Reconciling the Mitscherlich's law of diminishing returns with Liebig's law of the minimum. Some results on crop modeling

Reliable fertilizer recommendations depend on the correctness of the crop production models fitted to the data, but generally the crop models are built empirically, neglecting important physiological aspects related with response to fertilizers, or they are based in laws of plant mineral nutrition seen by many authors as conflicting theories: the Liebig's Law of the Minimum and Mitscherlich's Law of Diminishing Returns. We developed a new approach to modelling the crop response to fertilizers that reconcile these laws. In this study, the Liebig's Law is applied at the cellular level to explain plant production and, as a result, crop models compatible with the Law of Diminishing Returns are derived. Some classical crop models appear here as special cases of our methodology, and a new interpretation for Mitscherlich's Law is also provided.