Rogovska, Iowa State Univ., Dr. Thomas Morris, Univ. of Connecticut, and Dr. Brad Van De Woestyne, John Deere Intelligent Vehicle Systems. REFERENCES.
Characterizing and Classifying Variability in Corn Yield Response to Nitrogen Fertilization on Subfield and Field Scales P. M. Kyveryga,* A. M. Blackmer, and J. Zhang
Marked spatial and temporal variability in yield response to N fertilizer observed in individual yield response trials creates a high degree of uncertainty when estimating economic optimum rates (EORs) of N for a group of trials and when extrapolating these rates from one location to another. A survey was conducted to characterize and classify variability in yield response to N on subfield and field scales. Fertilizer N was applied at five rates (56, 84, 112, 140, and 168 kg N ha–1) in many (6–12) replicated strips within three 18- to 24-ha no-till fields during two corn (Zea mays L.) growing seasons. Yield responses or yield differences between two adjacent strips were measured in 22 to 25 grid cells ha–1 within each field. Cumulative probability distributions (CPDs) were used to estimate the probability that a given N rate produces a yield response less or equal to a specified quantity. The yield responses were classified into potential categories with different N fertilizer requirements using apparent soil electrical conductivity (ECa), digital soil map units, and relative elevation. Analysis indicated that the classifications explained 168 kg N ha–1 would be too low or too high to maximize return to N on the farm. The producer applied the fertilizer treatments so that rates of N in adjacent strips were as similar as possible to avoid border effects associated with plants in N-deficient strips removing N from strips having near-optimal rates. The producer did not attempt to randomize the treatments because of the need to apply additional strips (i.e., buffers) to remove the effects of adjacent strips with large differences in N rates applied and because the data were not intended to be interpolated to other fields, farms, or management practices. Randomizing the fertilizer treatments would decrease errors associated with applying fertilizer strips in the same directions as possible spatial trends found in soil characteristics or previous management (e.g., distribution of crop residues from the previous crop or uneven fertilizer applications). Randomizing and applying additional fertilizer treatments would reduce spatial resolution of the experiment and reduce the number of replications within each field. The Agronomy Journal
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similar conclusion about effects of randomization on spatial resolution and number of treatment replications in field-scale yield response trials was reached by Scharf et al. (2005). The producer harvested the fields using a combine equipped with an Ag Leader yield monitor (Ag Leader Technol., Ames, IA) connected to a differential global positioning system (DGPS) receiver. The yield data were collected at 1-s intervals. To minimize errors associated with the lag in yield measurements or other effects (i.e., combine ground speed, slope, etc.) when calculating yield differences between strips, care was taken to maintain a constant combine speed while harvesting. The adjacent strips were harvested by moving the combine in the same direction within each grid cell. Corn grain yields were expressed at a standard 15.5% moisture content. Remote sensing imagery was used to identify and remove errors in individual yield observations due to irregular plant density, weed pressure, flooded areas, or presence of grassed waterways within the fields. ArcView 3.3 GIS soft ware (Environ. Syst. Res. Inst., Redlands, CA) was used to divide the fields into individual trials or grid cells with approximately 22–25 grid cells ha–1. Each grid cell was 27 m wide and 14 m long, having five rates of N applied (Fig. 1). Six to eight yield observations were collected by the yield monitor for each treatment within each grid cell. Mean yields were calculated for each of five N treatments within a grid cell and yield responses (i.e., differences between yields of two adjacent N treatments) were calculated for four fertilizer increments within the same grid cell. To assess the possible bias resulting from not randomizing the fertilizer treatments within each grid cell, a bootstrap procedure was used to calculate median and mean yield responses as well as confidence intervals (CIs) for the means. The bootstrap procedure is based on empirical distribution of a sample and estimating distribution parameters (i.e., mean, median, and CIs) without making assumptions about the real form of the theoretical distributions (Chernick, 1999; Good, 2005). We