklahoma) provide few areas with the largest kernels. Drought and high temperatures during kernel filling can reduce kernel weight (Wardlaw, 2002) and these weather conditions are more prevalent in the South.Kernel hardness (Figure 4) also shows a clear spatial pattern. The area with the hardest kernels is Montana. Northern Kansas shows less kernel hardness than areas south of it. Stress environments, such as heat combined with drought (Elhadi et al., 2021), can create kernel hardness, so the high hardness in the Texas Panhandle and western Kansas is expected.Shrunken and broken kernels are more prevalent in southern and western areas of the wheat‐growing region (Figure 5). High temperatures during grain filling can create shrunken and broken kernels (Wu et al., 2016). Damaged kernels are low in Montana and high in eastern North Dakota (Figure 6). The high damaged kernels in a swath of North Dakota resulted from extreme weather in one or two years and may not be typical.The means of quality characteristics for combinations of states are shown in Table 2. These means support the conclusions from the figures. Heat and drought in southern areas lead to quality being lower for many factors (i.e., more dockage, lower test weight, more shrunken and broken kernels, more foreign material, more total defects, and smaller kernels) in southern areas. The southern areas do have higher protein and greater kernel hardness. Falling number, moisture, and ash content do not show a consistent geographical pattern.2TABLEMean hard red winter wheat quality characteristics by U.S. state or regionCharacteristicsTX & OKKS & CONE, SD & NDPNWGrading characteristicsDockage, %0.630.480.560.49Test weight, kg hl−178.7579.0779.7780.42Damage kernel, %0.290.300.330.00Shrunken and broken kernel, %1.311.080.941.02Foreign material, %0.220.130.140.10Total defects, %1.811.501.401.15Kernel characteristicsKernel size large, %54.6860.2267.7463.47Kernel size medium, %43.5838.4131.2835.39Kernel size small, %1.791.340.981.14Thousand kernel weights, g28.9229.6230.9231.41SKCS average diameters, mm2.562.572.612.61Other characteristicsProtein, 12% mb12.3212.2411.9311.78Individual wheat ash, 12% mb1.561.561.591.44Falling number, s388.28395.50386.64390.80Moisture, %11.5711.3011.7610.38SKCS average hardness67.0462.0959.5267.82Note. Single Kernel Characterization System (SKCS) hardness is an index. Below 50 is soft grain, and above 50 is hard grain.PNW, Pacific Northwest.The estimated spatial parameters (i.e., nugget, partial sill, and range) of the exponential variogram for dockage, foreign material, and protein content qualities are reported in Table 3. The variograms use each location's mean value across years, which is the same statistic that is shown in Figures 1–6. The strength of spatial relationships can be measured through variograms. Range is the distance that it takes for the fitted variogram to reach the plateau. It measures if spatial correlation is in a small region or a relatively large area. For dockage, foreign material, and protein, the estimated range parameters are all below 1,000 km (Table 3). The fitted variogram for foreign material and protein increased up to 600 km, but the variogram for dockage reached the sill at 175 km. This implies that spatial correlation in dockage decays quickly as distance increases. What is important about the information in Table 3 is that it verifies the visual information and shows that there is a strong spatial pattern to the wheat quality characteristics.3TABLEEstimated spatial parameters of U.S. hard red winter wheat characteristics using an exponential model for the semi‐variogram CharacteristicNuggetPartial sillRangeDockage0.030.05175.39Foreign material0.020.01497.68Protein0.190.48531.13Note. The data used were the least squares means for each location that were obtained from estimating Equation (1). Unit of range is km. Nugget and partial sill are similar to variance. Its unit depends on the unit of parameters. Squaring the corresponding unit in Table 1 will give the unit of nugget and partial sill. For example, the unit for nugget and partial sill of dockage is %2${\% ^2}$. Range measures the maximum distance at which two points are still spatially correlated. Nugget and partial sill together measure the spatial correlation behavior. The variograms of the above three wheat characteristics show plateau before 1,000 km, so an exponential model is fitted.Estimated spatial parameters (i.e., nugget and partial sill) of the linear variogram representing quality characteristics for test weight, damaged kernels, shrunken and broken kernels, total defects, kernel size, kernel test weight, kernel size, wheat ash, falling number, moisture, and hardness are reported in Table 4. Foreign material, test weight, shrunken and broken kernels, total defects, and the estimated nugget effects are bigger than the partial sill effects (Tables 3 and 4). A relatively large nugget implies that these measures are less repeatable (within a season and across nearby elevators). For example, test weight has a large nugget. Test weight can be high early in the harvest season and then can fall after a rain. Plains Grains, Inc. takes samples over a short period of time to reduce this noise, but it is still present in the data.4TABLEEstimated spatial parameters of U.S. hard red winter wheat characteristics using a linear model for the semi‐variogramCharacteristicNuggetPartial sillTest weight1.241.14Damaged kernels0.0200.066Shrunken & broken kernel0.120.04Total defects0.160.13Kernel size large22.992.1Kernel size medium20.583.0Kernel size small0.200.28Thousand kernel weights0.503.76SKCS average diameters0.00100.0032Individual wheat ash0.00220.0062Falling number233.3415.9Moisture0.231.06SKCS average hardness12.227.9Note. The data used