Skip to main content
SpringerLink
Log in

A multi-objective optimization approach for invasive species control

  • General Paper
  • Published:
Journal of the Operational Research Society

Abstract

In this paper, we formulate and analyse a long-term multi-objective dynamic model for controlling invasive species. This optimization framework is then applied to the case of buffelgrass control in the Arizona desert. The proposed model simultaneously optimizes three objectives corresponding to three different valued and threatened resources including saguaros (a native cactus species), buildings and vegetation. The model is used to decide the optimal allocation of labour to these resources to control the population of the species in a multi-period planning horizon. The computational method to solve this problem is based on multi-objective integer programming.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Figure 13

Similar content being viewed by others

References

  • Betancourt JL (2007). From fireproof desert to flammable grassland: buffelgrass invasion in the Sonoran Desert. Proceedings of the American Geophysical Union, 2007 Fall Meeting.

  • Bowers JE, Bean TM and Turner RM (2006). Two decades of change and distribution of exotic plants at the desert laboratory, Tucson, Arizona. Madroño 53 (3): 252–263.

    Article  Google Scholar 

  • Burnett K, Kaiser B and Roumasset J (2007). Economic lessons from control efforts for an invasive species: Miconia calvescens in Hawaii. Journal of Forest Economics 13 (2–3): 151–167.

    Article  Google Scholar 

  • Burquez-Montijo A, Miller ME and Martinez-Yrizar A (2002). Mexican grasslands, thornscrub, and the transformation of the Sonoran Desert by invasive exotic buffelgrass (Pennisetum ciliare). In Tellman B (ed). Invasive Exotic Species in the Sonoran Region. The University of Arizona Press and the Arizona-Sonora Desert Museum: Tucson, pp 126–146.

    Google Scholar 

  • Büyüktahtakın İE, Zhuo F, Olsson A, Frisvold G and Szidarovszky F (2010). Positive Analysis of Invasive Species Control as a Dynamic Spatial Process, In 2010 Annual Meeting, July 25–27, 2010, Denver, Colorado (No. 61753), Agricultural and Applied Economics Association.

  • Büyüktahtakın İE, Zhuo F, Olsson A, Frisvold G and Szidarovszky F (2011). A dynamic model of controlling invasive species. Computers and Mathematics with Applications 62 (9): 3326–3333.

    Article  Google Scholar 

  • Cacho OJ, Wise RM, Hester SM and Sinden JA (2008). Bioeconomic modeling for control of weeds in natural environments. Ecological Economics 65 (3): 559–568.

    Article  Google Scholar 

  • Clark C (1990). Mathematical Bioeconomics: The Optimal Management of Renewable Resources. 2nd edn. Wiley-Interscience: Hoboken, NJ.

    Google Scholar 

  • Clarke PJ, Latz PK and Albrecht DE (2005). Long-term changes in semi-arid vegetation: invasion of an exotic perennial grass has larger effects than rainfall variability. Journal of Vegetation Science 16 (2): 237–248.

    Article  Google Scholar 

  • Costello C, Springborn M, McAusland C and Slow A (2007). Unintended biological invasions: does risk vary by trading partner? Journal of Environmental Economics and Management 54 (3): 262–276.

    Article  Google Scholar 

  • D’Antonio CM and Vitousek PM (1992). Biological invasions by exotic grasses, the grass/fire cycle, and global change. Annual Review of Ecology and Systematics 23 (1): 63–87.

    Article  Google Scholar 

  • Eiswerth ME and Johnson WS (2002). Managing nonindigenous invasive species: insights from dynamic analysis. Environmental and Resource Economics 23 (3): 319–342.

    Article  Google Scholar 

  • Epanchin-Niell RS and Hastings A (2010). Controlling established invaders: Integrating economics and spread dynamics to determine optimal management. Ecology Letters 13 (4): 528–541.

    Article  Google Scholar 

  • Epanchin-Niell RS and Wilen J (2012). Optimal spatial control of biological invasions. Journal of Environmental Economics and Management 63 (2): 260–270.

