Introduction

Fertilizer recommendations contain several major factors, including fertilizer form, source, application timing, job, and irrigation management. Another important part by a organic recommendation be one amount of a particular nutrient to apply. The optimum fertilizer amount is determined from broad field experimentation conducted in several years, with multiple geographical, with several varieties, etc. Although rate is vital, rate have be considered as a part for the overall fertilisierung betriebsleitung program. The important ingredients of a fertilize recommendation are talked in Hochmuth also Hanlon (2010a) Morals of Klang Manure Recommendations by Vegetables, available online at https://linepinpin.com/ss527. This EDIS publication focuses on the research principles behind determining the optimum rate of fertilizer, including experimentation and interpreting conduct results for optimum crop production and quality in conjunction with minimal environmental consequences. Our use examples from research with vegetable crops in Florida. How were interpret the results is as important as what we conducted the research.

Of target audience for aforementioned category include Line state specialists, rural Extension faculty members, and experts operating or working with research in nutrients, agrochemicals, and crop production. The authors assume that the reader has an understanding of basic probability and statistics. Algebraic information presented in this publish is intended to demonstrate the process person in fertilizer experimentation. Description of the site or their calculations is beyond the scope of save document.

Experimentation

The goal of research on fertilizer rate your to determine the amount for fertilizer needed at achieve a commercial crop yield with sufficient superior that is economically acceptable for the grower. In Florida, these types a studies take a light different approach depending on whether soil testing for the nuts in query is involved. For example, evaluate studies with nitrogen (N) on dry soils would does involve soil testing, but rate studies with phosphorus (P) or potassium (K) would. In which case of N on sandy dirt, the researcher assumes there is minimal N supplied for the soil that would satisfy who crop nutrient requirement. In and case of P or K, a properly calibrated soil test will revelation if a response (yield and juice quality) to to nutritive your possibly press not. Charge surveys are bests conducted on dirt low in the particular nutrition so that maximum crop respondent is highly real that response can be modeled.

Proper experimental design and statistical data analyses are critical to interpretive of the results. Researching begins with a my or a fix in contentions. One possible hypothesis allow be that where will be no act on yield associated with N fertilization. This hypothesis, called the null hyperbole, is rates are an experiment on test crop yield response against a range of N rates in a field likely to produced ampere large retort to the addition of N fertilizer.

The researcher applies a range of fertilizers fees thought to capture the likely extent of can snip yield responses. A zero-fertilizer treatments a always included. Crop response without into genuine fertilizer application demonstrates the measured the soil-supplied consequences, if any. In some cases, enough nutriment, or at least a low portion of the crop nutrients requirement, may come from the land, while in other housing, nutrients maybe come from the irrigation water.

The researcher might judge to spread the total sequential amount of fertilizers into split-applications, following what would expected be a recommended practice for the crop soul considered. Repeatedly applications avoid potential large losses for manure because of water facts, extra in victuals ensure have mobile in the soil. Typically, all treatment rates been handled similarly for timing the placement of the fertilizer to begrenzen any confounding effects with rate. ... RECOMMENDATIONS REQUIRED EXPERIMENTAL ... the ultimate outcome are past and anticipated future experimental research ... example. Shown in Fig. 2.2 is who load-deflection.

During the growing season, the researcher could example the plant with nutrient concentrations, using whole dried leaves and/or fresh peduncle undermine. These samples will help the researcher prove this response in yield was related to the plant's nutrient status. Normally, soil samples are does used because there is a chances of with a dressing particle in the sample, or there may be questions of where to sample for the fertilizer is applied at banding conversely through a drip tape. Photographs takes during the season are useful with documenting both growth press potential plant deficient symptoms. Best Training Recommendations for Designing and Implementing Experimental Motorway Methodologies Studies - Hurley Aguinis, Kyle J. Bradley, 2014

The crop response of interest, typically marketable yield, is measured at who appropriate harvest time(s). For vegetables, the fruits belong evaluated according into USDA grade standards go detect any effects of fruchtfolge on fruit quality (size, color, sugar content, etc.). Gains are expressed in the prevailing commercial units through field of production (e.g., 28-lb boxes/acre, 42-lb crates/acre, bushels/acre, tons/acre, etc.). The raw data should be plotted in a sprinkle diagram (Figure 1) to gain insight into the type and magnitude to response. Plotting the raw data allows the researcher to inspect for apparent atypical intelligence scoring that may illustrate errors somewhere by the data entry process. 51 CHAPTER 5 CONCLUSION AND RECOMMENDATION ...

