Theoretical Ecology

, Volume 10, Issue 4, pp 493–501 | Cite as

Handling overheads: optimal multi-method invasive species control

  • Christopher M. BakerEmail author
  • Paul R. Armsworth
  • Suzanne M. Lenhart


Invasive species are a pervasive problem worldwide and considerable resources are directed towards their control. While there are many aspects to invasive species management, deciding how to allocate resources effectively when removing them is critical. There are often multiple control methods available, each with different characteristics. For example aerial baiting has very high overhead costs, while animal trapping incurs a handling time (the trap must be reset after each capture). Here, we examine a particular challenge that managers commonly face when designing eradication programmes—specifically what type of control measure to rely on at different times during the eradication effort? We solve for optimal resource allocation strategies when there are two control methods available and one has overhead costs and the other has a handling time. We find that, if both controls are being used, the control with overhead costs should be used only at the beginning of a project, the other control should be used in the latter part of the project, and that there is generally an overlap where both controls are used. This contrasts with the strategies employed in many eradication projects, where ground control does not begin until aerial baiting has ceased.


Optimal control Overhead cost Handling time Optimal control theory Ecological economics 



We would like to thank Michael Bode and Michael McCarthy for their input. Christopher Baker is the recipient of a John Stocker Postdoctoral Fellowship from the Science and Industry Endowment Fund. This work was assisted by attendance as a Short-term Visitor at the National Institute for Mathematical and Biological Synthesis, an Institute sponsored by the National Science Foundation through NSF Award #DBI-1300426, with additional support from The University of Tennessee, Knoxville and the Australian Research Council Centre of Excellence for Environmental Decisions.


