THE LONG-TERM BIOECONOMIC IMPACTS OF GRAZING ON PLANT SUCCESSION IN ARANGELAND ECOSYSTEM

he on-site environmental impacts of for-profit livestock grazing on pr ivate rangeland are conceptualized as an interdependent pair of interr elated-species models defined over different time scales, Slow-manifol d theory links the fast (annual) dynamics of an optimization-based gra zing-decision submodel (formulating the predator-prey relationship bet ween livestock and vegetation), with the slow (decade) dynamics of a s pecies-competition submodel (specifying grazing-induced succession fro m 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 desirabil ity) is analytically approximated, and the approximation is analyzed f or its mathematical accuracy under various bioeconomic conditions. The approximated stable manifold represents a 'successional threshold' me asuring the resilience of the rangeland ecosystem in recovering from h istoric overgrazing. The successional threshold provides a means of ev aluating the environmental efficacy of agricultural programs which wou ld promote recovery of private rangeland by offering financial incenti ves to induce for-profit livestock enterprises to reduce grazing. (C) 1997 Elsevier Science B.V.