Invasive Species Control Based on a Cooperative Game

İsmet Esra Büyüktahtakın, Zhuo Feng, George Frisvold, Ferenc Szidarovszky

Computer Science and Engineering, Arizona State University, Tempe, USA.
Department of Agricultural and Resource Economics, University of Arizona, Tucson, USA.
Department of Applied Mathematics, University of Pécs, Pécs, Hungary.
Department of Industrial and Manufacturing Engineering, Wichita State University, Wichita, USA.

DOI: 10.4236/am.2013.410A2005                

Abstract

We develop a long-term dynamic model for controlling invasive species using the theory of cooperative games. The model is applied to control of invasive buffelgrass in the Arizona desert, which directly competes with indigenous species and can increase wildfire risk. Interest groups care about damages to three threatened resources: saguaro, cactus, riparian vegetation, and buildings. The model optimally allocates labor and a budget to protect these resources by controlling the buffelgrass population over a multi-period planning horizon. The solution is based on computing the Shapley values for the interest groups. A homeowner strategy of creating defensible space around structures to protect against wildfire affords less protection to the other resources. A similar result holds for protection of saguaros, which are also spatially concentrated. Under the optimal solution, groups caring about spatially-dispersed, riparian vegetation would compensate homeowners and groups caring about saguaros for a reallocation of resources toward greater protection of dispersed vegetation. Results highlight the importance of the spatial configuration of players and the resources they wish to protect in invasive species control problems.

Keywords

Non-Native Invasive Species; Buffelgrass; Optimal Control; Integer Programming; Cooperative Games; Shapley Value

Conflicts of Interest

The authors declare no conflicts of interest.

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