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a Univ. of Arkansas Coop. Ext. Service, 2301 S. University Ave., Little Rock, AR 72203
b Dep. of Crops, Soils, and Environmental Sciences, Univ. of Arkansas, Fayetteville, AR 72701
c Jr. USDA-ARS, Poultry Production & Product Safety Research Unit, Fayetteville AR, 72701
d Agricultural Statistics Lab., Univ. of Arkansas, Fayetteville, AR 72701
* Corresponding author (mdaniels{at}uaex.edu)
Received for publication October 27, 2000.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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The use of soil P as an environmental threshold has sparked political controversy because it may place unreasonable economical constraints on producers. Others have questioned its scientific usefulness for making management decisions with regard to water quality (Sims, 1993; Combs and Bundy, 1995). Limitations of the threshold approach include: (i) not accounting for other soluble P sources that are not soil-derived (Sauer et al., 2000) and (ii) not considering the influence of transport factors on fate.
Implementing soil P thresholds on a field-by-field basis as a nutrient management strategy presents practical challenges as well. First, soil P thresholds may be soil dependent since there is evidence that the relationship between soil P and soluble P in runoff is soil dependent (Sharpley, 1995). Second, the threshold approach assumes that a single estimate of soil P from a given field can be obtained that accurately reflects the soil P level across the entire field for comparison with the threshold. This assumption may be violated if considerable variability of soil P within a given pasture is present.
It is generally accepted that soil properties such as soil P can vary both spatially and temporally. Sauer et al. (1998) found that soil P was statistically different among mapping units and landscape positions in the Ozark Highlands even though soil P levels were relatively low since no animal manure or inorganic fertilizer had been applied. Scott et al. (1992) found that soil P varied among 198 pastures in a watershed heavily concentrated with confined poultry operations. The associated frequency distribution was positively skewed with highest soil P levels found on shallow, well-drained, permeable soils close to poultry houses. Young et al. (1999) found only 5 of 60 soil properties to be normally distributed within an upland pasture and that 75% of the properties had a skewed frequency distribution while 80% were kurtotic. In another study, Young et al. (1998) found that the frequency distribution of soil properties that may influence phosphorus adsorption kinetics were significantly skewed within a soil mapping unit.
These studies point out that soil P variability can be influenced by intrinsic properties such as soils and topography as well as extrinsic properties such as repeated animal manure applications. Since soil mapping units, landscape positions, and management can vary within a single pasture, it seems inherent that soil P can vary within pastures. Assuming that soil P variability does exist within pastures, a question arises: Do current sampling recommendations that were developed for production purposes adequately account for spatial variability so that an unbiased estimate of soil P is obtained for comparison with an environmentally related threshold?
Soil sampling recommendations in many southern U.S. states were developed with the objective of obtaining a single estimate of central tendency of a given soil test parameter for a uniform management area (Hodges and Kirkland, 1994; Daniels et al., 2000). In practice, individual pastures have been defined as the management unit even though they may contain different soil mapping units and landscape positions. To reduce bias toward pasture areas of extreme high or low soil P values, most southern states recommend collecting 15 to 20 subsamples in a zig-zag pattern across the pasture and physically combining the subsamples to obtain a single measure of central tendency.
Sabbe and Marx (1987) found that the zig-zag pattern results in unbiased estimates of the mean soil P value for a given field even if samples were taken close enough together to be spatially dependent. They also emphasize that the number of subsamples is important to obtaining a good estimate of central tendency. Keogh and Maples (1967) found that soil P required more subsamples than other soil test parameters in 9 of 10 row-crop fields to obtain an estimate within a stated allowed variation from the mean. Friesen and Blair (1984) found similar results for soil P under permanent pastures in Australia. They found that 25 to 121 subsamples were needed for a 25-ha pasture to estimate the mean within 10%.
