Application of an Herbivore-Plant Model to Rest-Rotation Grazing Management on Shrub-Steppe Rangeland

Abstract

A graphical model of a discontinuously stable herbivore-plant system is used to demonstrate analytically relationships between the amount of rest, stocking rate, and seasons of use in restrotation livestock grazing management on shrub-grass ranges. All three of these components are important and their interaction determines the system's response. Important points applicable to management are enumerated. The science of range management is based on an understanding of the interactive effects of plants and herbivores on long-term forage production and range condition. A livestock grazing management system is one of the chief means of manipulating herbivore-plant interactions in efforts to improve the range resource and ensure a sustained yield of goods and services. A variety of grazing management systems have been applied to various ranges (e.g., Anderson 1967; Valentine 1967; Heady 1970; Stoddart et al. 1975), but basically there are three major categories: those based on continuous grazing, (2) those involving some type of deferment, and (3) those involving systematic rotation of the livestock. It is of prime importance that whatever management system is used must be tailored to the specific requirements of the range resource (Anderson 1967). Rest-rotation grazing management, as championed by Hormay (1970; Hormay and Evanko 1958), involves the use of deferment and rest (rest means that a pasture is not grazed at all in a given year) along with a rotation of livestock from pasture to pasture. Based on the philosophy that plants must be allowed time to recover vigor following defoliation, it typically involves various combinations of resting a pasture for one or more years, deferring grazing until after seed maturity of specified key species, and season-long grazing. It is intended to promote the vigor and seedling success of forage species by rest and deferment, promote seed planting of forage species by the mechanical action of animal movement following deferment, reduce ill effects of repeated overuse of preferred areas (such as near water) that commonly occur with continuous grazing, and increase animal productivity as a consequence of increasing forage productivity. Recently it seems that many misconceptions have developed concerning the applicability and successful design of restrotation grazing management systems. The need for a more general understanding of the applications of deferred and rest-rotation grazing management has been pointed out by The author is with the College of Forest Resources, ARtO, University of Washington, Seattle 98 195. The author wishes to express his appreciation to Imanuel Noy-Meir of the Hebrew University of Jerusalem, Israel, for his stimulating ideas, helpful suggestions, and permiission to use his figures. ManLuscript received February 5, 1978. Hyder and Bement (1977). A better understanding of the dynamics of herbivore-plant systems should provide a stronger basis upon which to assess the consequences of a particular grazing management plan. Considerable attention in the ecological literature has been given to analysis of predator-prey systems. Rosenzweig and MacArthur (1963) were first to show how graphical techniques, supplemented by mathematical analysis of the system behavior near equilibrium points, can be used to study the general stability properties of simple predator-prey systems. In a logical extension of the trophic relationships of predator-prey models, Noy-Meir (1975) has demonstrated a graphical analysis of herbivore (predator)-plant(prey) interactions. He described a simple model of grazing systems and analyzed its stability, seeking answers to the following questions: (1) What are the conditions for a specific grazing system (a given animal with a given vegetation) to be stable at a constant 'stocking rate (animal density)? (2) How does stability change with stocking and (3) What is the relation between productivity, stability, and stocking rate? It was found that in terms of system stability, five basic situations, or cases, could be distinguished. The purpose of the present paper is to extend Noy-Meir's analysis of herbivore-plant systems in general to rest-rotation grazing management of shrub-steppe range in the Great Basin, U.S.A., in particular. Only one of his cases will be considered, that of a discontinuously stable system with two distinct non-zero steady states and liable to extinction. Though the assumptions of such models can rightfully be questioned, there is considerable empirical evidence that their use in range systems is justified (Noy-Meir 1975).