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Optimal invasive species management under multiple uncertainties. (English) Zbl 1226.92067
Summary: Management programs for invasive species have been proposed and implemented in many regions of the world. However, practitioners and scientists have not reached a consensus on how to control them. One reason is the presence of various uncertainties associated with the management. To give some guidance on this issue, we characterize the optimal strategy by developing a dynamic model of invasive species management under uncertainties. In particular, focusing on (i) growth uncertainty and (ii) measurement uncertainty, we identify how these uncertainties affect optimal strategies and value functions. Our results suggest that a rise in growth uncertainty causes the optimal strategy to involve more restrained removals and the corresponding value function to shift up. Furthermore, we also find that a rise in measurement uncertainty affects optimal policies in a highly complex manner, but their corresponding value functions generally shift down as measurement uncertainty rises. Overall, a rise in growth uncertainty can be beneficial, while a rise in measurement uncertainty brings about an adverse effect, which implies the potential gain of precisely identifying the current stock size of invasive species.

MSC:
92D40 Ecology
91B76 Environmental economics (natural resource models, harvesting, pollution, etc.)
90C39 Dynamic programming
37N25 Dynamical systems in biology
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[1] Bomford, M.; O’Brien, P., Eradication or control for vertebrate pests, Wildlife society bulletin, 23, 249, (1995)
[2] Clark, C.W., A delayed-recruitment model of population dynamics, with an application to baleen whale populations, Journal of mathematical biology, 3, 381, (1976) · Zbl 0337.92011
[3] Clark, C.W., Mathematical bioeconomics, 2nd ed, (1990), John Wiley and Sons, Inc., · Zbl 0712.90018
[4] Clark, C.W.; Kirkwood, G.P., On uncertain renewable resource stocks: optimal harvest policies and the value of stock surveys, Journal of environmental economics and management, 13, 235, (1986) · Zbl 0601.90030
[5] Eisewerth, M.E.; Johnson, W.S., Managing nonindigenous invasive species: insights from dynamic analysis, Environmental and resource economics, 23, 3, 319, (2002)
[6] Eisewerth, M.E.; van Kooten, G., Uncertainty, economics, and the spread of an invasive plant species, American journal of agricultural economics, 84, 5, 1317, (2002)
[7] Ishii, N., Controlling mongooses introduced to amami-oshima island: a population estimate and program evaluation, Japanese journal of conservation ecology, 8, 73, (2003), (in Japanese)
[8] Judd, K.L., Numerical methods in economics, (1998), MIT Press · Zbl 0941.00048
[9] Kotani, K.; Kakinaka, M.; Matsuda, H., Dynamic economic analysis on invasive species management: some policy implications of catchability, Mathematical biosciences, 220, 1, 1, (2009) · Zbl 1169.92046
[10] Laffont, J.-J., The economics of uncertainty and information, (1989), The MIT Press, Translated by John P. Bonin and Helene Bonin.
[11] Loehle, C., Control theory and the management of ecosystems, Journal of applied ecology, 43, 957, (2006)
[12] Moxnes, E., Uncertain measurements of renewable resources: approximations, harvesting policies and value of accuracy, Journal of environmental economics and management, 45, 85, (2003) · Zbl 1026.90064
[13] Myers, J.H.; Savoie, A.; van Randen, E., Eradication and pest management, Annual review of entomology, 43, 471, (1998)
[14] Olson, L.J.; Roy, S., The economics of controlling a stochastic biological invasion, American journal of agricultural economics, 84, 5, 1311, (2002)
[15] L.J. Olson, S. Roy, Controlling a biological invasion: a non-classical dynamic economic model, 2004, Working Paper. · Zbl 1148.91032
[16] Olson, L.J.; Roy, S., Controlling a biological invasion: a non-classical dynamic economic model, Economic theory, 36, 453, (2008) · Zbl 1148.91032
[17] Perrings, C.; Williamson, M.; Dalmazzone, S., The economics of biological invasions, (2000), Edward Elgar
[18] Pimentel, D.; Zuniga, R.; Morrison, D., Update on the environmental and economic costs associated with alien-invasive species in the united states, Ecological economics, 52, 273, (2005)
[19] Reed, W.J., Optimal escapement levels in stochastic and deterministic harvesting models, Journal of environmental economics and management, 6, 350, (1979) · Zbl 0439.90020
[20] Roughgarden, J.; Smith, F., Why fisheries collapse and what to do about it?, Proceedings of national Academy of sciences of the united states of America, 93, 10, 5078, (1996)
[21] Sethi, G.; Costello, C.; Fisher, A.; Hanemann, M.; Karp, L., Fishery management under multiple uncertainty, Journal of environmental economics and management, 50, 300, (2005) · Zbl 1090.91072
[22] Simberloff, D.; Veitch, C.R.; Clout, M.N., Today tiritiri matangi, tomorrow the world! are we aiming too low in invasion control?, Turning the tide: the eradication of invasive species, 4, (2002)
[23] Skiba, A.K., Optimal growth with a convex-concave production function, Econometrica, 46, 527, (1978) · Zbl 0383.90020
[24] Supriatna, A.K.; Possingham, H.P., Optimal harvesting for a predator – prey metapopulation, Bulletin of mathematical biology, 60, 49, (1998) · Zbl 0955.92037
[25] Tuck, G.N.; Possingham, H., Optimal harvesting strategies for a metapopulation, Bulletin of mathematical biology, 56, 107, (1994) · Zbl 0789.92024
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