    Article  Google Scholar 

  • Esque TC, Schwalbe CR, Haines DF and Halvorson WL (2004). Saguaros under siege: invasive species and fire. Desert Plants 20 (1): 49–55.

    Google Scholar 

  • Frid L et al (2013). Using state-and-transition modeling to account for imperfect detection in invasive species management. Invasive Plant Science and Management 6 (1): 36–47.

    Article  Google Scholar 

  • Halvorson WL and Guertin P (2003). USGS weeds in the west project: status of introduced plants in Southern Arizona Parks. Factsheet for Pennisetum ciliare (L.) U.S. Geological Survey/Southwest Biological Science Center, Tucson, AZ. http://www.buffelgrass.org/sites/default/files/pennfacts.pdf, accessed 9 April 2013.

  • Hof J and Bevers M (1998). Spatial Optimization for Managed Ecosystems. Columbia University Press: New York.

    Google Scholar 

  • Hof J and Bevers M (2002). Spatial Optimization in Ecological Applications. Columbia University Press: New York.

    Book  Google Scholar 

  • ILOG CPLEX (2010). IBM ILOG CPLEX: high-performance mathematical programming engine. http://www-01.ibm.com/software/integration/optimization/cplex/, accessed 9 April 2013.

  • Jackson J (2005). Is there a relationship between herbaceous species richness and buffelgrass (Cenchrus ciliaris)? Austral Ecology 30 (5): 505–517.

    Article  Google Scholar 

  • Jetter KM, DiTomaso JM, Drake DJ, Klonsky KM, Pitcairn MJ and Sumner DA (2003). Biological control of yellow starthistle. In Sumner DA (ed). Exotic Pests and Diseases: Biology and Economics for Biosecurity. Iowa State University Press: Ames, pp 225–241.

    Chapter  Google Scholar 

  • Kulhanek SA, Leung B and Ricciardi A (2011). Using ecological niche models to predict the abundance and impact of invasive species: application to the common carp. Ecological Applications 21 (1): 203–13.

    Article  Google Scholar 

  • Levin SA, Muller-Landau HC, Nathan R and Chave J (2003). The ecology and evolution of seed dispersal: a theoretical perspective. Annual Review of Ecology Evolution and Systematics 34: 575–604.

    Article  Google Scholar 

  • Luken JO and Thieret JW (eds) (1997). Assessment and Management of Plant Invasions. Springer-Verlag: New York.

    Book  Google Scholar 

  • Martin B, Hanna D, Korb N and Frid L (2007). Decision analysis of alternative invasive weed management strategies for three Montana landscapes. Prepared by the Nature Conservancy of Montana, Helena, MT, and ESSA Technologies Ltd., Vancouver, BC, p 34.

  • Moody ME and Mack RN (1988). Controlling the spread of plant invasions: the importance of nascent foci. Journal of Applied Ecology 25 (3): 1009–1021.

    Article  Google Scholar 

  • Nemhauser GL and Wolsey LA (1988). Integer and Combinatorial Optimization. John Wiley & Sons: New York.

    Book  Google Scholar 

  • Niering WA and Lowe CH (1984). Vegetation of the Santa Catalina Mountains: community types and dynamics. Vegetation 58 (1): 3–28.

    Google Scholar 

  • Odom DIS, Cacho OJ, Sinden JA and Griffith GR (2003). Policies for the management of weeds in natural ecosystems: the case of Scotch broom (Cytisus scoparius, L.) in an Australian national park. Ecological Economics 44 (1): 119–135.

    Article  Google Scholar 

  • Odom D, Sinden JA, Cacho O and Griffith GR (2005). Economic issues in the management of plants invading natural environments: Scotch broom in Barrington Tops National Park. Biological Invasions 7 (3): 445–457.

    Article  Google Scholar 

  • Olson LJ (2006). The economics of terrestrial invasive species: a review of the literature. Agricultural and Resource Economics Review 35 (1): 178–194.

    Article  Google Scholar 

  • Olson LJ and Roy S (2002). The economics of controlling a stochastic biological invasion. American Journal of Agricultural Economics 84 (5): 1311–1316.

