Unifying Reserve Design Strategies with Graph Theory and Constraint Programming

  • Dimitri Justeau-AllaireEmail author
  • Philippe Birnbaum
  • Xavier Lorca
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11008)


The delineation of areas of high ecological or biodiversity value is a priority of any conservation program. However, the selection of optimal areas to be preserved necessarily results from a compromise between the complexity of ecological processes and managers’ constraints. Current reserve design models usually focus on few criteria, which often leads to an oversimplification of the underlying conservation issues. This paper shows that Constraint Programming (CP) can be the basis of a more unified, flexible and extensible framework. First, the reserve design problem is formalized. Secondly, the problem is modeled from two different angles by using two graph-based models. Then CP is used to aggregate those models through a unique Constraint Satisfaction Problem. Our model is finally evaluated on a real use case addressing the problem of rainforest fragmentation in New Caledonia, a biodiversity hotspot. Results are promising and highlight challenging perspectives to overtake in future work.


  1. 1.
    Beier, P., Spencer, W., Baldwin, R.F., McRAE, B.H.: Toward best practices for developing regional connectivity maps. Conserv. Biol. 25(5), 879–892 (2011)CrossRefGoogle Scholar
  2. 2.
    Baguette, M., Blanchet, S., Legrand, D., Stevens, V.M., Turlure, C.: Individual dispersal, landscape connectivity and ecological networks. Biol. Rev. 88(2), 310–326 (2013)CrossRefGoogle Scholar
  3. 3.
    Haddad, N.M., et al.: Habitat fragmentation and its lasting impact on Earths ecosystems. Sci. Adv. 1(2), e1500052 (2015)CrossRefGoogle Scholar
  4. 4.
    Prendergast, J.R., Quinn, R.M., Lawton, J.H., Eversham, B.C., Gibbons, D.W.: Rare species, the coincidence of diversity hotspots and conservation strategies. Nature 365(6444), 335–337 (1993)CrossRefGoogle Scholar
  5. 5.
    Sarkar, S.: Environmental philosophy: from theory to practice. Stud. History Philos. Sci. Part C Stud. History Philos. Biol. Biomed. Sci. 45, 89–91 (2013)CrossRefGoogle Scholar
  6. 6.
    Pressey, R.L., Humphries, C.J., Margules, C.R., Vane-Wright, R.I., Williams, P.H.: Beyond opportunism: key principles for systematic reserve selection. Trends Ecol. Evol. 8(4), 124–128 (1993)CrossRefGoogle Scholar
  7. 7.
    ReVelle, C.S., Williams, J.C., Boland, J.J.: Counterpart models in facility location science and reserve selection science. Environ. Model. Assess. 7(2), 71–80 (2002)CrossRefGoogle Scholar
  8. 8.
    Billionnet, A.: Solving the probabilistic reserve selection problem. Ecol. Model. 222, 546–554 (2011)CrossRefGoogle Scholar
  9. 9.
    Watts, M.E., et al.: Marxan with Zones: software for optimal conservation based land- and sea-use zoning. Environ. Model. Softw. 24(12), 1513–1521 (2009)CrossRefGoogle Scholar
  10. 10.
    Diamond, J.M.: The island dilemma: lessons of modern biogeographic studies for the design of natural reserves. Biol. Conserv. 7(2), 129–146 (1975)CrossRefGoogle Scholar
  11. 11.
    Williams, J.C., ReVelle, C.S., Levin, S.A.: Spatial attributes and reserve design models: a review. Environ. Model. Assess. 10(3), 163–181 (2005)CrossRefGoogle Scholar
  12. 12.
    Billionnet, A.: Designing connected and compact nature reserves. Environ. Model. Assess. 21(2), 211–219 (2016)CrossRefGoogle Scholar
  13. 13.
    Dilkina, B., et al.: Trade-offs and efficiencies in optimal budget-constrained multispecies corridor networks. Conserv. Biol. 31(1), 192–202 (2017)CrossRefGoogle Scholar
  14. 14.
    Jafari, N., Nuse, B.L., Moore, C.T., Dilkina, B., Hepinstall-Cymerman, J.: Achieving full connectivity of sites in the multiperiod reserve network design problem. Comput. Oper. Res. 81, 119–127 (2017)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Rodrigues, A.S., Cerdeira, J.O., Gaston, K.J.: Flexibility, efficiency, and accountability: adapting reserve selection algorithms to more complex conservation problems. Ecography 23(5), 565–574 (2000)CrossRefGoogle Scholar
