Positive Analysis of Invasive Species Control as a Dynamic Spatial Process

This paper models control of invasive buffelgrass (Pennisetum ciliare), a fire-prone African bunchgrass spreading rapidly across the southern Arizona desert as a spatial dynamic process. Buffelgrass spreads over a gridded landscape. Weed carrying capacity, treatment costs, and damages vary over grid cells. Damage from buffelgrass depends on its spatial distribution in relation to valued resources. We conduct positive analysis of recommended heuristic strategies for buffelgrass control, evaluating their ability to prevent weed establishment and to reduce damage indices over time. The high dimensionality of the problem makes full dynamic optimization intractable. However, two heuristic strategies – potential damage weighting and consecutive year treatment – perform well in terms of percent damage reduction relative to no treatment and to static optimization. Results also suggest specific recommendations for deployment of rapid rapid-response teams to prevent invasions in new areas. The long-run population size and spatial distribution of buffelgrass is sensitive to priority weights for protection of different resources. Land managers with different priorities may pursue quite different control strategies, which may pose a challenge for coordinating control across jurisdictions.