Rational basis for the logistic model for forage grasses

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Abstract
The logistic model has proven very useful in relating dry matter yields and plant N uptake of forage grasses to applied N. In the past the model has been treated simply as a regression model. This article provides a more rational mathematical foundation for the model. Differential response of dry matter to applied N was related to the product of filled and unfilled dry matter capacity of the system. Characteristics of the logistic and gaussian distributions were compared and refection symmetry of both noted. Symmetry in the logistic model was related to conservation of potential dry matter yield. At lower yields the logistic model approximates exponential behavior, while at higher yields it approximates the Mitscherlich model. Dry matter was coupled to plant N uptake through a hyperbolic equation. As a consequence, plant N uptake was also shown to follow logistic response to applied N with the same N response coefficient as for dry matter. In addition, plant N concentration exhibited linear dependence on plant N uptake. Field data were used to confirm all of these characteristics of the logistic model and to affirm its continued use to model forage grasses.

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