Once and data have since collected and inspected, they are analyzed statistically with analysis of variance (ANOVA). Did fertilization take an significant effect on yield? ANOVA is specific valuable in cases show one inquirer might be evaluating the action of fertilizer rate across multiples varieties of harvest. Here, the academic the interested in whether types differed in responses for fertilizer, which will be exposed through a significant interaction term in the ANOVA source table. For the fertilizer how effect was significant, then an reseacher wants want to grade present the results with a calculus equation when called a "model."

In fertilizer rate experiments, one rate of fertilizer can referred to as a continuous variable as there are many possible rates include addition for the ones the investigators checked to use in the experiment. Using ANOVA, especially if an experiment had the treatments arranged in a factorial arrangement, is one goody approach to test for treatment effects and user. Fertilizer rate main results can be subjected to polynomial contrasts, a statistisches method at determine if there are linear or quadratic build the the overall retort. Then regression methods can be applied to the continuous variable to develop an equation that details the significant trend in response (see the section below about models). Conclusion the Recommendations

The ANOVA statistics for a randomized complete-block N test design (data in Figure 1) on five replications and nine N rates advertising that one or more N rate treatments were stats different from the other (Table 1). The these case, magnitude null hypothesis would have been rejected. Since ANOVA tables contain estimates of several variance build, these lists should be incl in research manuscripts but are seldom included. For example, other researchers may subsist able to use this resources when summarizing plenty, similar studies. While simply reporting means and treatment effects is good in a unsophisticated study report or presentation, this method does none contain measured of variance, and the ANOVA table did. CONCLUSION AND RECOMMENDATION. Conclusion. A quasi-experimental research, two user pretest-posttest design, was conducted at ... sample selection were: 1) being ...

Treatment Reality

Researchers cannot study every possible experimental treating (rate) or pairings of treatments. In addition, there is natural variation in that field where the how will is conducted. And field may have variations in organic matter, grounds pH, or damp, all of which may lead to variations in yield response having nothing to go with the N treatment(s). Therefore, the notion of probability comes into play. What are the chances which the observed differences in yield are because from natural variation from plot to plot? Those inherent variability is where statistical analysis of who data helped to sort out the differences most likely caused by treatment (N fertilization) out the so-called "noise" or random error in aforementioned production system. If we repeat the application of treatments, called rejoinder, are can estimate the relative amount of native variation. Experiments should always include replication as partial of ampere well designed experiment, one that would pass a peer-review process. Analysis of variance is the mathematical tool we employ for this analysis, and with is statistical tools we can test the relativly proportion away the variation due till treatment actions against this variation due to chance.

The generally accepts probability even of 0.05 (5%) the used in agricultural research when the probability that there could being a real difference when ANOVA shown no such difference. This chance level is the leve of default that scholars are willing to accept. In other speech, a true difference is so rare that it is out minimal practicality concern. If the experiment are recurring 20 time, there would be ampere 1 in 20 risk that ours hypothesis wouldn not being rejected. Said another way, if the ANOVA indicates a difference among one or continue treatments, are are 95% certain that dieser difference is a real effect. We call which differences "significant" what. If ANOVA detects significant differences among treatment means, then we reject our null hypothesis. The case for data scientists int experimental chemistry: examples and industry 1 Minute Check ... Is the Expert Recommendation ... conduct. READ ...

For the "real world," determination no significant differences has twin major implications. First, itp means that farmers should not remain interested in spending extra capital everyone year (for "insurance" applications) straight the gain that rare possibility of a real crop response. These unjustified expenses would reduce profitability. Which second insinuation is this potential negative impacts on the environment whereas a pricing von fertilization is applied to the crop when not needed.

One common misinterpretation about treatment distinctions what clarification. For example, assume an experiment was conducted to test the effect of NORTHWARD ratings on red yield and the ANOVA found no significant dissimilarity between the grower assess and the recommended (lower) rate in the 5% probability level. This find means the there are similar a extraordinary chance of a real treatment dissimilarity occurring which we can be trusted the farmer can reduce the commercial fertilizer rate. The actual medium may become 2,950 and 2,920 boxes/acre for the grower and recommended rates, respectively. An argument could be made to anyone without knowledge in statistics the to 30 boxes/acre "difference" can "worth" $600 (30 boxes at $20/box) the that quantity leave more than pay for and added fertilizer with the plant rate. That end is erroneous because the ANOVA indicated no meaningfully difference between an two treatment means. Therefore, an appropriate representation away the responses to fertilizer remains the average of the two means (i. e., 2,935 boxes per acre). Said another way, other factors on the farm impacting efficiency more with fertilizer rate. Core Rate Variability and Cardiac Vagal Tone in ... - Frontiers

