A modified model for evaluating residual phosphate in soil

Abstract

A model described by J. S. Russell for evaluating the residual effects of nutrients was modified and applied to the residual effects of phosphate as measured over 6 years in a field trial. Losses of phosphate, and phosphate converted to organic forms, were modelled by using a curvilinear relation such that the proportion lost or converted was greatest at low levels of application. Because of this, the effectiveness of fertilizer in years subsequent to its application declined relatively faster at low levels of application and responses became increasingly sigmoid.

A function derived by Russell to describe the transfer of phosphate from available to unavailable forms was inadequate when this transfer was studied in isolated systems. For the field results, it was not possible to distinguish between Russell's function and two other functions and, provided the model was confined to the period to which it was fitted, it was immaterial which function was used. It is argued, however, that if the model were to be extrapolated it would be preferable to use component functions which can be separately justified.