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A Method to Determine the Appropriate Mathematical Form for Incorporating Soil Test Levels in Fertilizer Response Models for Recommendation Purposes¹

A method is proposed for developing fertilizer recommendations based upon a statistical estimate of the amount of "plantavailable" nutrient in the soil (d), and determining the appropriate mathematical form of the relationship of this estimate to soil test values (T). A function of soil test is then substituted into the fertilizer response model ford. Some comparisons of the effects of three different models (Mitscherlich, quadratic and square root) upon d estimates and on the form of their relationships to soil test values were made. Regressions of d estimates obtained using the three models upon soil test P values were carried out to determine empirically the appropriate mathematical form [called f(T)] for a set of Irish potato data from Maine and North Carolina. The f(T) was found to be linear for that particular set of data for all three models, i.e.,d a = b₀ + b₁T. From these data, it was concluded that environmental conditions between states did not affect f(T) but did affect the level of maximum response (A, in the Mitscherlich model) and a factor related to curve shape (c, in the Mitscherlich model). Once f(T) is known for a model, it may be substituted into the model ford and this equation then used for fertilizer recommendations based upon site-specific soil test information. Equations for estimating optimal P fertilizer rates assuming different cost-price ratios (p) and marginal rates of return (R) were given for this data set. Similar equations may be derived for other specific crop-soil conditions using the techniques described in this paper.

Key Words: Soil test calibration • Non-linear regression • Mitscherlich-Bray equation • P response models

² Former International Research Institute graduate fellow in the Dep. of Soil Science, associate professor of soil science and professor of statistics, respectively, at North Carolina State Univ. Present address of senior author: CRIDA 01, Apartado 10, La Coruña, Spain.

Received for publication May 27, 1980.

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