Fertilizer requirements for specified yield targets. I. Theoretical derivation of mathematical models for the computation of soil and fertilizer nutrient efficiencies

Abstract

The conventional deduction procedure of computation of soil (α) and fertilizer (β) nutrient efficiencies for the amount of fertilizer required for specified yield targets does not make provision of the amount of soil nutrient derived by crops from the available pool of soil nutrients not accounted for in the amount extracted by a soil test procedure. The derivation of two mathematical models, viz., Tamil Nadu Agricultural University Model I [TNAU Model I] and Model II [TNAU Model II] is reported in this paper which aim at computing the soil (α) and fertilizer (β) nutrient efficiencies not accounted for by the conventional method. In the case of TNAU Model I, the relationship between the nutrient uptake (U) and the soil (S) and the fertilizer (F) nutrients was established by assuming a functional relationship of the type U =αS +βF such that 0 ⩽α ⩽ 1 and 0 ⩽β ⩽ 1. In TNAU Model II the same relationship was established as U =αS +βF +γ such that 0 ⩽α ⩽ 1, 0 ⩽β ⩽ 1 andγ > 0. The termγ in the latter model is a measure of the amount of soil nutrient the crop absorbs from a slowly available pool of nutrients not accounted for in the amounts extracted by the soil test procedure employed or applied through fertilizer. The field verification of these models is reported elsewhere.