The Mitscherlich Plant Growth Model for Determining Critical Nutrient Deficiency Levels1

The success of a plant tissue analysis program depends on the calibration relating growth and nutrient concentration in specified plant tissues for each essential element. The minimal nutrient concentrations in tissues associated with maximum growth have been determined from calibration curves that were drawn free‐hand to best fit the respective Xand Yvalues in graphical plotting. Statistical models to establish critical deficiency levels related to 90% maximum growth are desirable to reduce the arbitrariness of the graphical procedure. A modified Mitscherlich response equation was used to quantify critical deficiency levels by characterizing plant growth as a function of tissue nutrient concentration. The model presented is y = β(1 — γe‐ax) where yis the plant yield at tissue concentration x, and α, β, and γ are parameters to be estimated. Critical deficiency levels determined from the Mitscherlich model were significantly greater (P < 0.05) than the previously reported nutrient values of the same studies utilizing the graphical procedure.