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Inefficiency of Fertilizer Use Resulting from Nonuniform Spatial Distribution: II. Yield Losses Under Selected Distribution Patterns¹

ABSTRACT

Yield losses due to nonuniform application of fertilizer to homogeneous soil areas were examined by methods developed previously. Cosine functions were chosen to represent spatial distributions of applied fertilizers and quadratic equations were selected to characterize yield responses to fertilizer inputs.

Yield depressions were estimated for cases in which nitrogenous fertilizers are nonuniformly applied to Iowa soils which differ in initial fertility. These losses vary directly with the square of the amplitude of the cosine distribution function, but they are inversely related to soil nitrification rate. Assuming a profit-maximizing fertilization rate and valid mathematical models, upper bounds for yield losses are 12.4, 4.3, and 0.6 bushels per acre for representative very low, low and medium soil test classes, respectively.

Physical characteristics of complete fertilizer materials were considered for the case of corn production on a Haynie soil. Yield losses due to nonuniform application of an aggregated material, which retains a constant nutrient ratio, exceed 4.3 bushels per acre when amplitude of the distribution function is larger than half the optimum fertilization rate. Physical segregation of dry-blended nutrient carriers may result in different distribution patterns for the component nutrients. As a consequence, nutrient ratios as well as rates may vary over the treated area when complete fertilizer materials are subject to physical separation.

¹ Journal Paper No. J-4035 of the Iowa Agr. and Home Econ. Exp. Sta., Ames. Project No. 1189. Research jointly sponsored by the National Science Foundation and the Department of Agronomy.

² National Science Foundation Graduate Fellow and Professor of Soils, respectively.

Received for publication February 6, 1961. Accepted for publication April 5, 1961.