Optimal Dynamic Allocation of Conservation Funding Among Priority Regions

  • Michael Bode
  • Kerrie Wilson
  • Marissa McBride
  • Hugh Possingham
Original Article


The optimal allocation of conservation resources between biodiverse conservation regions has generally been calculated using stochastic dynamic programming, or using myopic heuristics. These solutions are hard to interpret and may not be optimal. To overcome these two limitations, this paper approaches the optimal conservation resource allocation problem using optimal control theory. A solution using Pontryagin’s maximum principle provides novel insight into the general properties of efficient conservation resource allocation strategies, and allows more extensive testing of the performance of myopic heuristics. We confirmed that a proposed heuristic (minimize short-term loss) yields near-optimal results in complex allocation situations, and found that a qualitative allocation feature observed in previous analyses (bang-bang allocation) is a general property of the optimal allocation strategy.


Optimal control Conservation resource allocation 


  1. Armsworth, P.R., Daily, G.C., Kareiva, P., Sanchirico, J.N., 2006. Land market feedbacks can undermine biodiversity conservation. Proc. Natl. Acad. Sci. 103(14), 5403–408. CrossRefGoogle Scholar
  2. Balmford, A., Gaston, K., Blyth, S., James, A., Kapos, V., 2003. Global variation in terrestrial conservation costs, conservation benefits, and unmet conservation needs. Proc. Natl. Acad. Sci. 100(3), 1046–050. CrossRefGoogle Scholar
  3. Balmford, A., Bennun, L., Brink, B.T., Cooper, D., Cote, I.M., Crane, P., Dobson, A., Dudley, N., Dutton, I., Green, R.E., Gregory, R.D., Harrison, J., Kennedy, E.T., Kremen, C., Leader-Williams, N., Lovejoy, T.E., Mace, G., May, R., Mayaux, P., Morling, P., Phillips, J., Redford, K., Ricketts, T.H., Paul Rodríguez, J., Sanjayan, M., Schei, P.J., van Jaarsveld, A.S., Walther, B.A., 2005. The convention on biological diversity’s 2010 target. Science 307, 212–13. CrossRefGoogle Scholar
  4. Bellman, R.E., Dreyfuss, S.E., 1962. Applied Dynamic Programming. Princeton University Press, Princeton. zbMATHGoogle Scholar
  5. Bode, M., Wilson, K.A., Brooks, T.M., Turner, W.R., Mittermeier, R.A., McBride, M.F., Underwood, E.C., Possingham, H.P., 2008. Cost-effective global conservation spending is robust to taxonomic group. Proc. Natl. Acad. Sci. 105(17), 6498–501. CrossRefGoogle Scholar
  6. Brooks, T.M., Mittermeier, R.A., da Fonseca, G.A.B., Gerlach, J., Hoffmann, M., Lamoreux, J.M., Mittermeier, C.G., Pilgrim, J.D., Rodrigues, A.S.L., 2006. Global biodiversity conservation priorities. Science 313, 58–1. CrossRefGoogle Scholar
  7. CEPF 2006. Protecting nature’s hotspots for people and prosperity: annual report 2006. Critical Ecosystems Partnership Fund. Google Scholar
  8. Clark, C.W., 1990. Mathematical Bioeconomics, 2nd edn. Wiley, New York. zbMATHGoogle Scholar
  9. Costello, C., Polasky, S., 2004. Dynamic reserve site selection. Resour. Energy Econ. 26, 157–74. CrossRefGoogle Scholar
  10. Halpern, B.S., Gaines, S.D., Warner, R.R., 2004. Confounding effects of the export of production and the displacement of fishing effort from marine reserves. Ecol. Appl. 14, 1248–256. CrossRefGoogle Scholar
  11. IUCN, 2003. Recommendations of the 5th annual IUCN world parks congress. IUCN. Google Scholar
  12. James, A.N., Gaston, K.J., Balmford, A., 1999. Balancing the earth’s accounts. Nature 401, 323–24. CrossRefGoogle Scholar
  13. Kareiva, P., Marvier, M., 2003. Conserving biodiversity coldspots. Am. Sci. 91, 344–51. Google Scholar
  14. Leonard, D., Long, N.V., 1992. Optimal Control Theory and Static Optimization in Economics. Cambridge University Press, Cambridge. Google Scholar
  15. Margules, C., Pressey, R.L., 2000. Systematic conservation planning. Nature 405, 243–53. CrossRefGoogle Scholar
  16. McBride, M.F., Wilson, K.A., Possingham, H.P., 2005. Incorporating investment uncertainty into the prioritisation of conservation resource allocation. In Proceedings of the 2005 MODSIM International Congress on Modelling and Simulation. Google Scholar