  1. Algar D, Burbridge AA, Angus GJ (2002) Cat eradication on Hermite Island, Montebello Islands, Western Australia. In: Turning the tide: the eradication of invasive speciesGoogle Scholar
  2. Armsworth PR, Roughgarden JE (2001) An invitation to ecological economics. Trends Ecol Evol 16(5):229–234. CrossRefPubMedGoogle Scholar
  3. Armsworth PR, Block BA, Eagle J, Roughgarden JE (2011) The role of discounting and dynamics in determining the economic efficiency of time-area closures for managing fishery bycatch. Theor Ecol 4(4):513–526. CrossRefGoogle Scholar
  4. Baker CM (2016) Target the source: optimal spatiotemporal resource allocation for invasive species control. Conserv Lett.
  5. Baker CM, Bode M (2016) Placing invasive species management in a spatiotemporal context. Ecol Appl 26(3):712–725. CrossRefPubMedGoogle Scholar
  6. Baker CM, Gordon A, Bode M (2016), Ensemble ecosystem modeling for predicting ecosystem response to predator reintroduction. Conserv Biol.
  7. Baker CM, Hodgson JC, Tartaglia E, Clarke RH (2017) Modelling tropical fire ant (Solenopsis Geminata) dynamics and detection to inform an eradication project. Biological Invasions.
  8. Baxter PWJ, Sabo JL, Wilcox C, McCarthy MA, Possingham HP (2008) Cost-effective suppression and eradication of invasive predators. Conserv Biol 22(1):89–98. CrossRefPubMedGoogle Scholar
  9. Blackwood JC, Berec L, Yamanaka T, Epanchin-Niell RS, Hastings A, Liebhold AM (2012) Bioeconomic synergy between tactics for insect eradication in the presence of Allee effects. Proc R Soc B Biol Sci 279(1739):2807–2815. CrossRefGoogle Scholar
  10. Blomquist SM, Johnson TD, Smith DR, Call GP, Miller BN, Thurman WM, McFadden JE, Parkin MJ, Boomer GS (2010) Structured decision-making and rapid prototyping to plan a management response to an invasive species. J Fish Wildl Manag 1(1):19–32. CrossRefGoogle Scholar
  11. Bode M, Baker CM, Plein M (2015) Eradicating down the food chain: optimal multispecies eradication schedules for a commonly encountered invaded island ecosystem. J Appl Ecol 571–579.
  12. Carrasco LR, Mumford JD, MacLeod A, Knight JD, Baker RHA (2010) Comprehensive bioeconomic modelling of multiple harmful non-indigenous species. Ecol Econ 69(6):1303–1312. CrossRefGoogle Scholar
  13. Chades I, Martin TG, Nicol S, Burgman MA, Possingham HP, Buckley YM (2011) General rules for managing and surveying networks of pests, diseases, and endangered species. Proc Natl Acad Sci 108(20):8323–8328. CrossRefPubMedPubMedCentralGoogle Scholar
  14. Cook BA, McGaw RL (1996) Sport and commercial fishing allocations for the Atlantic salmon fisheries of the Miramichi River. Canadian Journal of Agricultural Economics/Revue canadienne d’agroeconomie 44(2):165–171. CrossRefGoogle Scholar
  15. Doherty TS, Dickman CR, Nimmo DG, Ritchie EG (2015) Multiple threats, or multiplying the threats? Interactions between invasive predators and other ecological disturbances. Biological Conservation 190:60–68. CrossRefGoogle Scholar
  16. Donlan CJ, Luque GM, Wilcox C (2014) Maximizing return on investment for island restoration and species conservation. Conserv Lett 171–179.
  17. Epanchin-Niell RS, Haight RG, Berec L, Kean JM, Liebhold AM (2012) Optimal surveillance and eradication of invasive species in heterogeneous landscapes. Ecol Lett 15(8):803–812. CrossRefPubMedGoogle Scholar
  18. Epanchin-Niell RS, Brockerhoff EG, Kean JM, Turner J (2014) Designing cost-efficient surveillance for early detection and control of multiple biological invaders. Ecol Appl.
  19. Fenichel EP, Horan RD (2007) Jointly-determined ecological thresholds and economic trade-offs in wildlife disease management. Nat Resour Model 20(4):511–547. CrossRefGoogle Scholar
  20. Gregory R, Long G (2009) Using structured decision making to help implement a precautionary approach to endangered species management. Risk Anal 29(4):518–532. CrossRefPubMedGoogle Scholar
  21. Gurevitch J, Padilla DK (2004) Are invasive species a major cause of extinctions. Trends Ecol Evol 19(9):470–474. CrossRefPubMedGoogle Scholar
