RATIONAL BASIS FOR THE LOGISTIC MODEL FOR FORAGE GRASSES

The logistic model has proven very useful in relating dry matter yield s and plant N uptake of forage grasses to applied N. In the past the m odel has been treated simply as a regression model. This article provi des a more rational mathematical foundation for the model. Differentia l response of dry matter to applied N was related to the product of fi lled and unfilled dry matter capacity of the system. Characteristics o f 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 logist ic 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 uptak e was also shown to follow logistic response to applied N with the sam e N response coefficient as for dry matter. in addition, plant N conce ntration exhibited linear dependence on plant N uptake. Field data wer e used to confirm all of these characteristics of the logistic model a nd to affirm its continued use to model forage grasses.