Long-term fertilizer field trials: comparison of three mathematical response models

Stefan T Bäckman,V.-M Taavitsainen,S Vermeulen

doi:10.23986/afsci.72778

Stefan T Bäckman, V.-M Taavitsainen + Show 1 more

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https://doi.org/10.23986/afsci.72778

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Abstract

Accession to the European Union caused a drop of nearly 60 per cent from 1994 to 1995 in prices of wheat, barley and oats in Finland. The economic use of fertilizer therefore decreased accordingly. To calculate the effect of the price changes on the economic optima, the physical production function must be known. Three physical production functions, the quadratic, the linear response and plateau (LRP) and the exponential function were estimated for this purpose. The models differed little in respect of the R2adj value (0.82-0.90) but the calculated optimum varied, depending on the production function. Data on a long-term field trial (21 years) were analysed. The field trial was established in 1973 to demonstrate the effect of mineral fertilizer in crop production. The crops grown in the trial were barley, wheat and oats. Different varieties were included in the models.

Highlights

(LRP) and the exponential function were estimated for this purpose
The crops grown in the trial were barley, wheat and oats
We found that nitrogen explained most of the yield response; fertilization with phosphorus did not increase the yield, though at the lowest levels the yield was determined by both nitrogen and phosphorus (YliHalla 1991)

Summary

Introduction

(LRP) and the exponential function were estimated for this purpose. The models differed little in respect of the R value. The field trial was established in 1973 to demonstrate the effect of mineral fertilizer in crop production. Fertilizer field trials yield a vast amount of data that cannot be analysed without the use of a proper mathematical model. The quadratic model, the exponential model usually known as the Mitscherlich model, and a modified form of the plateau model, are commonly used in crop response analyses Even though the models give comparable R 2 values, they may give different optimal fertilizer rates. Optima based on the quadratic function or on the exponential function have been criticised for giving excessively high optimal fertilizer rates. A model based on a linear response and plateau (LRP) function gives

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