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

OSU Soil Fertility Plant Growth and Soil Nutrient Supply Relationships 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/dx = (A - y) c Law of “diminishing returns” Plant Growth and Soil Nutrient Supply Relationships 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/dx = (A - y) c Law of “diminishing returns” x 1 x 2 y2y2 y2y2 y1y1 y1y1 A-y for x1 and  y 1 Yield (y) Increasing level of growth factor (nutrient, x)

OSU Soil Fertility 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.” 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.” % of Maximum Yield or “Yield Possibility ” % of Maximum Yield or “Yield Possibility ” Soil Phosphate (P) or Potassium (K) Supply (soil test index) Soil Phosphate (P) or Potassium (K) Supply (soil test index) Bray mobile nutrient

OSU Soil Fertility Plant Growth and Soil Nutrient Supply Relationships Mitscherlich – – Soil deficiency levels could be expressed as a “percent sufficiency” Plant Growth and Soil Nutrient Supply Relationships Mitscherlich – – Soil deficiency levels could be expressed as a “percent sufficiency” % of Maximum Yield or “Yield Possibility ” % of Maximum Yield or “Yield Possibility ” Soil Phosphate (P) or Potassium (K) Supply (soil test index) Soil Phosphate (P) or Potassium (K) Supply (soil test index)

OSU Soil Fertility Plant Growth and Soil Nutrient Supply Relationships Mitscherlich Soil Test Correlation and Calibration Soil TestPercentFertilizer P IndexSufficiencyP 2 O Plant Growth and Soil Nutrient Supply Relationships Mitscherlich Soil Test Correlation and Calibration Soil TestPercentFertilizer P IndexSufficiencyP 2 O

OSU Soil Fertility Wheat Response to Fertilizer-P at STP of P2O5 Rate (lb/acre) Yield (bu/acre)

OSU Soil Fertility Y = YG [ PSP +(2 FP/DP) (100 - PSP) - (FP/DP) 2 (100 - PSP)]/100 General response of crops to fertilizer P 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 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

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