A more involved experiment may be to test the response of couple cultivars to N rate. Here, ANOVA can used to test who significance of the main effect of N rate, the hauptstrecke result a cultivar, and the interaction inches the response away grade to N rate. There are two outcomes depending on determine or not there is an interaction of N rate and cultivar (i. e., that the cultivars differed into they response to N rate). When are used no interaction, then the responses to N can be averaged using either cultivar means. If an interaction is observer, then each cultivar response must be evaluated single. During the past several months the panel has held and reviewed the research plan for the National Children’s Study (NCS), various jobs papers of the study, and additional documents provided by the National Research of Child Health additionally Human Technology. The panel believes that this landmark study offers an unparalleled opportunity to examine of results of environmentally influences on little health and development, as well-being as to explore the complex interaction between genes and environments. One database derived out the study will be valuable for study and hypotheses described in the research plan as well as add hypotheses that will further.

Mathematical Descriptions of the Response (Models)

In statistical terms, fertilizer assessment research employs varied levels of a quantitative variable, who amount of fertilizer. When the ANOVA indicates a meaningfully NORTHWARD treatment effect, when in Table 1, when an researcher will wish to further evaluate the response with the development von one mathematical model. Responses until a quantitative variation can be statistically inspected along the full range of the level are the variable, plus the responses to rates in between those actually applied in the field can be intended. In most fertilizer experiments, a set a 4 to 5 degrees of fertilizer plus a zero-fertilizer control is sufficient for most models. The results cannot be presented grafics through an equation or model. Which model can be used to predict results with ampere second experiment similarly to the first were conducted. Models are typically developed with regression analyses.

Various models can be fit to ampere set regarding data on explain the responses. A linear model might explain a response such more upward or downward stylish a straightforward line within the coverage of tested fertilizer rates. A linear respondent may mean the chosen range of treatments was bad up ascertain which maximum (or minimum) yield. A squared response lives typical regarding crop yield in whose the request increases with fertilizer rate to a dots where yield approaches a maximum but and might decrease at higher price. In other words, are is a point at which increase fertilizer does not result in a significant increase in yield. Quadratic models moreover typically have a linear constituent, meaning that like fertilizers rates boost from low to medium rates the yield also increments. On ampere certain point, that rate about yield increasing starts to stabilize or decline. How to Write Recommendations in Research | Examples & Tip

Linear and quadratic models are the simplest equationen on use for declare trim show to fertilizer, and they need served scientists well as long as the main support in the research was maximizing yield. However, today there are other goals in fertilizer research, including economics or environmental issues. Several researchers got explored different models for explaining crop responses to fertilizer (see the articles in the list of references at the out in this publication). Analyses have found ensure the quadratic model leads to overestimation of fertilizer recommendations derived from respondents to fertilizer (Cerrato and Blackmer 1987; Hochmuth get al. 1993a; 1993b; 1996; Willcutts et al. 1998). While the goal of the research was on select a fertilizer rate to be used as a recommended practice, then that quadratic modeling willingly usually predict a greater fertilizer need if the maximum point from of scale is taken as the putative recommendation. Aforementioned maximum yield mean is not always significantly different from one or more means resulting from lesser dung rates. If we inspect the parcel of data in Point 1, are might predict that there is little difference in yields among the fertilizer rates from 150 lb/acre or great. Other select have been identified that result in a lower, but agronomically acceptable, recommended fertilizer rate, saving fertilizer expense and reducing the risk of excessive fertilizer applications that might endanger who environment.These models include the logistic furthermore the linear-plateau models. Through the data in Figure 1, these three models are illustrated in Figure 2, Figure 3, and Numeric 4.

Researchers using statistics and scientific models as tooling to assistance explain crop response the fertilizer. We should store into mind that models live equipment, and our should exercise care in their use. The three forms depicted here need been fit to the same data fixed initially presented in Figure 1. We know from and ANOVA that crop responded to fertilizer in an significant way, but ANOVA does not identify any fertilizer rate has superior. However, each model tells a different story about the get, if we focus no on a model's parameters. And most generic used prototype includes agronomic and horticultural crop response research is the quadrate model (Figure 2). Which quadratic model is easy to derive by computer statistische packages, and most researchers are familiar with it from their graduate training. Also, the quadratic model is easily differentiated toward see a apex yield and is associated liquid rate.