One of the limitations of current sampling recommendations is that spatial variability is not quantified since the variance associated with a measure of central tendency is not estimated. Sabbe and Marx (1987) point out that the zig-zag pattern produces estimates of variance that will be biased if spatial dependence is not accounted for. They felt that this was of little importance if the sole purpose of sampling was to obtain a soil test recommendation, but that the bias in the variance should prohibit its use in determining statistical inference of a hypothesis. Hession and Storm (2000) investigated the implications of watershed-level uncertainties for P management strategies. Their work points out that uncertainty in outcomes resulting from management strategies can be influenced by uncertainty in model parameters, which in turn can be influenced by spatial variability. Our hypothesis is that accounting for spatial variability of soil P within pastures is an important consideration for nutrient management strategies that use soil P thresholds.
The soil P value of 150 mg kg-1 soil P has most often been discussed for use as a threshold in Arkansas. Few data exist on the spatial variability of soil P in permanent pastures amended with animal waste and how this variability would influence the implementation of soil P thresholds. The soil sampling recommendations reviewed above were developed for the sole purpose of estimating crop nutrient needs. The implications of using these procedures for obtaining a single estimate of soil P for comparison with an environmental threshold is uncertain. Therefore, the objectives of this study were to (i) obtain baseline information on soil P variability in pastures with a varied history of animal manure applications, (ii) examine if current soil sampling recommendations related to the number of subsamples adequately account for any variability that may be encountered, and (iii) investigate the effect of spatial variability of soil P and soil sampling recommendations on implementation of a 150 mg kg-1 soil P threshold.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Spatial coordinates were determined for each soil sampling location as well as the field perimeter using either a real-time or post-process differential Global Positioning System (DGPS). If needed, the DGPS data were post-processed using base station data from the University of Arkansas campus to obtain the manufacturer's (Trimble Naviagtion Limited, 1996) horizontal accuracy of two to three meters. The RV1, OH1, and OH2 fields were initially sampled in May 1999 and resampled in October 1999. Real-time DGPS was used to navigate back to grid locations.
Soil P data for each pasture were tested for normality using the Shapiro–Wilk test (Hatcher and Stepnaski, 1994). To test for log-normality, the same procedure described above was performed on data transformed by the natural logarithm. The geometric mean was determined by taking the exponential of the mean of the data transformed by the natural logarithm.
Geostatistical analysis was conducted on pastures where at least 96 soil P samples were collected (OH3 through OH8) using GS+ software (Gamma Design Software, 1998). Semivariance for soil P was defined as:
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(h) = semivariance for lag distance class h, zi = measured soil P at point i, zi+h = measured soil P at point i + h, and N(h) = total number of sample pairs for the lag interval h. The lag class interval and number of lag classes were iteratively determined to ensure that at least six lag classes were created with the smallest lag class having at least 150 pairs (zi - zi+h) with succeeding classes having at least 200 pairs. Semivariance for each pasture was modeled with spherical, exponential, linear, linear to sill, and Gaussian isotopic models (Gamma Design Software, 1998). Model selection was based on best fit using regression coefficients (r2) and reduced sums of squares. The best model was subsequently used in kriging the concentration distributions.
The geographic information systems (GIS) software, SS-Toolbox (SST Development Group, 1999) was used to develop soil P surfaces with respect to the field boundary. Kriged values were determined on a 3- by 3-m grid. For fields where greater than 95 samples were collected (OH3 through OH8), kriging parameters were determined from the geostatistical analysis described above. For all other pastures, a linear isotropic model was assumed for use in kriging. Surfaces were further analyzed to determine pasture area that had less than 150 mg kg-1 soil P.
To investigate the effect of the number of subsamples collected on obtaining a single estimate of soil P for comparison with 150 mg kg-1, soil P populations were constructed from observations in pastures OH3 through OH8. For pastures RV1 through RV4, OH1, and OH2, where less than 30 actual observations were made, populations were constructed from interpolated data. This resulted in population sizes that were >200 depending on the size of the individual pasture.
To simulate producers collecting a given number of subsamples in a random zig-zag pattern, the constructed populations were sampled with simple random sampling without replacement (SAS Institute, 1999). This process was replicated 100 times for each given number of subsamples in each pasture. The number of subsamples varied from 1 to 80. The minimum number of subsamples needed to obtain an estimate within ±10%, ±20%, within the 95% confidence interval of the original and observed mean, and within 15 mg kg-1 soil P (10% of a 150 mg kg-1 threshold) was determined from the number of subsamples where the probability of obtaining an estimate within these intervals converged to >0.9.
