Discussion Paper

Optimal Control of Spatial-Dynamic Processes: The Case of Biological Invasions

Mar 3, 2011 | Rebecca Epanchin-Niell, James E. Wilen

Abstract

This study examines the spatial nature of optimal bioinvasion control. We develop a spatially explicit two-dimensional model of species spread that allows for differential control across space and time, and we solve for optimal spatial-dynamic control strategies. We find that the optimal strategies depend in interesting ways on the shape of the landscape and the location, shape, and contiguity of the invasion. For example, changing the shape of the invasion or using landscape features to reduce the extent of exposed invasion edge can be an optimal strategy because it reduces long-term containment costs. We also show that strategies should be targeted to slow or prevent the spread of an invasion in the direction of greatest potential long-term damages. These spatially explicit characterizations of optimal policies contribute to the largely nonspatial literature on controlling invasions and our general understanding of how to control spatial-dynamic processes.

Invasive species cause significant economic and ecological damage worldwide. An invasion may start with the arrival of only a couple of individuals (for example, wood-boring beetles), but can quickly spread, infesting an entire landscape. It is important to understand how to best manage an invasion in order to minimize damages to the environment and costs of control.

Most studies have focused on when to control an invasion, and to what extent. However, in a new RFF Discussion Paper, “Optimal Control of Spatial-Dynamic Processes: The Case of Biological Invasions,” authors Rebecca S. Epanchin-Nielland James E. Wilen develop a new bioeconomic model to explore exactly where to focus control efforts and how the landscape may impact those decisions.

The results of the study provide important insights into how space can affect solutions to dynamic problems. The authors demonstrate that the shape of a landscape and its boundaries, the location of an invasion within a landscape, and the shape of an invasion can significantly affect the best control strategy (for example, eradication versus containment). Epanchin-Niell and Wilen found that strategically employing landscape features, such as natural barriers to spread or constrictions in a species’ potential range, to contain the spread of an invasion can be an optimal strategy because it reduces long-term containment costs.

Overall, optimal invasion-control strategies should be spatially and temporally forward-looking, targeted to slow or prevent the spread of an invasion where there is the potential for the greatest long-term damages or where control costs are lowest.