AM  Vol.4 No.10 B , October 2013
Invasive Species Control Based on a Cooperative Game
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.


Cite this paper
İ. Büyüktahtakın, Z. Feng, G. Frisvold and F. Szidarovszky, "Invasive Species Control Based on a Cooperative Game," Applied Mathematics, Vol. 4 No. 10, 2013, pp. 54-59. doi: 10.4236/am.2013.410A2005.
References
[1]   R. Epanchin-Niell and A. Hastings, “Controlling Established Invaders: Integrating Economics and Spread Dynamics to Determine Optimal Management,” Ecology Letters, Vol. 13, No. 4, 2010, pp. 528-541. http://dx.doi.org/10.1111/j.1461-0248.2010.01440.x

[2]   J. Luken and J. Thieret, “Assessment and Management of Plant Invasions,” Springer-Verlag, New York, 1997. http://dx.doi.org/10.1007/978-1-4612-1926-2

[3]   R. Sheley and J. Clark, “Biology and Management of Noxious Rangeland Weeds,” Oregon State University Press, Oregon, 1999.

[4]   D. Pimentel, L. Lach, R. Zuniga and D. Morrison, “Environmental and Economic Costs of Nonindigenous Species in the United States,” BioScience, Vol. 50, No. 1, 2000, pp. 53-65. http://dx.doi.org/10.1641/0006-3568(2000)050[0053:EAECON]2.3.CO;2

[5]   M. Moody and R. Mack, “Controlling the Spread of Plant Invasions: The Importance of Nascent Foci,” Journal of Applied Ecology, Vol. 25, No. 3, 1988, pp. 1009-1021. http://dx.doi.org/10.2307/2403762

[6]   B. Martin, D. Hanna, N. Korb and L. Frid, “Decision Analysis of Alternative Invasive Weed Management Strategies for Three Montana Landscapes,” The Nature Conservancy of Montana, Helena, MT and ESSA Technologies Ltd., Vancouver, 2007.

[7]   R. Wadsworth, Y. Collingham, S. Willis, B. Huntley and P. Hulme, “Simulating the Spread and Management of Alien Riparian Weeds: Are They out of Control?” Journal of Applied Ecology, Vol. 37, Suppl. s1, 2000, pp. 2838. http://dx.doi.org/10.1046/j.1365-2664.2000.00551.x

[8]   K. Jetter, J. DiTomaso, D. Drake, K. Klonsky, M. Pitcairn and D. Sumner, “Biological Control of Yellow Starthistle,” In: D. A. Sumner, Ed., Exotic Pests and Diseases: Biology and Economics for Biosecurity, Iowa State University Press, Ames, 2003, pp. 121-150.

[9]   L. Olson, “The Economics of Terrestrial Invasive Species: A Review of the Literature,” Agricultural and Resource Economics Review, Vol. 35, No. 1, 2006, p. 178.

[10]   C. Clark, “Mathematical Bioeconomics: The Optimal Management of Renewable Resources,” 2nd Edition, Wiley, New York, 1990.

[11]   C. Taylor and A. Hastings, “Finding Optimal Control Strategies for Invasive Species: A Density Structured Model for Spartina Alterniflora,” Journal of Applied Ecology, Vol. 41, No. 6, 2004, pp. 1049-1057. http://dx.doi.org/10.1111/j.0021-8901.2004.00979.x

[12]   K. Burnett, B. Kaiser and J. Roumasset, “Economic Lessons from Control Efforts for an Invasive Species: Miconia Calvescens in Hawaii,” Journal of Forest Economics, Vol. 13, No. 2-3, 2007, pp. 151-167. http://dx.doi.org/10.1016/j.jfe.2007.02.007

[13]   L. Olson and S. Roy, “The Economics of Invasive Species Management: The Economics of Controlling a Stochastic Biological Invasion,” American Journal of Agricultural Economics, Vol. 84, No. 5, 2002, pp. 1311-1316. http://dx.doi.org/10.1111/1467-8276.00395

[14]   I. E. Büyüktahtakin, F. Zhuo, A. Olsson, G. Frisvold and F. Szidarovszky, “Positive Analysis of Invasive Species Control as a Dynamic Spatial Process,” 2010 Annual Meeting, Denver, 25-27 July 2010, pp. 1-33.

