An examination of the validity of hypotheses of two theories of soybean response to phosphorus and potassium

The theoretical hypotheses concerning crop response to nutrients must be reconciled with observable facts. This reconciliation is important to scientists, crop managers, and to those who assist crop managers. In this study the theories of Liebig and Mitscherlich are examined with respect to soybean response to phosphorus and potassium on the Memphis and Henry soil types of Western Tennessee. The theories are evaluated with respect to data coherency, data admissibility, valid conditioning, and encompassment. Because a complete specification of Mitscherlich's theory results in a nonlinear statistical specification, the logarithmic function was substituted throughout the study.

The results suggest that the logarithmic equation performed well with respect to data coherency; that is, its errors were more often normally distributed and homoskedastic than those associated with the Liebig equation. However, Liebig's equation was found to be data admissible, validly conditioned, and encompassing.

The results of this research supported the general conclusion that soybeans respond to potassium more so than to phosphorus, at least on the Memphis and Henry soil types. The results also supported Liebig's hypotheses that a single ratio of phosphorus to potassium be used no matter what yield level is desired and that phosphorus and potassium do not substitute for each other in maintaining a given yield level.

Fertilizer recommendations derived from the Liebig model were very conservative. Only prices that have never been observed for soybeans resulted in fertilizer being recommended. Fertilizer recommendations derived from the logarithmic equation were much more liberal. By comparison the University of Tennessee personnel recommendations were in between recommendations of the Liebig and logarithmic models.