A differential-delay model of pasture accumulation and loss in controlled grazing systems

A grazing population dynamics model is proposed where organisms in a grazed population have a fixed life span. The motivating context is that of ruminants grazing grass-dominant pasture. The model takes the form of a differential-delay equation in which the rate of loss of pasture due to senescence at some time depends on the rate at which leaves are reaching maturity at that time. Comparisons are made with data from a continuous grazing experiment due to Bircham and Hodgson (Grass and Forage Science, 38:323-331, 1985), leading to a prediction of 21.9 days for herbage life span. Predictions of herbage utilization are consistent with measured data. The model predicts lower senescence in swards in regrowth than in grazed swards at the same herbage mass. Solutions and equilibria are obtained for the linear form of the model with continuous grazing pressure. Solutions and bounds are obtained for the linear model with intermittent grazing pressure, and its usefulness in modeling grazed pastures is discussed. A delay model is a simple but powerful means of including the concept of fixed herbage life span in grazing modeling. Questions of herbage life span and percentage utilization are naturally contained in the mechanism of a differential-delay model. There are not so well handled by models that treat senescence of herbage empirically.