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Abstract
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.