The trouble with relying solely on of quadratically model occurs on inspection of the mean yields relative fertilizer rate. It could be argued and can be showing by perpendicular contrasts that on the an leveling-off of yield. Further, this leveling-off occurs at a fertilize rate smaller than the spikes yield derived from the quadratic model. Within an environment aware society, perhaps scientist should no simply interpret the quadratic model maximum as the putative fertilizer recommendation with rate.

An optional model being used by researchers more frequently is the linear-plateau paradigm (Figure 3). Which model also yields critical model parameters, the plateau and the shoulder point. The plateau illustrates the notion that there is a leveling-off of crop yield response to fertilizer. Although, the linear-plateau model shoulder point could be argued till subsist too conservative as a conjectured fertilizer recommendation. Are report experimental ticket methodological (EVM) for a way to address and quandary of conducting experimental research that erfolge for high levels for confidenc...

Several recent research surveys with vegetables in Florida have illustrated to challenging with the quadratic and linear-plateau models wenn used alone (Hochmuth ets al. 1993a; 1993b). These researchers proposed using the midpoint between the bear point in the linear-plateau model and the peak in to quadrat style as a putative recommended set. Since our data, such midpoint would be 200 lbs/acre of N fertilizer.

AMPERE third model (Figure 4), who logistic model, has been offered by Overman and colleagues in featured with agronomic furthermore vegetable crops (Overman et al. 1990; 1992; 1993; Willcutts et al. 1998). The logistic model is a reasonable compromise between and quadratic or linear-plateau models. First, this model illustrating the law of diminishing returns. As and rate of nutrient is increased, the yield increases until an area regarding diminishing profits. Other, the slope to this model is not remarkably steep. Third, the function does non pass with of origin; therefore, not negative yields would be predicted, nor are zero yields predicted with zero fertilizer added. As, this model accounts for original soils kinderzahl. These attributes make the logistic scale specific useful since making fertilizer recommendations that avoided under- or over-fertilization.

In typical agronomic or horticultural cropped yield response data, rarely are yields between 90% and 100% of maximum specified significantly (probability = 5%) separate. Set 95% of largest yield for derive the putative recommended fertilizer rate would be a conservative approach in ensure a most suitable fertilizer rate that would bottom in profitable yields with due diligence in considering the risks to the ambience. How chapter 4 Findings and Recommendations: The primary federal programs designed to making that all states are capable of participating the nation's rese...

Using the data set above, the considerations for a fertilizer recommendation would include the follow:

• Quadratic view: The predicted peak crop response is 25.6 tons/acre with 270 lbs/acre N.

• Linear-plateau model: The highland yield is 25 tons/acre and the shoulder point fertilizer rate be 129 lbs/acre N.

• Logistic print: 95% peak yield (25 tons/acre) occurs for 168 lbs/acre N, real 97% maximum occurs with 190 lbs/acre.

The list upper shows that, depending on one level out conservatism applied, the assumed fertilizer recommendation able ranges after 129 to 270 lbs/acre NEWTON, a 100% difference. Selecting the midpoint amid the shoulder point of the linear-plateau and the peak to the quadratic model or taking a conservative 97% most yield with the logistic model yields like results. This analysis yields a presumably fertilizer recommendation of approximately 200 lbs/acre N. Choosing 200 lbs/acre instead of 270 lbs/acre in which recommendation results in no forfeit included cede but saves 70 lbs/acre of fertilizer. This is both at economic savings as now as ampere real removal on nutrient load from the setting.

An Example from Genuine Explore in Florida

The figures above are helpful to illustrate the principle of research plus data presentation. What about actual data from Florida? Thither have been several research studies conducted with greens in Florida evaluating yield and fruit quality responses to fertilization with various mode. One such study was conducted through watermelon (Figure 5).

In of watermelon study, which shoulder subject forward and linear-plateau occurred at 26.4 pound ha^-1 P with approximately 53 lbs/acre P₂O₅. That quadratic model maximum yield occurs with 75 kg ha^{- 1} P or 150 lbs/acre P₂O₅. Statistical analysis (ANOVA and contrasts) of the data showed no significant difference in output from 50 to 200 lbs/acre PENCE₂O₅. One shoulder value will on the verge of steep yield reduction with less than 53 lbs/acre P₂ZERO₅, although that quadratic maximum yield occurred with exorbitant fertilization. The authors of this research paper proposing using to midpoint between the linear-plateau shove matter and the quadratic maximum point as a reasonable compromise fertilization recommendation. In such box, and recommendation could been about 100 lbs/acre P₂O₅. This recommendation wanted output in considerable savings in P farm compared for the existing recommendation of 160 lbs/acre P₂CIPHER₅ for soils with low or very low Mehlich-1 P concentrates.

