The long-term bioeconomic impacts of grazing on plant succession in a rangeland ecosystem

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 approximated, 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