".~ ~" • • t'J ELSEVIER EcologicalModelling97 (1997) 59-73 mooL n6 The long-term bioeconomic impacts of grazing on plant succession in a rangeland ecosystem Kevin Cooper a,., Ray Huffaker b a Department of Pure and Applied Mathematics, Washington State University, Pullman WA 99164, USA b Department of Agricultural Economics, Washington State University, Pullman WA 99164, USA Received3 May 1995;accepted8 August 1996 Abstract The on-site environmental impacts of for-profit livestock grazing on private rangeland are conceptualized as an interdependent pair of interrelated-species models defined over different time scales. Slow-manifold theory links the fast (annual) dynamics of an optimization-based grazing-decision submodel (formulating the predator-prey relationship between livestock and vegetation), with the slow (decade) dynamics of a species-competition submodel (specifying grazing-induced succession from perennial grasses to less environmentally-desirable annual species). A stable manifold (partitioning phase space into basins-of-attraction to equilibria representing plant states of differing social desirability) is analytically approxi- mated, and the approximation is analyzed for its mathematical accuracy under various bioeconomic conditions. The approximated stable manifold represents a 'successional threshold' measuring the resilience of the rangeland ecosystem in recovering from historic overgrazing. The successional threshold provides a means of evaluating the environmental efficacy of agricultural programs which would promote recovery of private rangeland by offering financial incentives to induce for-profit livestock enterprises to reduce grazing. © 1997 Elsevier Science B.V. Keywords: Plant succession;Livestock grazing economics; Successionalthreshold 1. Introduction The ecological structure of seral grassland com- munities is significantly determined by competition among constituent plant species (Evans and Young, 1972). In the intermountain region of the United States, and in the absence of grazing livestock, rangeland is dominated by highly competitive peren- nial grasses (e.g., bluestem, grama and bunch grasses) as understory species to sagebrush. However, his- * Correspondingauthor.Tel.: + 1-509-3354308. toric overgrazing by livestock on preferred perennial grasses has reduced these grasses' vigor, and thus their ability to withstand the invasion of highly competitive alien annual grasses, introduced inadver- tently by immigrant settlers. Currently, millions of acres in the intermountain region are dominated by alien annual grasses, principally cheatgrass (Bromus tectorura L.) (Evans and Young, 1972). Cheatgrass is not valueless in livestock production, but several drawbacks render it less productive than perennial grasses. Moreover, cheatgrass promotes several envi- ronmental problems. It is more superficially rooted 0304-3800/97/$17.00 © 1997ElsevierScienceB.V. All fights reserved. PH S0304-3 800(96)00072-5