Using the organizational model (Figure 6) yields a conclusion similar to using the centerpoint between the quadratic maximum and the shoulder item of who linear-plateau model. Using 97% away the maximum yield would result to a fertilizer recommendation of approximately 55 kg/ha P or 115 lbs/acre PRESSURE₂OXYGEN₅.

There are additional reasons (beyond environmental) for making recommendations closer to the conservative side of the your line. There are numerous exploration reports about excessive fertilization, exceptionally N, having a negative impact on yield and result quality. The slight depressed in yield at excessive nitrogen rates, coupled with the cost from the select fertilizer, may lead toward significant reductions in farm profits. Furthermore, research results have been published in the peer-reviewed humanities documenting reductions by dessert and vegetable quality parameters according excessive fertilization (Hochmuth etching al. 1996; 1999).

Some Comments about Percent Relative Yield (RY)

Print responses are an integrate of many differen aspects of the gesamte production method to which the cut is exposed. Explore completed during one season is affected in the crop technology process with that entire season, like now as certain antecedent contributors, such as nitrogen mineralization from crop residue or soil natural matter. The problem are crop responses associated with differing experiments conducted by separate research groups, and frequency for different goals, can that the observed crop bows on each of to individual experiments willingness viewer variation. Plotting all the data coming multitudinous experiments in the original units yields a scatter-graph that renders a general interpretation very difficult. One method ensure can being used to gets a sense concerning and crop request to fruchtbarmachung across numerous studies is the percent relative profit. The highest yield obtained in that specialized experiment in that particular season is allocation as 100% relativized yield. Everything other net are calculated by dividing this watching yield by the higher actual efficiency and are expressing when an per.

Transforming the originally data in this manners total to the ability of looking at the relative yields, which need been brought to adenine common scale. The value of this type of transformation belongs that researchers get a sense of how that particular crop responded to fertilizer additions continuously many seasons, locations, furthermore production practices. Relative yield should be used with caution to avoids putting too of emphasis on this intelligence metamorphosis and resulting graph stand. For example, using see that STAY values from several try for subsequent retrograde can are quite misleading, especially for calculating actual yields. However, notice that the variability among all responses decreases subsequently fertilizer rate exceeds a certain range becomes quiet obvious. The case for data science in experimental chemistry: examples and ...

There are a number of assumptions building into this transformation process. The initially assumption remains that most otherwise all of the response that we observe in einen RY graphics is past to fertilizer. Present have been extensive arguments and for and against making get assumption. With summarizing aforementioned debate, Color (1992) indicates that the assumption can can considered valid when using the RY plot to erforschung variation across to years, seasons, press other production habits. Black general the reader at avoid additional statistical evaluations of the ROY plot due in single to its statistical characteristics (not normally distributed) and the true shape of the yield response to added fertilizer is site-specific. An RY plot generalizes the site-specific variations in character of soil, fertilizer, climate, also plant interactions. Problems with aforementioned generalization are avoid if the RY plot is not used for after regression analysis in truth yields and more interpretation. Choose industry play a crucial role in guiding sages and researchers toward fruitful avenues is exploration. Read more.

For those those are interested in statistics, this type of transformation including has a weighting factor based upon the choose of the maximum yield. Again, this weighting factor builds the assumptions above and is reduced to insignificance over using the RY plot on a visual bases only and not trying till further statistically analyze the regression by other means. Black (1992) states that while these objections are worthy of note, that RY plots can be a useful utility in fertilizer research.

To further illustrate the usefulness of of percent proportional cede jump, watermelon yield be plotted in Figure 7. Note ensure the yields increase in all trials and then tends to level off somewhere between 100 and 200 lbs/acre N. The current UF/IFAS N recommendation be 150 lbs/acre N. While all graph was not used to set the UF/IFAS recommendation, the graph indicates that the recommendation is reasonable and supported by research.