were the least squares means for each location that were obtained from estimating Equation (1). The variogram of these wheat characteristics does not have a plateau before 1,000 km. Thus, the range is fixed at 1,000 km, and partial sill is calculated based on that. SKCS, Single Kernel Characterization System.For each wheat characteristic, variograms of residuals were estimated by year. Examples of these variograms are provided in Figure 7. Each curve in the plot is a fitted variogram. The distance at which the fitted variogram line reaches the plateau is the maximum distance at which the residuals are still correlated.7FIGUREVariograms of residuals from models of wheat quality characteristics. The residuals are the estimated uit from Equation 1Test weight residuals is an example of a characteristic that does not have much spatial correlation for most years. In one year, the test weight fitted variogram went from a low level to a plateau, which means test weight residuals showed strong spatial correlation only once out of eight sampling years. This means that although the spatial correlation exists, it is limited in a small region. For the rest of the fitted variogram, they are almost horizontal and at a low level, implying little spatial correlation.Since the variograms (Figure 7) of protein, kernel size large, and hardness are not horizontal lines from the beginning, this shows that there is still some remaining spatial correlation in the residuals, especially for protein and kernel hardness. There are some increasing straight lines in protein and hardness residuals, and they are still increasing around 1,000 km. It implies that protein and hardness residuals have strong spatial correlation in some years. Even if fitted variograms of residuals, like hardness, share the same pattern across years (i.e., increase followed by a plateau) , the maximum plateau varies across years. This means the variability of wheat characteristics changes across years. It implies that PGI is collecting useful and unique information of wheat characteristics every year for wheat buyers.Table 5 is used to even more directly address the question of whether sampling is needed every year. Of particular interest in Table 5 is the column with the residual standard deviation. While the year effects are substantial, they could be determined with a much smaller sample. Most residual standard deviations are larger than the standard deviation of year effects. Key measures like test weight, kernel size, protein, and kernel hardness all show substantial residual variation. For example, the residual standard deviation for protein is a little over one, meaning that a 95% confidence interval for a location that averages 12% protein would vary from about 10% protein to 14% protein. Thus, Table 5 shows that there is considerable value in conducting the survey every year.5TABLEStandard deviations (SD) of nonspatial effects on U.S. hard red winter wheat quality characteristicsSDCategoryYearResidualGrading characteristicsDockage, %0.110.5Test weight, kg hl−10.944.08Damage kernel, %0.150.46Shrunken and broken kernel, %0.280.72Foreign material, %0.010.27Total defects, %0.260.86Kernel characteristicsKernel size large, %9.812.55Kernel size medium, %9.4211.88Kernel size small, %0.491.06Thousand kernel weights, g2.232.51SKCS average diameters, mm0.060.1Other characteristicsProtein, 12% mb0.841.08Individual wheat ash, 12% mb0.050.11Falling number, s18.9536.3Moisture, %0.421.1SKCS average hardness6.427.21Note. The standard deviations were obtained by estimating Equation (1) and specifying year as a random effect. The null hypothesis of no year effect was rejected in all cases (P < .05). SKCS, Single Kernel Characterization System.CONCLUSIONSWheat buyers such as bakers and noodle‐makers target different niche food markets and are very specific about certain quality levels of the HRWW that they purchase. Hard red winter wheat quality characteristics showed spatial patterns with some areas consistently producing higher values of quality factors than other locations. The importance of spatial variation was shown by mean wheat quality characteristics and residuals having strong spatial correlation. The measures at each location vary considerably by year, which indicates there is value in conducting the sample every year.ACKNOWLEDGMENTSFunding for this research was provided by the Oklahoma Agricultural Experiment Station and National Institute of Food and Agriculture Hatch Project OKL03170 as well as the A.J. and Susan Jacques chair. We express gratitude to Plains Grains, Inc. and Mark Hodges for making the data available to us. The data for the research could not have been collected without the participation of numerous elevators, initial support from the Oklahoma Wheat Commission, and many others. Considerable editorial assistance from Jon Biermacher is gratefully acknowledged.AUTHOR CONTRIBUTIONSYikuan Chen: Formal analysis; Investigation; Methodology; Resources; Software; Validation; Visualization; Writing – original draft; Writing – review & editing. B. Wade Brorsen: Conceptualization; Data curation; Funding acquisition; Investigation; Methodology; Project administration; Resources; Software; Supervision; Validation; Visualization; Writing – review & editing.CONFLICT OF INTERESTThe authors declare no conflict of interest.REFERENCESBarkley, A. P., & Porter, L. L. (1996). The determinants of wheat variety selection in Kansas, 1974 to 1993. American Journal of Agricultural Economics, 78, 202–211. https://doi.org/10.2307/1243791Bongiovanni, R. G., Robledo, C. W., & Lambert, D. M. (2007). 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"Agrosystems, Geosciences & Environment"Wiley

Published: Jan 1, 2022

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