Optimal Resource Management in the Presence of a Deleterious Alien Species: A Stochastic Model for an Orchard

Abstract

Various plants and 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 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 function mentioned above.

An approach to the management of orchards that are vulnerable to attack by invasive species

“…Batabyal and Yoo (2007a) contend that judicious orchard management involves solving an optimization problem in which an economic objective function is minimized subject to an ecological constraint which says that the probability that the orchard under study is not Holling resilient 1 is at most as large as an exogenously given value. Finally, in a paper that is similar in spirit to our paper, Batabyal and Nijkamp (2008a) have used a renewal theoretic approach to show that the critical number of trees in an orchard that must be infected and diseased before the manager takes his prophylactic tree removal and replanting actions is the solution to a particular minimization problem.…”

“…Therefore, efficient orchard management ought to clearly account for this aspect of the management problem. Now, even though the Batabyal and Yoo (2007a) and the Batabyal and Nijkamp (2008a) papers mentioned in the preceding paragraph have begun the process of modeling the above stated two points explicitly, the systematic study of these two salient points in the context of orchard management is still in its infancy.…”