A theory for fertilizer response

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Abstract
A model is derived that relates yield to levels of applied fertilizer in terms of parameters that have direct physical meaning. N8, P8, and K8 define the contribution of the soil to the supply of nitrogen, phosphorus and potassium for plant growth; BN, BP and BK define the responses to nitrogen, phosphorus and potassium fertilizer at low nutrient levels and aN is the level of nitrogen required to raise the osmotic pressure sufficiently to prevent growth.To test the model, field experiments were carried out on French beans and summer cabbage in which 125 different combinations of levels of nitrogen, phosphate and potassium fertilizers were applied. The yield data from each block of each experiment fitted the model very well. Fitted values differed from block to block but these differences could be attributed to the fact that for each block equally good fits were often obtained with widely differing parameter values. Estimates of N8 were made from chemical analysis of the (NH4 + NO3) — N of soil samples from the field plots, and P8, and K8 from chemical studies of the adsorption of phosphate and potassium on untreated soil. They were in substantial agreement with the average values obtained by the entirely different procedure of fitting the model to the yield data. Also estimated values for BN, BP and BK and aN from other chemical studies were consistent with those obtained by model fitting.It is concluded that although the theory has limitations it is broadly in accord with the results of the detailed field experiments.