Crop absorption of immobile nutrients P and K

Crop absorption of immobile nutrients (P and K). Absorption is from just a thin cylinder of soil around each root.

Plant Growth and Soil Nutrient Supply Relationships dy/dx = (A - y) c Law of “diminishing returns” Yield (y) • Mitscherlich (1909) “…increase in yield of a crop as a result of increasing a single growth factor is proportional to the decrement from the maximum yield obtainable by increasing the particular growth factor. ” Dy 2 A-y for x 1 and Dy 1 x 1 x 2 Increasing level of growth factor (nutrient, x)

Plant Growth and Soil Nutrient Supply Relationships • Bray “…as the mobility of a nutrient in the soil decreases, the amount of that nutrient needed in the soil to produce a maximum yield (the soil nutrient requirement) increases from a value determined by the magnitude of the yield and the optimum percentage composition of the crop, to a constant value. ” Bray mobile nutrient 100 % of Maximum Yield or “Yield Possibility” 75 50 10 40 70 100 Soil Phosphate (P) or Potassium (K) Supply (soil test index)

Plant Growth and Soil Nutrient Supply Relationships • Mitscherlich – Soil deficiency levels could be expressed as a “percent sufficiency” 100 % of Maximum Yield or 75 “Yield Possibility” 50 10 40 70 100 Soil Phosphate (P) or Potassium (K) Supply (soil test index)

Plant Growth and Soil Nutrient Supply Relationships • Mitscherlich Soil Test Correlation and Calibration Soil Test P Index Percent Sufficiency Fertilizer P 2 O 5 0 10 20 40 65+ 25 45 80 90 100 80 60 40 20 0

Wheat Response to Fertilizer-P at STP of 20 Yield (bu/acre) 45 40 35 30 25 20 0 10 20 30 P 2 O 5 Rate (lb/acre) 40 50

General response of crops to fertilizer P Y = YG [ PSP +(2 FP/DP) (100 - PSP) - (FP/DP)2 (100 - PSP)]/100 Where: • PSP = Percent sufficiency P determined from calibrated soil test. • FP = Rate of Fertilizer P 2 O 5 applied. • DP = P 2 O 5 deficiency determined from calibrated soil test Y = YG [ PSP +(2 FP/DP) (100 - PSP) - (FP/DP)2 (100 - PSP)]/100 Y = YG [ a + x b 1 - x 2 b 2]/100