A Dynamic Optimisation Model of Weed Control

It is argued in this paper that static approaches to weed management, where the benefits and costs are only considered within a single season, are inappropriate for assessing the economic benefits of weed control technologies. There are carryover effects from weed management as weeds that escape control in one season may reproduce and replenish weed populations in following seasons. Consequently, it is appropriate to view weed control in the context of a resource management problem where the goal is to determine the optimal inter-temporal level of weed control that maximises economic benefits over some pre-determined period of time. A dynamic optimisation model for weed control is presented. Using the tools of comparative static analysis and Pontryagin's maximum principle, the conditions for optimal input use (ie weed control) are compared for static and dynamic situations. It is shown that a higher level of input use for a given weed population is optimal using a dynamic framework than would be derived under a static framework. The analysis is further extended by the incorporation of uncertainty and shows that the optimal level of weed control is also affected by uncertainty in herbicide efficacy and the survival of weed seeds produced. A case study of the optimal long-term management under deterministic and stochastic conditions of an annual cropping weed, Avena fatua, is presented