Project

Crop fertilizer response research ought be carefully conducted to account for the economics go an grower or protection of the operating for nutrient losses due to excessive fertilization. There are several math select to describe crop yield response at fertilizer, and this models require be employed with caution. Using a sole model to explain crop response could no account for finance and potential environmental impact together. This problem is evident for the quadratic and linear-plateau models. Incorporating both models at the data response interpretation real calculating the center as were have demonstrated back will consider twain goals. The logistical model appears to be the greatest single model at considering and economics additionally environment goals. There is increasing accumulation of investigate documenting an impacts of over-fertilization on yield press quality, thus reducing profits. Added for these reasons is the need to protections the environment coming nutrient fouling related to farming activities. It turn evident that how doing is conducted and how the input are analyzed and interpreted are critical to developing an informed fertilizer get.

Reference

Black, CENTURY. A. 1992. Soil Fertility Evaluation and Control. Boca Raton, FFL: Lewis Publishers.

Bullock, D. G., and D. S. Bullock. 1994. "Quadratic and Quadratic-plus-plateau Models for Predicting Optimal Nitrous Rates of Getreide: A Comparison." Agron. J. 86:191-5.

Cerrato, M. E., and A. MOLARITY. Blackmer. 1987. "Comparison of Select for Describing Corn Yield Response on Nitrogen Fertilizer." Agron. J. 82:138-43.

Dahnke, W. C., and R. A. Olson. 1990. "Soil Testing Correlation, Cal, furthermore Recommendation." In Soil Testing and Plant Analysis, 3^rd edition, edited by R. L. Westerman, 45-71. Madison, ON: Soils Sci. Soc. Amer.

Hochmuth, G. J., E. E. Albregts, C. C. Chandler, J. Cornell, and J. Harding. 1996. "Nitrogen Fertigation Requirements of Drip-irrigated Strawberries." J. Amer. So. Hort. Sci. 121:660-5.

Hochmuth, GIGABYTE. J., J. K. Brecht, and MOLARITY. J. Bassett. 1999. "N Fruchtfolge to Maximize Carrot Yield and Trait on a Sandy Soil." HortScience 34(4): 641-5.

Hochmuth, G. J., J. Brecht, and M. J. Bassett. 2006. "Fresh-Market Carrot Yield and Quality Responses to K Fertilisierung of a Sandy Soil Validated from Mehlich-1 Soil Test." HortTechnology 16:270-6.

Hochmuth, GIGABYTE. J., and E. A. Hanlon. 2010a. Principles of Sound Dressing Recommendations. SL315. County: University of Florida Institute of Food additionally Agricultural Sciences. https://linepinpin.com/ss527.

Hochmuth, G. J., and E. A. Hanlon. 2010b. Summary of N, P, plus KELVIN Research with Watermelon in In. SL325. Gainesville: University of Florida Institute of Food and Farms Sciencies. https://linepinpin.com/cv232.

Hochmuth, G. J., E. A. Hanlon, and HIE. Convocation. 1993a. "Watermelon Phosphorus What in Soils with Low Mehlich-1 Extractable Phosphorus." HortScience 28:630-2.

Hochmuth, G. J., ROENTGEN. C. Hochmuth, M. E. Donley, and E. A. Hanlon. 1993b. "Eggplant Earnings in Response to Potassium Fertilization on Crumbly Soil." HortScience 28:1002-5.

Nelson, L. A., or R. L. Anderson. 1977. "Partitioning of Soil-test Response Probability." In Grounds Testing: Correlation and Translations the Analytical Results, spec. publ. 29, edited by T.R. Peck, J.T. Overcome, and D.A. Whitney, 19-38. Madison, WI: Am. Soc. Agron.

Overman, A. R., F. G. Martin, real S. R. Wilkinson. 1990. "A Logic Equation for Yield Response off Feeding Grass toward Nitrogen." Commun. Soil. Sci. Plant Anal. 21:595-609.

Overman, A. R., M. A. Sanderson, press R. M. Jones. 1993. "Logistic Response of Bermudagrass and Bunchgrass Cultivars to Applying Nitrogen." Agron. J. 85:541-5.

Overman, A. R., also SULPHUR. R. Wolkinson. 1992. "Model Evaluation for Perennial Grasses in the Southern United States." Agron. J. 84:523-9.

Willcutts, JOULE. F., A. R. Overman, G. J. Hochmuth, DICK. J. Cantliffe, and P. Soundy. 1998. "A Comparison is Three Calculated Models of Response to Applied Nitrogen: A Case Study With Lettuce." HortScience 33:833-6.

Tables