Economic control of fertilizer in highly productive pastoral systems. I. A theoretical framework for the fertilization problem

Abstract

A hypothetical model, based on plant physiology and termed ‘Mitscherlich-Liebig’, is proposed as a general solution to the problem of estimating an optimum fertilizer rate from results in a field trial; in combining the ideas of Liebig and Mitscherlich the model involves the following proposals:

• (1) Diminishing returns in a smooth exponential relation between input and output culminating in a yield-plateau.

• (2) The difference between this plateau and the ideal asymptotic maximum is the result of an unavoidable osmotic depression caused by salts in the root zone.

• (3) Liebigian nonsubstitution of one essential elemental nutrient by another.

• (4) Quantitative equivalence in output from essential inputs when each is expressed in terms of a physiologically standardized amount defined as a Baule unit.

• (5) Pooling response data according to a relative yield theory and the Baule unit concept, rather than grouping data according to a soil type theory and the concept of a response curve unique for the element concerned.

In addition to certain other biometrical implications, these concepts provide an explicit method for estimating the composition of a balanced fertilizer mixture, whereby a profit maximising calculation may be applied through the ratio: cost of applied fertilizer/price of harvested yield. This approach to the problem permits a formulation of fertilizer advice theoretically sound in plant physiology as well as economics.