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RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Accounting for spatial variability within a pasture is an important consideration in obtaining unbiased estimates of soil P. In general, the variance increased with increasing mean although there was not a strong mathematical relationship between these parameters. The mean standard deviation across all pastures and sampling times, 51 mg kg-1 soil P, was one-third the 150 mg kg-1 threshold. Current sampling recommendations do not provide an estimate of variance, only of central tendency. Thus, most producers have little insight into spatial variability of their fields. For this reason, we decided to relate the variances (standard deviation) to their respected mean values using the coefficient of variation (CV). The CV data demonstrated a trend of less variation with respect to its mean as the mean increased. For instance, in pastures where the arithmetic mean soil P was below 150 mg kg-1 (RV1, RV2, RV3, OH4, OH6, and OH7), the CV values ranged from 35 to 65%, except for pasture OH, which had a CV of 27%.
Relating variance to its respective mean may be important since the threshold approach implies comparing an estimate of central tendency with an established threshold. This may be especially true for pastures with mean soil P that approaches but does not exceed an established threshold. For instance, the mean and the respective variance in pasture OH4 may be smaller than those same parameters in pasture OH8. However, the variance in pasture OH4 may have far greater implications with regard to a soil P threshold, especially if sampling procedures produce a biased estimate of central tendency.
Soil P variability in these pastures was also reflected by the fact that the range (maximum–minimum) exceeded 150 mg kg-1 in 9 of 12 pastures. When the arithmetic mean soil P level was less than this threshold, the range exceeded its respective mean. These data imply that estimates of soil P can be biased toward extremely low or high values if proper sampling techniques are not employed, including not collecting the minimum number of subsamples in an appropriate pattern.
Effect of Subsample Numbers for Zig-Zag Sampling
Many states recommend a zig-zag sampling pattern for collecting subsamples across the pasture. The probability of obtaining a reliable estimate of central tendency increased with the number of subsamples collected across the pasture (Fig. 1)
. This same trend was true for pastures with a much smaller number of measurements (number of grid locations <30). For pastures of the size in this study, the University of Arkansas recommends 15 to 20 subsamples (Daniels et al., 2000). In practice, many producers often collect fewer subsamples than recommended. For data in Fig. 1, the probability of obtaining an estimate within the 95% confidence interval of the measured mean was reduced to less than 0.5 when less than 15 subsamples were taken.
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When using the criterion of obtaining an estimate within 10% of the measured mean, these data indicate that more subsamples are needed for pastures where the mean soil P is below or approaching the 150 mg kg-1 threshold than for pastures with mean soil P greater than this threshold. The use of this criterion may bias a larger minimum number of subsamples toward pastures with smaller means since a smaller mean produces a smaller acceptance interval.
An acceptance interval that does not vary with the measured mean can reduce this bias. For this study, a criterion of obtaining an estimate within 15 mg kg-1 soil P, or 10% of the threshold of 150 mg kg-1, was employed. The minimum number of subsamples required to meet this criterion increased with increasing variance (number of subsamples = 0.85 x standard deviation - 14; R2 = 0.80). For pastures with absolute standard deviation greater than 40 mg kg-1 soil P, which includes seven pastures, the number of subsamples currently recommended would not satisfy the stated criterion.
One possible scenario of not following sampling recommendations with regard to subsamples is obtaining an estimate exceeding an imposed threshold even though the best estimate is below the threshold. For example, pasture RV1 had a mean soil P of 133 and 148 mg kg-1 in the spring and fall, respectively. To obtain an estimate within 10% of these means with a probability of >0.9, 18 and 19 subsamples would have been required. If only 5 subsamples were collected, the probability of exceeding the threshold would be nearly 0.27 in the spring and >0.37 in the fall (Fig. 4) . If 20 samples had been collected, there was only a small chance of exceeding the threshold in the spring, but still greater than a 30% chance in the fall.
