Skip to main content
Log in

Designing Connected and Compact Nature Reserves

  • Published:
Environmental Modeling & Assessment Aims and scope Submit manuscript

Abstract

It is generally accepted that for many species, the ability to get around a reserve promotes their long-term persistence. Here, we measure the ease with which species can move by two spatial criteria: (i) the connectivity of the reserve, that is to say, the possibility to go through the whole reserve without leaving it, and (ii) the compactness of the reserve, that is to say, the remoteness of the sites in relation to each other, the distance between two sites being measured by the shortest distance to travel to get from one site to another without leaving the reserve. To protect the reserve of external disturbances, we also impose a connectivity constraint for the area outside the reserve. This article presents a method based on integer linear programming to define connected and compact reserves. Computational experiments carried out on artificial instances with 400 sites and 100 species are presented to illustrate the effectiveness of the approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Alagador, D. (2011). Quantitative methods in spatial conservation planning. Thesis, Instituto Superior de Agronomia, Universidade Técnica de Lisboa.

  2. Barnhart, C., Johnson, E. L., Nemhauser, G. L., Savelsbergh, M. W. P., & Vance, P. H. (1998). Branch-and-price: column generation for solving huge integer programs. Operations Research, 46, 316–329.

    Article  Google Scholar 

  3. Billionnet, A. (2012). Designing an optimal connected nature reserve. Applied Mathematical Modelling, 36, 2213–2223.

    Article  Google Scholar 

  4. Billionnet, A. (2013). Mathematical optimization ideas for biodiversity conservation. European Journal of Operational Research, 231, 514–534.

    Article  Google Scholar 

  5. Briers, R. A. (2002). Incorporating connectivity into reserve selection procedures. Biological Conservation, 103, 77–83.

    Article  Google Scholar 

  6. Camm, J. D., Polasky, S., Solow, A., & Csuti, B. (1996). A note on optimal algorithms for reserve site selection. Biological Conservation, 78, 353–355.

    Article  Google Scholar 

  7. Carvajal, R., Constantino, M., Goycoolea, M., Vielma, J. P., & Weintraub, A. (2013). Imposing connectivity constraints in forest planning models. Operations Research, 61, 824–836.

    Article  Google Scholar 

  8. Cerdeira, J. O., Gaston, K. J., & Pinto, L. S. (2005). Connectivity in priority area selection for conservation. Environmental Modeling and Assessment, 10, 183–192.

    Article  Google Scholar 

  9. Cerdeira, J. O., Pinto, L. S., Cabeza, M., & Gaston, K. J. (2010). Species specific connectivity in reserve-network design using graphs. Biological Conservation, 143, 408–415.

    Article  Google Scholar 

  10. Church, R. L., Stoms, D. M., & Davis, F. W. (1996). Reserve selection as a maximal covering location problem. Biological Conservation, 76, 105–112.

    Article  Google Scholar 

  11. Conrad, J. M., Gomes, C. P., van Hoeve, W. J., Sabharwal, A., & Suter, J. F. (2012). Wildlife corridors as a connected subgraph problem. Journal of Environmental Economics and Management, 63, 1–18.

    Article  Google Scholar 

  12. CPLEX. (2013). IBM ILOG CPLEX version 12.6.

  13. Fischer, D. T., & Church, R. L. (2003). Clustering and compactness in reserve site selection: an extension of the biodiversity management area selection model. Forest Science, 49, 555–565.

    Google Scholar 

  14. Fischer, D. T., & Church, R. L. (2005). The SITES reserve selection system: a critical review. Environmental Modeling and Assessment, 10, 215–228.

    Article  Google Scholar 

  15. Fourer, R., Gay, D. M., & Kernighan, B. W. (1993). AMPL, a modeling language for mathematical programming. Danvers: Boyd & Fraser Publishing Company.

    Google Scholar 

  16. Groeneveld, R. A. (2010). Species-specific spatial characteristics in reserve site selection. Ecological Economics, 69, 2307–2314.

    Article  Google Scholar 

  17. Jafari, N., & Hearne, J. (2013). A new method to solve the fully connected reserve network design problem. European Journal of Operational Research, 231, 202–209.

