Optimizing the use of suppression zones for containment of invasive species

Despite efforts to prevent their establishment, many invasive species continue to spread and threaten food production, human health, and natural biodiversity. Slowing the spread of established species is often a preferred strategy; however, it is also expensive and necessitates treatment over large areas. Therefore, it is critical to examine how to distribute management efforts over space cost-effectively. Here we consider a continuous-space bioeconomic model and we develop a novel algorithm to find the most cost-effective allocation of treatment efforts throughout a landscape. We show that the optimal strategy often comprises eradication in the yet-uninvaded area, and under certain conditions, it also comprises maintaining a "suppression zone," an area between the invaded and the uninvaded areas, where treatment reduces the invading population but without eliminating it. We examine how the optimal strategy depends on the demographic characteristics of the species and reveal general criteria for deciding when a suppression zone is cost effective.