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.

Abstract: Strategies for controlling invasive species can be aimed at any or all of the stages in the life cycle. In this paper we show how to combine biological data on population dynamics with simple economic data on control cost options to determine the least costly set of strategies that will halt an invasion. We then apply our methods to oyster drills (Ocinebrellus inornatus), an economically important aquaculture pest that has been accidentally introduced worldwide. If the costs of intervention were the same across life stages, extermination of adults would be an inefficient way to control species with the population dynamics characteristics of invaders. In the oyster drill case, however, efficient control targets adults because they are much easier to find.