  22. Hastings A, Hall RJ, Taylor CM (2006) A simple approach to optimal control of invasive species. Theor Popul Biol 70(4):431–435. CrossRefPubMedGoogle Scholar
  23. Hauser CE, McCarthy MA (2009) Streamlining ‘search and destroy’: cost-effective surveillance for invasive species management. Ecol Lett 12(7):683–692. CrossRefPubMedGoogle Scholar
  24. Hodgson JC, Abbott KL, Clarke RH (2014) Eradication plan “Tropical Fire Ant Solenopsis geminata at Ashmore Reef Commonwealth Marine Reserve”. Tech. rep. Monash UniversityGoogle Scholar
  25. Holling CS (1959) Some characteristics of simple types of predation and parasitism. Can Entomol 91(07):385–398. CrossRefGoogle Scholar
  26. Holmes ND, Campbell KJ, Keitt BS, Griffiths R, Beek J, Donlan CJ, Broome KG (2015) Reporting costs for invasive vertebrate eradications. Biol Invasions 17(10):1–13. CrossRefGoogle Scholar
  27. Horan RD, Wolf CA, Fenichel EP, Mathews KH (2008) Joint management of wildlife and livestock disease. Environ Resour Econ 41(1):47–70. CrossRefGoogle Scholar
  28. Jones HP, Holmes ND, Butchart SHM, Tershy BR, Kappes PJ, Corkery I, Aguirre-Muñoz A, Armstrong DP, Bonnaud E, Burbidge AA, Campbell K, Courchamp F, Cowan PE, Cuthbert RJ, Ebbert S, Genovesi P, Howald GR, Keitt BS, Kress SW, Miskelly CM, Oppel S, Poncet S, Rauzon MJ, Rocamora G, Russell JC, Samaniego-Herrera A, Seddon PJ, Spatz DR, Towns DR, Croll DA (2016) Invasive mammal eradication on islands results in substantial conservation gains. Proc Natl Acad Sci p 201521179.
  29. Kern DL, Lenhart S, Miller R, Yong J (2007) Optimal control applied to native–invasive population dynamics. J Biol Dyn 1(4):413–426. CrossRefPubMedGoogle Scholar
  30. Kessler D (2002) Eradication of feral goats and pigs and consequences for other biota on Sarigan Island, Commonwealth of the Northern Mariana Islands. In: Turning the tide: the eradication of invasive speciesGoogle Scholar
  31. Lampert A, Hastings A, Grosholz ED, Jardine SL, Sanchirico JN (2014) Optimal approaches for balancing invasive species eradication and endangered species management. Science 344(6187):1028–1031. CrossRefPubMedGoogle Scholar
  32. Lenhart S, Workman JT (2007) Optimal control applied to biological models. Mathematical and computational biology series. Chapman & Hall/CRC, LondonGoogle Scholar
  33. Li S-L, Bjørnstad ON, Ferrari MJ, Mummah R, Runge MC, Fonnesbeck CJ, Tildesley MJ, Probert WJM, Shea K (2017) Essential information: uncertainty and optimal control of ebola outbreaks. Proc Natl Acad Sci 114(22):5659-5664.
  34. Macdonald N, Leaman AA (2002) An attempt to eradicate feral goats from Lord Howe Island. In: Turning the tide: the eradication of invasive speciesGoogle Scholar
  35. Marten AL, Moore CC (2011) An options based bioeconomic model for biological and chemical control of invasive species. Ecol Econ 70(11):2050–2061. CrossRefGoogle Scholar
  36. McCarthy DP, Donald PF, Scharlemann JPW, Buchanan GM, Balmford A, Green JMH, Bennun LA, Burgess ND, Fishpool LDC, Garnett ST, Leonard DL, Maloney RF, Morling P, Schaefer HM, Symes A, Wiedenfeld DA, Butchart SHM (2012) Financial costs of meeting global biodiversity conservation targets: current spending and unmet needs. Science 338(6109):946–949. CrossRefPubMedGoogle Scholar
  37. McClelland PJ (2002) Eradication of Pacific rats (Rattus exulans) from Whenua Hou Nature Reserve (Codfish Island), Putauhinu and Rarotoka Islands, New Zealand. In: Turning the tide: the eradication of invasive speciesGoogle Scholar
  38. Mehta SV, Haight RG, Homans FR, Polasky S, Venette RC (2007) Optimal detection and control strategies for invasive species management. Ecol Econ 61(2–3):237–245. CrossRefGoogle Scholar
  39. Moore JL, Rout TM, Hauser CE, Moro D, Jones M, Wilcox C, Possingham HP (2010) Protecting islands from pest invasion: optimal allocation of biosecurity resources between quarantine and surveillance. Biol Conserv 143(5):1068–1078. CrossRefGoogle Scholar