used a nonparametric bootstrap procedure with replacement, and random samples were taken 2000 times by using the statistical soft ware R (R Development Core Team, 2004). A quadratic model was used to calculate EORs of N fertilization for the data in each year and for the combined data for 2 yr. The quadratic model was sufficient because continuous models usually agree on calculated EORs when the models are fit to yield response data that do not include extremely low and high N fertilizer rates (Kyveryga et al., 2007). The EORs were calculated by taking the first derivatives of the models, equating the first derivatives to the fertilizer-to-grain price ratio, and solving for the N rates. The price of N fertilizer was $0.44 kg–1, and the price of corn grain was $86.5 Mg–1. The cost of additional fertilizer increment of N or marginal input cost was expressed as 0.14 Mg of grain needed to pay for the cost of 28 kg of N. Yield response at each fertilizer increment was considered profitable when the value of the yield response was higher than the marginal cost of fertilization. Monthly rainfall from March through August measured at the nearest climate station (3–10 km) from the fields, and 30-yr mean monthly rainfall (1970–2001) were obtained from the Iowa Environmental Mesonet, Agronomy Department, Iowa State University (available at http://mesonet.agron.iastate.edu/ climodat/index.phtml; cited 15 Oct. 2008, verified 6 Jan. 2009). Agronomy Journal
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Cumulative Probability Distributions of Yield Responses The CPDs of observed yield responses within individual grid cells were used to show the probability that a given fertilizer increment produces a yield response smaller than or equal to a specific (critical) value of yield response. In probability theory, CPDs are described by the following equation CPD (x) = P (X ≤ x),
[1]
where X is a random variable, P is probability, and x is a specific (critical) value of yield response. The CPDs of yield response for each increment of N were calculated by using the PROC UNIVARIATE procedure in Statistical Analysis System (SAS Institute, 2002). We weighted numbers of observations from each year when calculating probabilities of yield response observed for the combined data for 2 yr. This was done to avoid the influence of a year with the greater number of observations and with the greater area of study. The number of observations was not weighted when analyzing the sample of yield responses within each year because the fields were approximately the same size and the numbers of yield response observations were almost identical within each field within a year. Classification Analysis Georeferenced ECa measurements were collected in the spring within each field before the crop was planted by using an electromagnetic induction (EM-38) based sensor (Geonic Limited, Mississauga, ON, Canada), and relative elevation measurements were collected at the same time by using a real time kinematic GPS system (Trimble Navigation Limited, Sunnyvale, CA). Both measurements were collected at 1-s intervals or from 4 to 7 m by driving an all-terrain vehicle along the rows of the previous crop (i.e., soybean). Soil ECa and relative elevation data were interpolated by using the inverse distance interpolation procedure in ArcView 3.3 (Environ. Syst. Res. Inst., Redlands, CA) with 12 neighboring points in 4.5- by 4.5-m grid cells that corresponded to the width of the combine. The interpolated maps were classified into two or four classes with a difference of 1 or 1.5 standard deviations from the means. We used several classifiers to explain the observed spatial variability in yield responses. The classifiers used were: years, soil series, soil map units, ECa, and relative elevation. The complement of the relative variance method was used to calculate the percentage of variability in yield responses explained by each classifier (Webster and Oliver, 1990). Efficiency of classification was calculated as E = 100(1 – δw/δtotal),
[2]
where E refers to efficiency of classification (%), δw is within the class pooled variance, and δtotal is the total pooled variance. RESULTS AND DISCUSSION The cumulative monthly rainfall from March through August for the 2 yr of the study and mean cumulative monthly rainfall for the last 30 yr are shown in Fig. 2. The amount of rainfall in the first year was 29% above normal in May and 15% 271
Table 2. Summary statistics and bootstrap confidence intervals (CIs) for yield responses observed in individual fields in the first year. Year 1 Increase in Field N rate kg N ha–1 1 56–84 84–112 112–140 140–168
Fig. 2. Cumulative monthly rainfall from March through August in the first (2001) and second (2000) year of the study.
