Mitscherlich Yield Response

Y = Y_{\max}(1 - e^{-cN})

Diminishing returns of nitrogen fertilizer on crop yield.

By Wilhelm Mitscherlich

Agricultural Sciences

1909 · Wilhelm Mitscherlich

Why it matters: Optimized fertilizer rates, reducing waste and groundwater nitrate pollution.

Discoverers: Wilhelm Mitscherlich (1909)

What does it mean?

Diminishing returns of nitrogen fertilizer on crop yield.

Optimized fertilizer rates, reducing waste and groundwater nitrate pollution.

Symbol	Name	Unit	Meaning
$Y$	Yield	—	t/ha
$Y_max$	Asymptotic yield	—	t/ha
$N$	Nitrogen applied	—	kg/ha
$c$	Response constant	—	ha/kg

Each additional N band adds less yield until plateau near Y_max.

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Y = Y_{\max}(1 - e^{-cN})

Real-world impact

Precision agriculture

Equations optimize food production for billions.

Photo: Unsplash — precision farming

Diminishing returns of nitrogen fertilizer on crop yield.

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