Abstract
Invasive species impact human activities. We can respond using a range of strategies, including detection, adaptation, and control (via prevention and eradication). But what strategies are best, and when should we use them? To answer these questions, we couple models for species establishment and spread with those for impact and control. A final level of modeling puts associated costs and benefits into an economic framework. Optimal strategies are then based on a cost–benefit analysis that involves methods of optimization, including optimal control theory, stochastic dynamic programming, and linear programming.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Blackwood, J., Hastings, A., Costello, C.: Cost-effective management of invasive species using linear-quadratic control. Ecol. Econ. 69, 519–527 (2010). doi:10.1016/j.ecolecon.2009.08.029
Bogich, T.L., Liebhold, A.M., Shea, K.: To sample or eradicate? A cost minimization model for monitoring and managing an invasive species. J. Appl. Ecol. 45, 1134–1142 (2008). doi:10.1111/j.1365-2664.2008.01494.x
Burnett, K.M., D’Evelyn, S., Kaiser, B.A., Nantamanasikarn, P., Roumasset, J.A.: Beyond the lamppost: optimal prevention and control of the Brown Tree Snake in Hawaii. Ecol. Econ. 67, 66–74 (2008). doi:10.1016/j.ecolecon.2007.11.012
Caswell, H.: Matrix Population Models: Construction, Analysis, and Interpretation. Sinauer Associates, Sunderland (2001)
Clark, C.W.: Mathematical Bioeconomics: The Optimal Management of Renewable Resources. Wiley, New York (1990)
Clark, C.W., Mangel, M.: Dynamic State Variable Models in Ecology. Oxford Series in Ecology and Evolution. Oxford University Press, Oxford (2000)
Dantzig, G.B.: Linear Programming and Extensions. Princeton University Press, Princeton (1998)
Epanchin-Niell, R.S., Haight, R.G., Berec, L., Kean, J.M., Liebhold, A.M.: Optimal surveillance and eradication of invasive species in heterogeneous landscapes. Ecol. Lett. 15, 803–812 (2012). doi:10.1111/ j.1461-0248.2012.01800.x
Field, S.A., Tyre, A.J., Possingham, H.P.: Optimizing allocation of monitoring effort under economic and observational constraints. J. Wildl. Manag. 69(2), 473–482 (2005). doi:10.2193/0022-541x(2005) 069[0473:oaomeu]2.0.co;2
Finnoff, D., Potapov, A., Lewis, M.A.: Control and the management of a spreading invader. Resour. Energy Econ. 32, 534–550 (2010). doi:10.1016/j.reseneeco.2010.04.003
Hastings, A., Hall, R.J., Taylor, C.M.: A simple approach to optimal control of invasive species. Theor. Popul. Biol. 70(4), 431–435 (2006). doi:10.1016/j.tpb.2006.05.003
Hauser, C.E., McCarthy, M.A.: Streamlining “search and destroy”: cost-effective surveillance for invasive species management. Ecol. Lett. 12, 683–692 (2009). doi:10.1111/j.1461-0248.2009.01323.x
Keller, R.P., Lodge, D.M., Lewis, M.A., Shogren, J.F.: Bioeconomics of Invasive Species: Integrating Ecology, Economics, Policy, and Management. Oxford University Press, Oxford (2009)
Leung, B., Lodge, D.M., Finnoff, D., Shogren, J.F., Lewis, M.A., Lamberti, G.: An ounce of prevention or a pound of cure: bioeconomic risk analysis of invasive species. Proc. R. Soc. B 269, 2407–2413 (2002). doi:10.1098/rspb.2002.2179
Lewis, M.A., Potapov, A.B., Finnoff, D.C.: Modeling integrated decision-making responses to invasive species. In: Keller, R.P., Lodge, D.M., Lewis, M.A., Shogren, J.F. (eds.) Bioeconomics of Invasive Species: Integrating Ecology, Economics, Policy, and Management, pp. 180–204. Oxford University Press, Oxford (2009)
Mehta, S.V., Haight, R.G., Homans, F.R., Polasky, S., Venette, R.C.: Optimal detection and control strategies for invasive species management. Ecol. Econ. 61, 237–245 (2007). doi:10.1016/j.ecolecon. 2006.10.024
Petrovskii, S., Petrovskaya, N., Bearup, D.: Multiscale approach to pest insect monitoring: random walks, pattern formation, synchronization, and networks. Phys. Life Rev. 11, 467–525 (2014). doi:10.1016/j.plrev. 2014.02.001
Pimentel, D., Zuniga, R., Morrison, D.: Update on the environmental and economic costs associated with alien-invasive species in the United States. Ecol. Econ. 52, 273–288 (2005). doi:10.1016/j.ecolecon.2004.10. 002
Pontryagin, L.S.: The Mathematical Theory of Optimal Processes. Classics of Soviet Mathematics. Gordon and Breach, New York (1986). Translated from the Russian by K. N. Trirogoff
Potapov, A.B., Lewis, M.A., Finnoff, D.C.: Optimal control of biological invasions in lake networks. Nat. Resour. Model. 20(3), 351–379 (2007). doi:10.1111/j.1939-7445.2007.tb00211.x
Potapov, A.B., Lewis, M.A.: Allee effect and control of lake system invasion. Bull. Math. Biol. 70, 1371–1397 (2008). doi:10.1007/ s11538-008-9303-8
Puterman, M.L.: Markov Decision Processes: Discrete Stochastic Dynamic Programming. Wiley, Hoboken (2005)
Regan, T.J., McCarthy, M.A., Baxter, P.W.J., Panetta, F.D., Possingham, H.P.: Optimal eradication: when to stop looking for an invasive plant. Ecol. Lett. 9, 759–766 (2006). doi:10.1111/j.1461-0248. 2006.00920.x
Rout, T.M., Moore, J.L., McCarthy, M.A.: Prevent, search or destroy? A partially observable model for invasive species management. J. Appl. Ecol. 51, 804–813 (2014). doi:10.1111/1365-2664.12234
Taylor, C.M., Hastings, A.: Finding optimal control strategies for invasive species: a density-structured model for Spartina alterniflora. J. Appl. Ecol. 41, 1049–1057 (2004)
Zanden, M.J.V., Hansen, G.J.A., Higgins, S.N., Kornis, M.S.: A pound of prevention, plus a pound of cure: early detection and eradication of invasive species in the Laurentian Great Lakes. J. Great Lakes Res. 36, 199–205 (2010). doi:10.1016/j.jglr.2009.11.002
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Lewis, M.A., Petrovskii, S.V., Potts, J.R. (2016). Responding to Invasions: Detection, Control, and Adaptation. In: The Mathematics Behind Biological Invasions. Interdisciplinary Applied Mathematics, vol 44. Springer, Cham. https://doi.org/10.1007/978-3-319-32043-4_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-32043-4_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-32042-7
Online ISBN: 978-3-319-32043-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)