Median 1.22 0.65 0.62 –0.10
Bootstrap Mean 95% CIs Mg ha–1 1.18 1.12 1.25 0.63 0.56 0.70 0.61 0.54 0.69 –0.12 –0.22 –0.03
2
56–84 84–112 112–140 140–168
0.94 0.46 0.32 0.24
0.94 0.45 0.32 0.18
0.89 0.37 0.25 0.10
1.10 0.53 0.38 0.27
3
56–84 84–112 112–140 140–168
0.66 0.71 0.24 0.27
0.58 0.69 0.29 0.17
0.49 0.59 0.18 0.01
0.67 0.80 0.40 0.29
year could be also explained by sufficient supply of soil N to the plants and minimal losses of soil derived-N from spring rainfalls. Losses of N from excessive spring rainfall have been identified as a major factor affecting N sufficiency for corn in Iowa (Balkcom et al., 2003). Table 2 shows summary statistics and bootstrap CIs for mean yield responses for each fertilizer increment observed in each field. The CIs for mean yield responses were relatively small (Table 2). Because the CIs were calculated from 2000 samples that were randomly selected from the sample yield response distributions, the effects of not randomizing the fertilizer treatments in each grid cell were probably minimal. However, to minimize the residual fertilizer effects, randomizing the treatments would be necessary if the same fertilizer rates were applied within the same fields in the succeeding years. Cumulative Probability Distributions of Yield Responses
Fig. 3. Cumulative probability distributions of corn yield response to incremental N fertilizer additions within six fields during 2 yr.
in June. On contrary, the cumulative monthly rainfall during the second year was about 25 to 75% below normal from April to the end of August, which decreased the responsiveness to N fertilizer (Table 2). The lack of yield response in the second 272
The CPDs of yield responses are illustrated in Fig. 3 for each year and for the combined data of 2 yr. The CPDs indicate the probability that a given fertilizer increment produces a yield response smaller than or equal to a given critical value. For example, there was a 50% chance of obtaining a yield response of 1.0 Mg ha–1 or less when applying the first fertilizer increment (i.e., 56 to 84 kg N ha–1) during the first year (Fig. 3A), and there was a 12% chance of obtaining a yield response smaller than zero for the same fertilizer increment. The 50% probability corresponds to median (i.e., the number separating a population into two equal parts) yield responses on the CPDs curves, as indicated by the dotted horizontal lines in Fig. 3. Figure 3 shows the effects of fertilization on the magnitude of yield response received in each year and for the combined data of 2 yr. Unlike the CPDs observed during the second, nonresponsive year (Fig. 3B), the CPDs observed during the first year and for the combined data do not intersect each other (Fig. 3A, C). This suggests the effects of fertilization observed in the first year and for the combined data of 2 yr, therefore, were relatively constant over the wide range of yield responses observed. The CPDs of yield responses presented in Fig. 3 emphasize that any given median yield response is calculated from many larger and smaller yield responses observed in each Agronomy Journal
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Table 3. Summary statistics and bootstrap confidence intervals (CIs) for yield responses observed in individual fields in the second year.
Table 4. Characteristics of distributions of yield responses to incremental N fertilizer additions within six fields.
