Optimal resource management in the presence of a deleterious alien species: a stochastic model for an orchard

Resources such as orchards are vulnerable to the detrimental effects of successful invasions by alien animal or plant species. To outline an appropriate policy response, we first use renewal theory to construct a stochastic model of optimal orchard management in the presence of a deleterious alien species. Next, we derive the orchard manager’s long run expected cost (LREC) of orchard management per unit time. Finally, we show that when confronted with a successful biological invasion, the optimal number of trees that need to be removed and replanted in order to keep the orchard under study sustainable in the long run minimizes the LREC function mentioned above.

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