[15]   I. E. Büyüktahtakin, F. Zhuo, G. Frisvold and F. Szidarovszky and A. Olsson, “A Dynamic Model of Controlling Invasive Species,” Computers and Mathematics with Applications, Vol. 62, No. 9, 2011, pp. 3326-3333. http://dx.doi.org/10.1016/j.camwa.2011.08.037

[16]   I. E. Büyüktahtakin, F. Zhuo and F. Szidarovszky, “A Multi-Objective Optimization Model for Invasive Species Control,” Journal of Operational Research Society, 2013, in Press.

[17]   I. E. Büyüktahtakin, F. Zhuo, G. Frisvold and F. Szidarovszky, “A Game Theoretical Approach to Invasive Species Management,” Proceedings of the 2011 Industrial Engineering Research Conference, Reno, 20-22 May 2011.

[18]   F. Forgó, J. Szép and F. Szidarovszky, “Introduction to the Theory of Games: Concepts, Methods, Applications,” Kluwer Academic Publishers, Dordrecht, 1999.

[19]   M. Osborne, “An Introduction to Game Theory,” Oxford University Press, New York, 2004.

[20]   J. Nash, “The Bargaining Problem,” Econometrica, Vol. 18, No. 2, 1950, pp. 155-162. http://dx.doi.org/10.2307/1907266

[21]   A. Roth, “Axiomatic Models of Margaining,” SpringerVerlag, New York, 1979. http://dx.doi.org/10.1007/978-3-642-51570-5

[22]   F. Szidarovszky, M. Gershon and L. Duckstein, “Techniques for Multiobjective Decision Making in Systems Management,” Elsevier, Amsterdam, 1986.

[23]   R. Cyert and M. DeGroot, “An Analysis of Cooperation and Learning in a Duopoly Context,” The American Economic Review, Vol. 63, No. 1, 1973, pp. 24-37.

[24]   S. S. Lloyd, “A Value for N-Person Games,” In: H. W. Kuhn and A. W. Tucker, Eds., Contributions to the Theory of Games, Volume II, Annals of Mathematical Studies, Princeton University Press, Princeton, 1953, pp. 307-317.

[25]   A. Roth, “Axiomatic Models of Margaining,” SpringerVerlag, New York, 1979. http://dx.doi.org/10.1007/978-3-642-51570-5

[26]   O. Cacho, R. Wise, S. Hester and J. Sinned, “Bioeconomic Modeling for Control of Weeds in Natural Environments,” Ecological Economics, Vol. 65, No. 3, 2008, pp. 559-568. http://dx.doi.org/10.1016/j.ecolecon.2007.08.006

[27]   A. Rogstad, “Southern Arizona Buffelgrass Strategic Plan: A Regional Guide for Control, Mitigation, and Restoration,” U. B. W. Group, Tucson, 2008.

[28]   J. E. Bowers, T. M. Bean and R. M. Turner, “Twodecades of Change and Distribution of Exotic Plants at the Desert Laboratory, Tucson, Arizona,” Madrono, Vol. 53, No. 3, 2006, pp. 252-263. http://dx.doi.org/10.3120/0024-9637(2006)53[252:TDOCID]2.0.CO;2

[29]   G. L. Nemhauser and L. A. Wolsey, “Integer and Combinatorial Optimization,” John Wiley & Sons, New York, 1988.

[30]   ILOG CPLEX, “IBM ILOG CPLEX: High-Performance Mathematical Programming Engine,” 2013. http://www-01.ibm.com/software/integration/optimization/cplex

 
 
Top