Year 2 Field 1
Increase in N rate kg N ha–1 56–84 84–112 112–140 140–168
0.04 –0.16 0.01 0.08
Bootstrap Mean 95% CIs Mg ha–1 0.12 0.01 0.22 0.25 –0.16 –0.07 0.03 0.05 –0.10 0.10 0.06 0.24
Median
2
56–84 84–112 112–140 140–168
–0.10 0.08 –0.08 0.10
–0.10 0.02 –0.08 0.12
–0.02 –0.10 –0.01 0.07
0.18 0.06 0.16 0.21
3
56–84 84–112 112–140 140–168
–0.18 –0.08 –0.07 0.04
–0.19 –0.14 –0.06 0.06
–0.26 –0.18 0.13 –0.02
–0.13 –0.05 –0.01 0.11
grid cell. The curves illustrate that some of the variability in yield responses should be attributed to measurement errors. A noteworthy source of the measurement error results from the assumption that any two plots within a grid are identical in all ways except for effects of the added N. This assumption is violated by differences among plots in plant density, weed pressure, insect or wind damage, supplies of water or nutrients other than N, supplies of N from sources other than fertilizer, incorrect or nonuniform application of fertilizer N, and many other factors. These errors, like errors introduced during taking yield measurements in individual grid cells, should be randomly distributed and, therefore, tend to become less important when means or medians are calculated from large numbers of observations. The use of medians offers the advantage of not having to include procedures to remove extreme values that can have undue effects on mean yield responses. The median yield responses were similar to the mean yield responses calculated from individual grid cells (Tables 2 and 3). These observations present the evidence that yield responses tended to be normally distributed. In fact, analysis for the degree of skewness (i.e., a measure of asymmetry) for the distributions showed that deviation from normality was relatively small (Table 4). The exception was only the distribution of yield responses for the second fertilizer increment observed during the first year. Yield response distributions observed during the responsive year were all slightly negatively skewed (left skewed) as compared with those observed during the nonresponsive year. Negatively skewed distributions of yield responses should be expected when distributions have a small number of negative yield responses. In this study, the CPDs of yield responses are essentially used for the same purpose as using CPDs to estimate the reliability of one specific treatment to outperform another treatment (Eskridge and Mumm, 1992; Lambert and LowenbergDeBoer, 2003; Piepho, 1996). In the above-mentioned studies, the reliability was defined as the probability that one treatment yields higher than the other by more than a certain amount of grain. The major difference with our use of CPDs, however, is that we focus our analyses on incremental comparisons of several N rates rather than on a comparison of one specific Agronomy Journal
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Increase in N rate kg N ha–1
Mean
Median
56–84 84–112 112–140 140–168
0.93 0.58 0.41 0.08
0.96 0.61 0.42 0.14
56–84 84–112 112–140 140–168
–0.09 –0.09 –0.04 0.06
–0.12 –0.06 –0.05 0.05
56–84 84–112 112–140 140–168
0.58 0.34 0.25 0.10
Interquartile range Skewness Kurtosis Mg ha–1 First year 1.02 2.71 –0.33 1.04 9.44 –1.13 1.04 4.25 –0.03 1.12 3.99 –0.81 Second year 0.75 0.78 0.82 0.84
0.44 –0.43 –0.07 0.06
1.41 1.61 0.39 0.97
Combined sample of 2 yr 0.57 1.29 0.08 0.31 1.07 –0.06 0.23 1.02 0.16 0.13 1.02 –0.72
0.83 6.89 3.99 4.62
fertilizer rate to a control without N as described by Barreto and Bell (1995). Estimating Economic Optimum Rates from Cumulative Probability Distributions of Yield Responses Cumulative distribution functions as illustrated in Fig. 3 offer a simple way to estimate approximate EORs by using median yield responses. Fertilizer N increments with CPDs having median yield responses crossing the 0.5 probability line on the right side of the marginal fertilizer cost line (i.e., the cost of a fertilizer increment, 28 kg N ha–1, expressed in amount of grain) are profitable to apply. Conversely, fertilizer increments with median yield responses crossing the 0.5 probability line on the left side of the marginal cost line are not profitable to apply. During the first year, for example, the median yield responses to the first three incremental increases in rate of N were substantially more than needed to pay for the extra N (Fig. 3A and Table 4), so the highest rate clearly was more profitable. The median yield response for the fourth incremental increase was equal to the marginal cost of fertilization, which means that the two rates were equally profitable. Median yield responses for the first three fertilizer increments observed during the second year indicate that the N fertilization resulted in a large number of grid cells with negative yield responses (Fig. 3B). The exception was the last increment of N that produced a small, positive yield response, but that median yield response was less than enough to pay for the marginal fertilizer cost. It is difficult to explain why the last increment produced a positive yield response when the rest of N rates produced negative yield responses. The last increment tended to give small positive responses in all three fields during the second year (Table 3). A possible explanation could be that a portion of N fertilizer applied at the highest rate moved deeper into the soil compared with the lowest rates, and therefore, corn plants with roots located deeper within the soil benefited from higher soil moisture content and produced a positive yield response compared with plants at the lower N rates. The combined data of yield responses for 2 yr is more informative than samples for individual years because EORs calculated from pooled data are usually used to estimate 273
