A DIFFERENTIAL-DELAY MODEL OF PASTURE ACCUMULATION AND LOSS IN CONTROLLED GRAZING SYSTEMS

A grazing population dynamics model is proposed where organisms in a g razed population have a fixed life span. The motivating context is tha t of ruminants grazing grass-dominant pasture. The model takes the for m of a differential-delay equation in which the rate of loss of pastur e due to senescence at some time depends on the rate at which leaves a re 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 da ys for herbage life span. Predictions of herbage utilization are consi stent with measured data. The model predicts lower senescence in sward s in regrowth than in grazed swards at the same herbage mass. Solution s and equilibria are obtained for the linear form of the model with co ntinuous grazing pressure. Solutions and bounds are obtained for the l inear model with intermittent grazing pressure, and its usefulness in modeling grazed pastures is discussed. A delay model is a simple but p owerful means of including the concept of fixed herbage life span in g razing modeling. Questions of herbage life span and percentage utiliza tion are naturally contained in the mechanism of a differential-delay model. These are not so well handled by models that treat senescence o f herbage empirically.