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The required sample size to meet established criteria can also be calculated with variance and detection limits using classical sample size equations for design of experiments. For pastures in this study, calculated sample size was on average six times greater than the simulated sizes in Fig. 2 and 3. These large sample sizes are unpractical for sampling pastures.
Soil Phosphorus Kriging
Geostatisical methods can help describe spatial variability. Semivariance of soil P was best described by an isotropic, spherical model in pastures with mean soil P values below 163 mg kg-1 (Table 3). Pasture OH5 (mean soil P = 284 mg kg-1) was best fit with a linear model while soil P in pasture OH8 displayed no spatial dependence. Pastures with mean soil P values below or near the threshold of 150 mg kg-1 displayed greater spatial dependence than pastures with soil P exceeding this threshold.
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Geostatistical analysis does provide good estimates of kriging parameters for interpolating between points to develop soil P surfaces. Kriged soil P surfaces were used to calculate the percentage of area below the threshold in each pasture. When the mean soil P and associated variance are sufficiently small, then all the pasture area is below the threshold of 150 mg kg-1 (Fig. 5) . As the mean soil P increased and approached the 150 mg kg-1 threshold, percentage of pasture less than the threshold of 150 mg kg-1 decreased. Once the mean soil P was above the threshold, the percentage of pasture less than the threshold of 150 mg kg-1 continued to decrease until the mean soil P increased to more than 250 mg kg-1. In all remaining pastures, all pasture area was greater than the 150 mg kg-1 threshold with increasing soil P mean.
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Mapping soil P surfaces offers three advantages over statistical approaches for accounting for spatial variability: (i) it reveals how soil P is distributed across a pasture, (ii) it allows area determination for various ranges of soil P values, and (iii) it potentially allows soil P, an indication of source, to be related more appropriately to transport properties that also exhibit spatial variability.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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The pastures in this study had a mean standard deviation of 51 mg kg-1 soil P, or one-third the proposed threshold. Variance in pastures generally increased with increasing mean. These results certainly indicate enough variability in soil P to create uncertainty in soil P estimates. Because estimates of central tendency are compared with a threshold, relating the variance of each pasture to its respective mean (CV) may be an important consideration in implementing the soil P threshold approach. For example, a smaller variance associated with a pasture with a mean approaching, but not exceeding, an established threshold could exert more influence on management decisions made with the threshold than a larger variance in a pasture with a mean that far exceeds the threshold. Thus, the smaller variance could induce uncertainty in soil P estimates in pastures with a "true value" that is approaching but not exceeding the threshold, which in turn could lead to improper decisions made with respect to the threshold.
In light of the presence of soil P variability, following soil sampling recommendations, especially with regard to the number and collection pattern of subsamples, is a critical consideration for reducing uncertainty in estimates of soil P. The number of subsamples required to satisfy the criterion of obtaining an estimate within 15 mg kg-1 soil P increased linearly with increasing standard deviation of soil P. Thus, a greater number of subsamples is needed to reduce uncertainty in obtaining soil P estimates from pastures with greater soil P variance. For this study, if the standard deviation of soil P was greater than 40 mg kg-1, then more than the recommended number of subsamples is needed to reduce uncertainty to an allowable level. This may be true for pastures with standard deviations less than 40 mg kg-1 if the associated mean soil P is approaching but not exceeding the threshold.
Even if spatial variability is properly accounted for and good estimates are obtained, concerns about the logic of using thresholds still exist. By mapping kriged soil P distributions in pastures with GIS, it was observed that as much as 50% of the pasture area was actually below the threshold even though the mean equaled or slightly exceeded the threshold. This implies that the threshold approach may not be accurately targeting management strategies to the landscape. Constructing kriged soil P surfaces for the purposes of making nutrient management plans may be neither economical nor practical at this time for routine implementation. However, it may offer several advantages to zig-zag patterns in accounting for spatial variability in terms of achieving water quality objectives.
However, the results of this study indicated that current sampling recommendations can adequately account for spatial variability to produce an single, appropriate estimate of soil P if the recommendations are carefully followed, especially with regard to the number of subsamples.
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ACKNOWLEDGMENTS |
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REFERENCES |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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