Table 5. Probability of positive yield response and positive marginal return (profit) to incremental N fertilizer additions within six fields. Median Increase in N yield rate response kg N ha–1 Mg ha–1
$gain/ $spent
56–84 84–112 112–140 140–168
0.96 0.61 0.42 0.14
6.76 4.30 2.89 0.99
56–84 84–112 112–140 140–168
–0.12 –0.06 –0.05 0.05
–0.85 –0.42 –0.42 0.42
56–84 84–112 112–140 140–168
0.57 0.31 0.23 0.13
Probability of Probability positive yield of positive response profit % First year 0.88 0.84 0.78 0.72 0.71 0.65 0.57 0.50
Second year 0.42 0.45 0.48 0.52
Combined sample of 2 yr 4.01 0.72 2.18 0.66 1.62 0.62 0.92 0.56
0.32 0.35 0.38 0.42
0.66 0.60 0.55 0.50
recommended rates. The median yield responses for observations pooled over the 2 yr (Fig. 3C) were somewhat similar to those observed in the first year. The median yield responses to the first three incremental increases in rate of N were more than needed to pay for the extra N as shown by the ratios of dollars gained to dollars spent (Table 5). The fourth incremental increase in N rate produced a yield increase that was slightly less than needed to pay for the extra fertilizer. Figure 3C indicates that the EOR for the 2-yr period was between 140 and 168 kg N ha–1. This is almost in agreement with the EOR of 152 kg N ha–1 calculated by fitting a yield response model to the mean yields observed at the five rates of N (Fig. 4C). These observations suggest that the two different methods for calculating EORs give essentially the same answers. The CPD method, however, is more accurate because calculation of CPDs does not include errors associated with interpolating when fitting yield response models, which can affect EORs, especially when a range of N rates used in the model is wide (Kyveryga et al., 2007). The curves in Fig. 3A and 3C indicate that yield responses tended to decrease with each increment of added N and, made it easy to estimate approximate EORs. The effects of changes in the cost of fertilizer relative to grain can be estimated by repositioning the marginal fertilizer cost line. This enables one to address the uncertainty associated with changing the cost of inputs other than N fertilizer (i.e., cost of drying grain, fuel). Probability of Positive Yield Response and Profits The probability of positive yield response at each fertilizer increment calculated from CDFs is shown in Table 5. The probability values were estimated at the intersection of “the zero response line” for each fertilizer increment with a corresponding distribution curve, and then interpolating to the y axis (Fig. 3). The general trend was a decrease in a number of grid cells that positively responded to N with the increase in N rates. The exception was only the data for the nonresponsive year (Table 5). The probability of a positive response to the first increment (from 56 to 84 kg N ha–1) ranged from 42% in the 274
Fig. 4. Relationship between corn grain yields and rates of N fertilization.
second year to 88% in the first year. It could be concluded that only 12% of the area on the farm would be expected to have a negative yield response to N in the below-optimal range during the first year. It is difficult to determine whether negative yield responses in the below-optimal range were caused by random effects of weather, lower total N uptake, larger-than-expected supply of soil-derived N, or factors other than N fertilization or measurement errors. However, the data suggest that applying N at rates < 56 kg N ha–1 would probably provide little additional information if we had to calculate a single rate to maximize returns on average for the whole farm unless there was a high degree of certainty (high probability) that we could identify the nonresponsive areas before applying fertilizer. The probability of a positive yield response to N applied in the near-optimal range was 57% to the last fertilizer increment in the first year, 42% to the first increment during the second year, and 56% to the last increment for the combined data (Table 5). These observations suggest that the considerable percentage of grid cells had negative yield responses at N rates applied in the near-optimal range. Analysis of data for the Agronomy Journal
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Table 7. Mean yield responses by categories from classifying the combined sample of two years.
