Optimizing the use of suppression zones for containment of invasive species

Abstract

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.

Optimizing strategies for slowing the spread of invasive species

“…This is because, if α > 0, it is more cost-effective to reduce the population in locations where its density is higher, and treatment in areas where n ( x ) is larger reduces propagule pressure in areas where n ( x ) is close to zero. This result is consistent with the result of [ 21 ], who examined the special case in which v = 0 and considered a similar (though not identical) model. They showed that, if α = 0, treatment is needed only in locations x where n ( x ) = 0 (i.e., only a “barrier zone” is needed); but if treatment efficiency is proportional to the population size ( α = 1), treatment is needed in some areas where n ( x ) > 0 (i.e., optimal treatment dictated treating in some “suppression zone”).…”

“…Specifically, if the dynamics are time-continuous, they are given by [ 21 , 49 , 50 , 52 ] where d ( n ) is the rate of adult natural mortality, R ( n , A ) is the rate of adult removal due to the treatment, b ( n ) is the rate of propagule production, and G is the dispersal kernel that determines how propagules disperse over space [ 51 ]. Note that the rates d , R , and b vary over time and space due to their dependency on n ( x , t ) and A ( x , t ).…”

“…We begin here with a simple and general model, while in the next sub-section we describe the model that applies to the spongy moth. For the simple model, we consider continuous-time dynamics (Eq ( 1 )) with the following birth and death rates [ 21 ]: where γ is the rate of adult natural mortality, r is the per-capita rate of juvenile production when the population is small, and k is the carrying capacity. We consider the following, widely-used form of the dispersal kernel function [ 51 ]: where σ is the characteristic dispersal length.…”

“…Note that this algorithm extends the algorithm developed in [ 21 ] to cases in which v ≠ 0, and also to the study of more general response functions of the species to the treatment, such as those incorporated in Eqs ( 5 ) and ( 6 – 8 ). The complete code can be found on Zenodo [ 59 ]. Results as raw data can be found on Dryad [ 60 ].…”

“…In turn, containment often necessitates treatment over large areas and includes surveillance and eradication in regions close to the invasion area, suppression of the population in regions where it has already been established, and limiting the dispersal of the species into uninvaded areas at the borders between these regions to reduce propagule pressure, where all these treatment strategies are interrelated and can be used simultaneously [ 21 ]. A major question is, therefore, how managers should distribute the treatment efforts over space and time to minimize the net cost due to both treatment and damage.…”