Some problems in the estimation of simultaneous fertilizer requirements of crops from response surfaces

Abstract

The estimation of the optimal fertilizer requirements of a crop from the data of fertilizer experiments depends on the response exhibiting the form of the law of diminishing returns with respect to all fertilizers. Deviations from the diminishing form are frequently encountered, particularly with experiments involving several fertilizers, because of experimental errors, extrapolation errors, and inappropriate choices of fertilizer treatment levels. Since the time required to repeat inadequate experiments is usually considerable the experimenter has to make the best use of admittedly inadequate data to obtain interim estimates of fertilizer requirements. A procedure is described for obtaining estimates of fertilizer requirements with such data despite the deviations from the expected diminishing response form. The procedure is based on the use of a polynomial model to represent the multidimensional response surface. Interaction terms which would normally be expected to make only small and negligible contributions to the model, are eliminated to avoid the influence of non-significant responses to particular fertilizers on the calculation of other fertilizer requirements. Where a fertilizer has given a significant but non-diminishing response, approximate estimates of the requirements of that fertilizer are substituted to allow approximately for interaction effects in the estimation of the remaining fertilizer requirements. The problems and the application of the procedure is illustrated with data from three fertilizer experiments involving nitrogen, phosphorus, potassium, and sulphur fertilizers.