Table 6. Efficiency† of classification of yield responses for the combined sample of two years.
Increase in N rate, kg N ha–1
Increase in N fertilizer rate, kg N ha–1 Classifier
56–84
84–112
112–140
140–168
6 0 3 2 1
0 0 1 0 0
Classifier
Category†
% Year Soil series Soil map units Relative elevation ECa‡
25 4 16 3 5
11 0 5 0 3
Year Soil map units
55 (165, 190) 107 (150, 112) 138B1 (432, 183) 138B2 (78, 18) 138C2 (76, 31) 138D2 (130, 50) 507 (275, 338)
0.72 0.58 0.81 0.28 0.64 0.61 0.72
0.33 0.36 0.40 0.14 0.56 0.24 0.51
0.23 0.33 0.34 –0.03 0.42 0.13 0.34
0.20 0.16 0.08 0.05 –0.06 0.14 0.02
55 (165, 90) 107 (150, 112) 138 (655, 480) 507 (275, 138)
0.72 0.58 0.73 0.72
0.33 0.36 0.38 0.51
0.23 0.33 0.29 0.34
0.20 0.16 0.09 0.02
Relative elevation very high (122, 57) high (189, 416) middle (90, 537) low (414, 494)
0.81 0.63 0.49 0.33
0.52 0.28 0.37 0.18
0.36 0.34 0.19 0.19
0.05 0.04 0.12 0.09
ECa‡
0.51 0.58
0.35 0.30
0.17 0.29
0.13 0.07
† Percentage of variance in yield response explained by classification. ‡ ECa , apparent soil electrical conductivity.
nonresponsive year revealed that a high percentage of grid cells had positive yield responses when fertilizer had essentially no effects (i.e., mean or median yield responses were close to zero), and the number of grid cells with positive yield responses was only slightly larger than the number of cells with negative yield responses. These results were also confirmed by the analyses for normality of yield response distributions (Table 4). More information is provided by presenting the probability of profits from applying N (Table 5). A fertilizer increment was considered profitable when the value of the yield response was larger than the cost of N associated with applying this increment. To calculate the probability of positive profit, the cost of fertilizer expressed in units of grain was subtracted from the observed yield response at each grid cell. The probability values for positive profits were estimated at the intersection of “the marginal fertilizer cost line” with a distribution curve for each increment and then interpolating to the y axis (Fig. 3). The percentage of grid cells with positive profits decreased with an increase in N rate except for the data for the nonresponsive year. An important point illustrated in Table 5 is that the probability of profits is approximately 50% (applying N 5 out of 10 times was profitable) to a fertilizer increment identified as the optimal for yield responses observed in the first year and for the combined data of 2 yr. Thus, the number of grid cells with positive profit tended to be equal to the number of grid cells with negative profit in a fertilizer range identified as being optimal. Analyses that include the probability of profits that would have been received by applying a given fertilizer increment provide an assessment of the uncertainty and risk associated with fertilization at each increment. The highest level of uncertainty was found to be in the near-optimal range of fertilization where the probability of receiving positive profit was equal to the probability of receiving negative profit (Table 5). Overall, considerable variability in yield response among grid cells is shown by observing the large interquartile ranges (i.e., the differences between the 75th and 25th percentiles for yield response distributions) of CPDs for some fertilizer increments (Table 4). This suggests the need to look for some factors (e.g., soil characteristics, management practices) that could be potentially responsible for some variability in yield response and to divide the areas sampled into smaller areas that have different N fertilizer requirements.