  40. Morrison SA, Macdonald N, Walker K, Lozier L, Shaw MR (2007) Facing the dilemma at eradication’s end: uncertainty of absence and the Lazarus effect. Front Ecol Environ 5(5):271–276.[271:FTDAEE]2.0.CO;2 CrossRefGoogle Scholar
  41. Mowbray D (2002) Eradication of introduced Australian marsupials (brushtail possum and brushtailed rock wallaby) from Rangitoto and Motutapu Islands, New Zealand. In: Turning the tide: the eradication of invasive speciesGoogle Scholar
  42. Noble M, Rose M (2013) Managing African boxthorn (Lycium ferocissimum) in Australia. Tech. rep. Department of Agriculture, Fisheries and Forestry, TasmaniaGoogle Scholar
  43. Pimentel D, Zuniga R, Morrison D (2005) Update on the environmental and economic costs associated with alien-invasive species in the United States. Ecol Econ 52(3):273–288. CrossRefGoogle Scholar
  44. Ramsey DSL, Parkes JP, Will D, Hanson CC, Campbell KJ (2011) Quantifying the success of feral cat eradication, San Nicolas Island, California. N Z J Ecol 35(2):163–173Google Scholar
  45. Reed WJ (1974) A stochastic model for the economic management of a renewable animal resource. Math Biosci 22:313–337. CrossRefGoogle Scholar
  46. Regan TJ, Chadès I, Possingham HP (2011) Optimally managing under imperfect detection: a method for plant invasions. J Appl Ecol 48(1):76–85. CrossRefGoogle Scholar
  47. Robinson SA, Copson GR (2014) Eradication of cats (Felis catus) from subantarctic Macquarie Island. Ecol Manag Restor 15(1):34–40. CrossRefGoogle Scholar
  48. Rout TM, Moore JL, Possingham HP, McCarthy MA (2011) Allocating biosecurity resources between preventing, detecting, and eradicating island invasions. Ecol Econ 71:54–62. CrossRefGoogle Scholar
  49. Rout TM, Moore JL, McCarthy MA (2014) Prevent, search, or destroy? A partially observable model for invasive species management. J Appl Ecol.
  50. Simberloff D, Martin JL, Genovesi P, Maris V, Wardle DA, Aronson J, Courchamp F, Galil B, García-Berthou E, Pascal M, Pyšek P, Sousa R, Tabacchi E, Vilà M (2013) Impacts of biological invasions: what’s what and the way forward. Trends Ecol Evol 28(1):58–66. CrossRefPubMedGoogle Scholar
  51. Sims C, Finnoff D (2013) When is a “wait and see” approach to invasive species justified? Resour Energy Econ 35(3):235–255. CrossRefGoogle Scholar
  52. Sims C, Finnoff D, Shogren JF (2016) Bioeconomics of invasive species: using real options theory to integrate ecology, economics, and risk management. Food Secur 8(1):61–70. CrossRefGoogle Scholar
  53. Spulber DF (1982) Adaptive harvesting of a renewable resource and stable equilibrium. In: Mirman L, Spulber DF (eds) Essays in the economics of renewable resources. North-Holland Publishing, Amsterdam, pp 117–139Google Scholar
  54. Terauds A, Doube J, McKinlay J, Springer K (2014) Using long-term population trends of an invasive herbivore to quantify the impact of management actions in the sub-Antarctic. Polar Biol 37(6):833–843. CrossRefGoogle Scholar
  55. Veitch D (2002) Eradication of Norway rats (Rattus norvegicus) and house mouse (Mus musculus) from Motuihe Island, New Zealand. In: Turning the tide: the eradication of invasive speciesGoogle Scholar
  56. Veitch CR, Clout MN (2002) Turning the tide: the eradication of invasive species (Proceedings of the International Conference on Eradication of Island Invasives). IUCN SCC Invasive Species Specialist Group, IUCN, Gland, Switzerland and CambridgeGoogle Scholar
  57. Walker AN, Poos JJ, Groeneveld RA (2015) Invasive species control in a one-dimensional metapopulation network. Ecol Model 316:176–184. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.School of BioSciencesThe University of MelbourneMelbourneAustralia
  2. 2.School of Biological SciencesThe University of QueenslandSt LuciaAustralia
  3. 3.CSIRO, Ecosciences PrecinctDutton ParkAustralia
  4. 4.National Institute of Mathematical and Biological SciencesThe University of TennesseeKnoxvilleUSA
  5. 5.Department of Ecology and Evolutionary BiologyThe University of TennesseeKnoxvilleUSA
  6. 6.Mathematics DepartmentThe University of TennesseeKnoxvilleUSA

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