Ungar, E.D., Dept. of Agronomy and Nat. Resources, Agricultural Research Organization, Volcani Center, Israel, Dept. of Agronomy and Nat. Resources, Institute of Field and Garden Crops, Volcani Center, P.O.B. 6, Bet Dagan 50250, Israel
Seligman, N.G., Dept. of Agronomy and Nat. Resources, Agricultural Research Organization, Volcani Center, Israel, Dept. of Agronomy and Nat. Resources, Institute of Field and Garden Crops, Volcani Center, P.O.B. 6, Bet Dagan 50250, Israel
Noy-Meir, I., Department of Agricultural Botany, Fac. Agric., Food Environ. Qual. S., Hebrew University of Jerusalem, Israel

We describe a simple, yet intellectually challenging model of grazing systems that introduces basic concepts in ecology and systems analysis. The practical is suitable for high-school and university curricula with a quantitative orientation, and requires only basic skills in mathematics and spreadsheet use. The model is based on Noy-Meir's (1975) application of predator-prey theory to grazing systems. It comprises two rate functions which capture the essence of all grazing systems: grass growth and animal consumption. For simplicity, both rates are defined as functions of a single state variable - the grass mass per unit area. Superimposition of the two functions over a range of animal densities yields a graphical model with emergent properties of directionality, and with points of equilibrium which may be stable or unstable. In order to extend the model to conditions of seasonal growth, the rates are integrated numerically using a spreadsheet model, for which step-by-step instructions are given. The model output is depicted as three-dimensional surfaces that explore system response to two key management variables. The perspective gained on the complexities and behaviour of such simple systems is usually a rewarding eye-opener.