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Relationships Among Some Biological and Empirical Fertilizer Response Models and Use of the Power Family of Transformations to Identify an Appropriate Model
Author(s) -
Mombiela F. A.,
Nelson L. A.
Publication year - 1981
Publication title -
agronomy journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.752
H-Index - 131
eISSN - 1435-0645
pISSN - 0002-1962
DOI - 10.2134/agronj1981.00021962007300020025x
Subject(s) - mathematics , transformation (genetics) , quadratic equation , series (stratigraphy) , inverse , power (physics) , yield (engineering) , polynomial , linear model , statistics , mathematical optimization , mathematical analysis , paleontology , biochemistry , chemistry , physics , geometry , materials science , quantum mechanics , biology , metallurgy , gene
A systematic procedure is often needed to select the best model for representing response to fertilizer input. Several traditional fertilizer response models are shown to belong to a series consisting of the Power Family of transformations of (A‐y) where y is the yield and A is the maximum yield. Transformations of both A‐y and x, the level of added nutrient, also belong to the series. Tukey’s method of plotting the data and trying different transformations of (A‐y) (and perhaps x) to linearize the data is recommended for finding a model which best approximates the relationship. There is a great deal of flexibility in the system so the best model may turn out to be one of the traditional fertilizer response models or it may be a less common member of the series of transformations of (A‐y) in the Power series. Of the traditional models the quadratic model represents the weakest transformation that will linearize the A‐y vs. x plot; Balmukand’s and Nelder’s inverse polynomial models are among the strongest. Mitscherlich’s model represents an intermediate transformation between the quadratic and Nelder’s model.