Soil series
† Number of grid cells in the first year and in the second year.
categories that have different EORs. Tables 6 and 7 summarize efforts for classifying yield responses by years, soil series, soil map units, soil ECa, and relative elevation. Year was included only to show its relative importance; it is not a useful classifier because the effects of year (i.e., weather) are usually not known at the time of fertilization and it can be used only in the analysis after the fact. The remaining classifiers were selected because they are commonly available for producers, and they do not change drastically over time. Yield response at each increment was analyzed individually to minimize confounding of relatively large yield responses at low rates of fertilization with relatively small yield responses at near-optimal rates of N fertilization. Use of the complement of the relative variance method (Webster and Oliver, 1990) to analyze the sample for the combined data of 2 yr showed that the classifier “year” explained the highest percentage of the variability in yield response than did other classifiers (Table 6). Year explained 25, 11, 6, and 0% of the variability in yield response associated with the first, second, third, and fourth incremental increases, respectively, in rate of fertilization. Soil map units explained 16, 5, 3, and 1% of the variability in yield response for the same incremental increases in N fertilizer. Soil series explained 4, 0, 0, and 0% of the variability in yield response associated with these incremental increases. Soil ECa explained 5, 3, 1, 0% of the variability and relative elevation explained 3, 0, 2, 0%. When the effects of fertilization at relatively low rates are separated from the effects of N applied at near-optimal rates, the analyses showed that none of the classifiers had much ability to account for a considerable percentage of the variability in yield responses at near-optimal rates of fertilization. This analysis illustrates the need to use methods that can separate the relatively small yield responses observed at near-optimal rates of fertilization from the larger yield responses observed at lower rates. This distinction is important because the large yield responses often
Calculating an EOR for a sample of yield responses should not be considered the final step before calculating a recommendation for a sample of 2 yr because the possibility that profits can be increased by dividing the area sampled into two or more •
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‡ ECa , apparent soil electrical conductivity.
Classification of Yield Responses
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first (1563) second (1150)
56–84 84–112 112–140 140–168 Mg ha–1 0.89 0.54 0.38 0.14 0.07 –0.09 –0.09 –0.04
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observed at the lower rates overwhelm the small yield responses often observed at near-optimal rates. Mean yield responses associated with the first two incremental increases in N rate exceeded the marginal costs of fertilization (i.e., 0.14 Mg ha–1 of grain) for all map units (Table 7). Yield responses associated with the third and fourth increases in N rate exceeded the marginal fertilizer cost for all map units except for four map units: 138B2, 138C2, 138D2 and 507, but they were not the same map units across the rates. The differences between the soil map units are probably not reliable because the yield responses were small and because only a small percentage of the overall variability in yield response was explained by soil map units (Table 6). Moreover, these areas were often too small to give an adequate number of observations and the numbers of observations made within each soil map unit differed among years. Mean yield responses associated with the first three fertilizer increments exceeded the marginal fertilizer cost for all soil series (Table 7). For the fourth increment, the mean yield responses for soil series 55 and 107 were larger than the marginal fertilizer cost, whereas mean yield responses for soil series 138 and 507 were smaller than the marginal fertilizer cost. These observations show that the last fertilizer increment could be potentially applied only to the two soil series 55 and 107, which suggests the possibility for increasing profits by varying fertilizer rates based on soil series. However, classification analyses revealed that soil series as a classifier explained little variability in yield response for the last fertilizer increment (Table 6). Thus, the use of soil series as a basis for applying variable rates of N applications would not be justified. Other classifiers not measured in our study such as soil organic matter, corn canopy reflectance, and terrain attributes may be useful for explaining an additional percentage of variability in yield response. The classification analysis illustrates that the price ratio for grain and fertilizer used in this study is such that a yield response of 0.14 Mg ha–1 (about 2% of