  16. 16.
    Prud’homme, C., Fages, J.G., Lorca, X.: Choco Documentation (2017)Google Scholar
  17. 17.
    Sahr, K., White, D., Kimerling, A.J.: Geodesic discrete global grid systems. Cartography Geogr. Inf. Sci. 30(2), 121–134 (2003)CrossRefGoogle Scholar
  18. 18.
    Birch, C.P.D., Oom, S.P., Beecham, J.A.: Rectangular and hexagonal grids used for observation, experiment and simulation in ecology. Ecol. Model. 206(3), 347–359 (2007)CrossRefGoogle Scholar
  19. 19.
    Guisan, A., Zimmermann, N.E.: Predictive habitat distribution models in ecology. Ecol. Model. 135(2), 147–186 (2000)CrossRefGoogle Scholar
  20. 20.
    Elith, J., Leathwick, J.R.: Species distribution models: ecological explanation and prediction across space and time. Ann. Rev. Ecol. Evol. Syst. 40(1), 677–697 (2009)CrossRefGoogle Scholar
  21. 21.
    Etienne, R.S., Heesterbeek, J.A.: On optimal size and number of reserves for metapopulation persistence. J. Theor. Biol. 203(1), 33–50 (2000)CrossRefGoogle Scholar
  22. 22.
    Dooms, G.: The CP(Graph) Computation Domain in Constraint Programming. Ph.D. thesis, UCL - Université Catholique de Louvain (2006)Google Scholar
  23. 23.
    Beldiceanu, N., Carlsson, M., Rampon, J.X., Truchet, C.: Graph Invariants as Necessary Conditions for Global Constraints. Swedish Institute of Computer Science (2005)Google Scholar
  24. 24.
    Beldiceanu, N., Carlsson, M., Demassey, S., Petit, T.: Graph properties based filtering. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 59–74. Springer, Heidelberg (2006). Scholar
  25. 25.
    Beldiceanu, N., Carlsson, M., Rampon, J.X.: Global Constraint Catalog, 2nd edn., (Revision A). Swedish Institute of Computer Science (2012)Google Scholar
  26. 26.
    Fages, J.G., Prud’homme, C., Lorca, X.: Choco Graph Documentation, February 2018Google Scholar
  27. 27.
    Bockmayr, A., Pisaruk, N., Aggoun, A.: Network flow problems in constraint programming. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 196–210. Springer, Heidelberg (2001). Scholar
  28. 28.
    Ibanez, T., Hequet, V., Chambrey, C., Jaffré, T., Birnbaum, P.: How does forest fragmentation affect tree communities? a critical case study in the biodiversity hotspot of New Caledonia. Landscape Ecol. 32(8), 1671–1687 (2017)CrossRefGoogle Scholar
  29. 29.
    Pouteau, R., et al.: Accounting for the indirect area effect in stacked species distribution models to map species richness in a montane biodiversity hotspot. Divers. Distrib. 21(11), 1329–1338 (2015)CrossRefGoogle Scholar
  30. 30.
    Schmitt, S., Pouteau, R., Justeau, D., Boissieu, F., Birnbaum, P.: SSDM: an R package to predict distribution of species richness and composition based on stacked species distribution models. Methods Ecol. Evol. 8(12), 1795–1803 (2017)CrossRefGoogle Scholar
  31. 31.
    Steiger, R., van Hoeve, W.J., Szymanek, R.: An efficient generic network flow constraint. In: Proceedings of the 2011 ACM Symposium on Applied Computing, SAC 2011, pp. 893–900. ACM, New York (2011)Google Scholar
  32. 32.
    Downing, N., Feydy, T., Stuckey, P.J.: Explaining flow-based propagation. In: Beldiceanu, N., Jussien, N., Pinson, É. (eds.) CPAIOR 2012. LNCS, vol. 7298, pp. 146–162. Springer, Heidelberg (2012). Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Dimitri Justeau-Allaire
    • 1
    • 2
    • 3
    Email author
  • Philippe Birnbaum
    • 1
    • 2
    • 3
  • Xavier Lorca
    • 4
  1. 1.CIRAD, UMR AMAPMontpellierFrance
  2. 2.Institut Agronomique néo-Calédonien (IAC)NoumeaNew Caledonia
  3. 3.AMAP, Univ Montpellier, CIRAD, CNRS, INRA, IRDMontpellierFrance
  4. 4.ORKID, Centre de Génie Industriel, IMT Mines AlbiAlbi cedex 09France

Personalised recommendations