Invasive Species Control Optimization as a Dynamic Spatial Process: An Application to Buffelgrass (Pennisetum ciliare) in Arizona

Abstract Buffelgrass (Pennisetum ciliare) is a fire-prone, African bunchgrass spreading rapidly across the southern Arizona desert. This article introduces a model that simulates buffelgrass spread over a gridded landscape over time to evaluate strategies to control this invasive species. Weed-carrying capacity, treatment costs, and damages vary across grid cells. Damage from buffelgrass depends on its density and proximity to valued resources. Damages include negative effects on native species (through spatial competition) and increased fire risk to land and buildings. We evaluate recommended “rule of thumb” control strategies in terms of their ability to prevent weed establishment in newly infested areas and to reduce damage indices over time. Two such strategies—potential damage weighting and consecutive year treatment—used in combination, provided significant improvements in long-term control over no control and over a strategy of minimizing current damages in each year. Results suggest specific recommendations for deploying rapid-response teams to prevent establishment in new areas. The long-run population size and spatial distribution of buffelgrass is sensitive to the priority given to protecting different resources. Land managers with different priorities may pursue quite different control strategies, posing a challenge for coordinating control across jurisdictions. Nomenclature: Buffelgrass, Pennisetum ciliare (L.) Link. Management Implications: A key challenge facing land managers is how best to allocate limited resources to control invasive plant species across space and time. Optimization models are useful tools for exploring alternative strategies to optimally allocate scarce resources, such as treatment control teams and budgets, and to protect valued resources from invasion of nonnative species. In this article, we developed a mathematical model to provide guidance to land managers for addressing the following concerns: (1) the optimal size of treatment teams; (2) where, when, and what size of infestation those teams should target; and (3) the number of years for which follow-up treatments should continue. Because of the many variables interrelated across both space and time, solving such a completely forward-looking (i.e., takes full account of how all current decisions affect all future options and decisions) problem may prove intractable. Instead, we compare three “rules-of-thumb” strategies: (1) minimize current invasive species damage; (2) minimize current damage, given that any areas treated are treated in at least 3 consecutive yr; and (3) prioritize treatment based not only on current damages but also on the potential future damages of leaving an infested area untreated. The second and third strategies are also considered in combination. We evaluate those rules of thumb for their ability to prevent weed establishment in newly infested areas and to reduce damage indices over time. The rules have the advantage of telling land managers to “treat these lands now. ” Another advantage of this approach is its applicability because Microsoft Excel spreadsheets—used broadly by land and resource managers in the area—are customized to (1) manage data layers, (2) use cell formulae to maintain relationships across space and time, and (3) use the chart function to produce maps of costs, damages, weed population, and treatment recommendations. The ILOG CPLEX software package (IBM), a powerful tool for solving linear integer (binary) programs, interfaces with Excel programs so that model solutions can be readily converted to treatment priority (and other) maps. We found that the long-run population size and spatial distribution of buffelgrass are sensitive to priority weights for protecting resources. Results also indicate that resources must be increased because they are currently insufficient to control the spread of buffelgrass.