On Temporal Controls and the Stochastic Behavior of Renewable Natural Resources

This paper provides a theoretical analysis of the effects of temporal controls on the stochastic behavior of renewable natural resources such as fisheries and rangelands. First, we show that temporal resource management is characterized by the existence of a threshold effect. Second, we point out that in the presence of environmental uncertainty, the ability of a manager to move a resource to a desirable state depends on the magnitude of the effect that the temporal control has on the state of the resource. Third, we show that if this magnitude is below a critical threshold then it will be impossible for the manger to reach any desirable state of the resource in a finite amount of time. Finally, we solve an optimization problem from the standpoint of a resource manager. Our analysis of this problem shows that the proper course of action involves choosing the temporal control in a way so that the resource is able to provide society with a flow of consumptive and non-consumptive services, and the persistence of the undesirable state is minimized