A theoretical analysis of the potential productivity of ryegrass under grazing

Abstract

The potential productivity of a grassland under grazing is defined in this paper as the total dry matter of grass harvested by the grazing animals over the whole growing season. It has been analysed by applying optimal control theory to the mathematical model of ryegrass growth under grazing developed by Johnson & Parsons (1985a); J. theor. Biol. 112, 345), the productivity being regarded as the objective function to be maximized through optimization of the time course of the stocking density, the control variable. It is shown that the potential productivity under grazing is higher than that under infrequent cutting, and the optimal time course of the stocking density consists of three stages, with zero density in the first stage, the highest density in the last stage and a constant (under constant environmental conditions) or a variable (under variable environmental conditions) stocking density in between. Under constant environmental conditions, the biological significance implied in the second stage is that the stocking density takes such a value that the grass keeps its highest intrinsic growth rate. The influence of the environmental conditions on potential productivity and on optimal grazing management is also discussed.