    Article  Google Scholar 

  • Olson LJ and Roy S (2010). Dynamic sanitary and phytosanitary trade policy. Journal of Environmental Economics and Management 60 (1): 21–30.

    Article  Google Scholar 

  • Olsson AD, Betancourt JL, Crimmins MA and Marsh SE (2012). Constancy of local spread rates for buffelgrass (Pennisetum ciliare L.) in the Arizona Upland of the Sonoran Desert. Journal of Arid Environments 87 (1): 136–143.

    Article  Google Scholar 

  • Pimentel D, Lach L, Zuniga R and Morrison D (2000). Environmental and economic costs of nonindigenous species in the United States. BioScience 50 (1): 53–65.

    Article  Google Scholar 

  • Rogstad A (ed) (2008). Southern Arizona buffelgrass strategic plan: a regional guide for control, mitigation, and restoration. Buffelgrass Working Group. Tucson, AZ, p 204.

  • Sheley RL and Petroff JK (eds) (1999). Biology and Management of Noxious Rangeland Weeds. Oregon State University Press: Corvallis, OR.

    Google Scholar 

  • Smith M, Sanchirico J and Wilen J (2009). The economics of spatial-dynamic processes: applications to renewable resources. Journal of Environmental Economics and Management 57 (1): 104–121.

    Article  Google Scholar 

  • Southern Arizona Buffelgrass Coordination Center (2007). Buffelgrass invasion in the Sonoran Desert: imminent risks and unavoidable mitigation http://www.buffelgrass.org/sites/default/files/invasion.pdf, accessed 9 April 2013.

  • Stevens J and Falk DA (2009). Can buffelgrass invasions be controlled in the American Southwest? using invasion ecology theory to understand buffelgrass success and develop comprehensive restoration and management. Ecological Restoration 27 (4): 417–427.

    Article  Google Scholar 

  • Szidarovszky F, Gershon M and Duckstein L (1986). Techniques of Multiobjective Decision Making in Systems Management. Elsevier: Amsterdam.

    Google Scholar 

  • Taylor CM and Hastings A (2004). Finding optimal control strategies for invasive species: a density-structured model for Spartina alterniflora. Journal of Applied Ecology 41 (6): 1049–1057.

    Article  Google Scholar 

  • VanDerWal J, Shoo LP, Johnson CN and Williams SE (2009). Abundance and the environmental niche: environmental suitability estimated from niche models predicts the upper limit of local abundance. American Naturalist 174 (2): 282–291.

    Article  Google Scholar 

  • Vitousek PM, D’Antonio CM, Loope LL and Westbrooks R (1996). Biological invasions as global environmental change. American Scientist 84 (5): 468–478.

    Google Scholar 

  • Wadsworth RA, Collingham YC, Willis SG, Huntley B and Hulme PE (2000). Simulating the spread and management of alien riparian weeds: are they out of control? Journal of Applied Ecology 37 (Supplement 1): 28–38.

    Article  Google Scholar 

  • Wilen JE (2007). Economics of spatial-dynamic processes. American Journal of Agricultural Economics 89 (5): 1134–1144.

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank George Frisvold and Aaryn Olsson for providing insights to the model and the data needed to conduct the experiments in this paper. The authors are also grateful to three anonymous referees and the associate editor for their insightful comments.

Author information

Authors and Affiliations

  1. Wichita State University, Wichita, USA

    İ Esra Büyüktahtakın

  2. Arizona State University, Phoenix, USA

    Zhuo Feng & Ferenc Szidarovszky

  3. University of Pécs, Pécs, Hungary

    Ferenc Szidarovszky

Authors
  1. İ Esra Büyüktahtakın
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhuo Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ferenc Szidarovszky
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to İ Esra Büyüktahtakın.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Büyüktahtakın, İ., Feng, Z. & Szidarovszky, F. A multi-objective optimization approach for invasive species control. J Oper Res Soc 65, 1625–1635 (2014). https://doi.org/10.1057/jors.2013.104

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1057/jors.2013.104

Keywords

Search

Navigation