  17. McBride, M.F., Wilson, K.A., Bode, M., Possingham, H.P., 2007. Incorporating the effects of socioeconomic uncertainty into priority setting for conservation investment. Conserv. Biol. 21(6), 1463–474. Google Scholar
  18. Meir, E., Andleman, S., Possingham, H.P., 2004. Does conservation planning matter in a dynamic and uncertain world? Ecol. Lett. 7, 615–22. CrossRefGoogle Scholar
  19. Mittermeier, R.A., Gil, P.R., Hoffman, M., Pilgrim, J., Brooks, T., Mittermeier, C.G., Lamoreux, J., da Fonseca, G.A.B., 2005. Hotspots revisited. University of Chicago Press, Chicago. Google Scholar
  20. Myers, N., Mittermeier, R.A., Mittermeier, C.G., da Fonseca, G.A.B., Kent, J., 2000. Biodiversity hotspots for conservation priorities. Nature 403, 853–58. CrossRefGoogle Scholar
  21. Naidoo, R., Balmford, A., Ferraro, P.J., Polasky, S., Ricketts, T.H., Rouget, M., 2007. Integrating economic costs into conservation planning. Trends Ecol. Evol. 21, 681–87. CrossRefGoogle Scholar
  22. Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., Mishchenko, E.F., 1962. The Mathematical Theory of Optimal Processes. Wiley, New York. zbMATHGoogle Scholar
  23. Possingham, H.P., Wilson, K.A., 2005. Turning up the heat on hotspots. Nature 436, 919–20. CrossRefGoogle Scholar
  24. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., 1992. Numerical Recipes in C: the Art of Scientific Computing. Cambridge University Press, Cambridge. Google Scholar
  25. Pressey, R.L., Tully, S.L., 1994. The cost of ad hoc reservation: a case study in western new south wales. Aust. J. Ecol. 19, 375–84. CrossRefGoogle Scholar
  26. Richards, S.A., Possingham, H.P., Tizard, J., 1999. Optimal fire management for maintaining community diversity. Ecol. Appl. 9(3), 880–92. CrossRefGoogle Scholar
  27. Rodriguez, J.P., Rodriguez-Clark, K.M., Oliveira-Miranda, M.A., Good, T., Grajal, A., 2006. Professional capacity building: the missing agenda in conservation priority setting. Conserv. Biol. 5, 1340–341. CrossRefGoogle Scholar
  28. Rosenzweig, M.L., 1995. Species Diversity in Space and Time. Cambridge University Press, Cambridge. Google Scholar
  29. Rout, T.M., Hauser, C.E., Possingham, H.P., 2007. Minimise long-term loss or maximise short-term gain? Ecol. Model. 201(1), 67–4. CrossRefGoogle Scholar
  30. Stewart, R.R., Noyce, T., Possingham, H.P., 2003. Opportunity cost of ad hoc marine reserve design decisions: an example from South Australia. Marine Ecol. Prog. Ser. 253, 25–8. CrossRefGoogle Scholar
  31. Tenhumberg, B., Tyre, A.J., Shea, K., Possingham, H.P., 2004. Linking wild and captive populations to maximize species persistence: optimal translocation strategies. Conserv. Biol. 18(5), 1–1. Stochastic dynamic programming. CrossRefGoogle Scholar
  32. Wilson, K.A., Pressey, R.L., Newton, A., Burgman, M., Possingham, H., Weston, C., 2005. Measuring and incorporating vulnerability into conservation planning. Environ. Manag. 35, 537–43. CrossRefGoogle Scholar
  33. Wilson, K.A., McBride, M.F., Bode, M., Possingham, H.P., 2006. Prioritizing global conservation efforts. Nature 440, 337–40. CrossRefGoogle Scholar
  34. Wilson, K.A., Underwood, E.C., Morrison, S.A., Klausmeyer, K.R., Murdoch, W.W., Reyers, B., Wardell-Johnson, G., Marquet, P.A., Rundel, P.W., McBride, M.F., Pressey, R.L., Bode, M., Hoekstra, J.M., Andelman, S., Looker, M., Rondinini, C., Kareiva, P., Shaw, M.R., Possingham, H.P., 2007. Conserving biodiversity efficiently: what to do, where, and when. Public Libr. Sci. Biol. 5, e223. Google Scholar

Copyright information

© Society for Mathematical Biology 2008

Authors and Affiliations

  • Michael Bode
    • 1
  • Kerrie Wilson
    • 2
  • Marissa McBride
    • 3
  • Hugh Possingham
    • 4
  1. 1.Applied Environmental Decision Analysis Research Facility, School of BotanyThe University of MelbourneMelbourneAustralia
  2. 2.The Nature ConservancyMelbourneAustralia
  3. 3.Australian Centre of Excellence for Risk Analysis, School of BotanyThe University of MelbourneMelbourneAustralia
  4. 4.The Ecology Centre, School of Integrative BiologyThe University of QueenslandBrisbaneAustralia

Personalised recommendations