TITLE:
Invasive Species Control Based on a Cooperative Game
AUTHORS:
İsmet Esra Büyüktahtakın, Zhuo Feng, George Frisvold, Ferenc Szidarovszky
KEYWORDS:
Non-Native Invasive Species; Buffelgrass; Optimal Control; Integer Programming; Cooperative Games; Shapley Value
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.10B,
October
4,
2013
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.