yield at the highest N rate) must be detectable with a reasonable degree of certainty to determine whether a final increment of 28 kg N ha–1 should be applied. This complicates developing methods for refining estimates of fertilizer needs for corn because it would take a large number of observations to determine a yield response of this size with reasonable certainty. There is no immediate practical need to identify EORs to the nearest kg N ha–1 because most fertilizer application equipment is only accurate within a 10 kg N ha–1. It is possible, however, that a collection of a few hundred to a few thousand observations of yield responses at near-optimal rates of N fertilization over several years could be adequate to identify EORs within a few kg N ha–1 for any specified area. CONCLUSIONS When large numbers of observations are available, cumulative probability distributions of yield responses to N fertilizer could be a simple and efficient tool for characterizing variability in yield response, providing a measure of the uncertainty and risk associated with applying N, and estimating approximate EORs. The analyses showed that yield responses observed at rates significantly below the optimal range were estimated 276
with greater certainty than those observed at the near-optimal range. Although the variability in yield response at different ranges of fertilization is often considered unimportant when estimating EORs, this variability is important for identifying potential response categories by utilizing information available at the time of fertilization. Errors caused by unimportant variability in yield response could be minimized by calculating median yield responses of very large numbers of observations. Presenting probabilities of yield response and marginal returns (profits) at different ranges of fertilization rather than reporting individual EORs provides the basis for assessing the risk associated with the variable effects of weather (i.e., losses of the soil and fertilizer-derived N) and variable supply of N from the soil. The temporal variability in yield response was found to be more important than the spatial variability. The task of selecting the best method for classifying soils was found to be complex due to interactions of soil properties and weather. The task, however, requires continuous analyses as the new knowledge is acquired and management practices evolve. The effect of weather can be assessed by studying large areas of soils and management practices in the systematic way over time and estimating the probabilities of yield response for different management practices (e.g., N forms, timing, and methods of application) and soil response categories. ACKNOWLEDGMENTS Cooperation of James Andrew, a producer, from Jefferson, IA, is much appreciated. We are also thankful for valuable comments from Dr. Natalia Rogovska, Iowa State Univ., Dr. Thomas Morris, Univ. of Connecticut, and Dr. Brad Van De Woestyne, John Deere Intelligent Vehicle Systems. REFERENCES Adams, M.L., S. Cook, and R. Corner. 2000. Managing uncertainty in sitespecific management: What is the best model? Precis. Agric. 2:39–54. Balkcom, K.S., A.M. Blackmer, D.J. Hansen, T.F. Morris, and A.P. Mallarino. 2003. Testing soils and cornstalks to evaluate nitrogen management on the watershed scale. J. Environ. Qual. 32:1015–1024. Barreto, H.J., and M.A. Bell. 1995. Assessing risk associated with N fertilizer recommendations in the absence of soil tests. Fert. Res. 40:175–183. Blackmer, A.M., and S.E. White. 1998. Using precision farming technologies to improve management of soil and fertilizer nitrogen. Aust. J. Agric. Res. 49:555–564. Blackmer, A.M., T.F. Morris, and B.G. Meese. 1992. Estimating nitrogen fertilizer needs for corn at various management levels. p. 121–134. In Proc. of the 47th Annual Corn and Sorghum Industry Res. Conf., Chicago, IL. 9–10 Dec. 1992. Am. Seed Trade Assoc., Washington, DC. Brevik, E., T. Fenton, and A. Lazari. 2006. Soil electrical conductivity as a function of soil water content and implications for soil mapping. Precis. Agric. 7:393–404. Cerrato, M.E., and A.M. Blackmer. 1990. Comparison of models for describing corn yield response to nitrogen fertilizer. Agron. J. 82:138–143. Chernick, M.R. 1999. Bootstrap methods: A practitioner’s guide. John Wiley & Sons, New York. Eskridge, K.M., and R.F. Mumm. 1992. Choosing cultivars based on the probability of outperforming a check. Theor. Appl. Genet. 84:494–500. Fleming, K.L., D.F. Heermann, and D.G. Westfall. 2004. Evaluating soil color with farmer input and apparent soil electrical conductivity for management zone delineation. Agron. J. 96:1581–1587. Fridgen, J.J., N.R. Kitchen, K.A. Sudduth, S.T. Drummond, W.J. Wiebold, and C.W. Fraisse. 2004. Management zone analyst (MZA): Soft ware for subfield management zone delineation. Agron. J. 96:100–108. Good, P.I. 2005. Introduction to statistics through resampling methods and R/S-Plus. Wiley, Hoboken, NJ.
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