    Article  Google Scholar 

  18. Lindenmayer, D., et al. (2008). A checklist for ecological management of landscapes for conservation. Ecology Letters, 11, 78–91.

    Google Scholar 

  19. Margules, C., Nichols, A., & Pressey, R. (1988). Selecting networks of reserves to maximize biological diversity. Biological Conservation, 43, 63–76.

    Article  Google Scholar 

  20. Marianov, V., ReVelle, C., & Snyder, S. (2008). Selecting compact habitat reserves for species with differential habitat size needs. Computers & Operations Research, 35, 475–487.

    Article  Google Scholar 

  21. McDonnell, M., Possingham, H., Ball, I., & Cousins, E. (2002). Mathematical methods for spatially cohesive reserve design. Environmental Modeling and Assessment, 7, 107–114.

    Article  Google Scholar 

  22. Moilanen, A., Wilson, K.A., Possingham, H.P. (Eds.) (2009). Spatial conservation prioritization. Oxford: Oxford University Press.

  23. Önal, H., & Briers, R. A. (2002). Incorporating spatial criteria in optimum reserve network selection. Proceedings of the Royal Society of London B, 269, 2437–2441.

    Article  Google Scholar 

  24. Önal, H., & Briers, R. A. (2005). Designing a conservation reserve network with minimal fragmentation: a linear integer programming approach. Environmental Modeling and Assessment, 10, 193–202.

    Article  Google Scholar 

  25. Önal, H., & Briers, R. A. (2006). Optimal selection of a connected reserve network. Operations Research, 54, 379–388.

    Article  Google Scholar 

  26. Polasky, S., Camm, J., Solow, A., Csuti, B., White, D., & Ding, R. (2000). Choosing reserve networks with incomplete species information. Biological Conservation, 94, 1–10.

    Article  Google Scholar 

  27. Possingham, H. P., Ball, I. R., & Andelman, S. (2000). Mathematical methods for identifying representative reserve networks. In S. Ferson & M. Burgman (Eds.), Quantitative methods for conservation biology (pp. 291–305). New York: Springer.

    Chapter  Google Scholar 

  28. Pressey, R. L., Possingham, H. P., & Day, J. R. (1997). Effectiveness of alternative heuristic algorithms for identifying indicative minimum requirements for conservation reserves. Biological Conservation, 80, 207–219.

    Article  Google Scholar 

  29. ReVelle, C. S., Williams, J. C., & Boland, J. J. (2002). Counterpart models in facility location science and reserve selection science. Environmental Modeling and Assessment, 7, 71–80.

    Article  Google Scholar 

  30. Sarkar, S., Pressey, R. L., Faith, D. P., Margules, C. R., Fuller, T., Stoms, D. M., Moffett, A., Wilson, K. A., Williams, K. J., Williams, P. H., & Andelman, S. (2006). Biodiversity conservation planning tools: present status and challenges for the future. Annual Review of Environment and Resources, 31, 123–159.

    Article  Google Scholar 

  31. Underhill, L. (1994). Optimal and suboptimal reserve selection algorithms. Biological Conservation, 35, 85–87.

    Article  Google Scholar 

  32. Urban, D., & Keitt, T. (2001). Landscape connectivity: a graph theoretic perspective. Ecology, 82, 1205–1218.

    Article  Google Scholar 

  33. Vogiatzis, C., Veremyev, A., Pasiliao, E.L., Pardalos, P.M. (2014). An integer programming approach for finding the most and the least central cliques. Optimization Letters, available online.

  34. Walteros, J. L., Vogiatzis, C., Pasiliao, E. L., & Pardalos, P. M. (2014). Integer programming models for the multidimensional assignment problem with star costs. European Journal of Operational Research, 235, 553–568.

    Article  Google Scholar 

  35. Wang, Y., & Önal, H. (2013). Designing a connected nature reserve using a network flow theory approach. Acta Ecologica Sinica, 33, 253–259.

    Article  Google Scholar 

  36. Williams, J. C. (2008). Optimal reserve site selection with distance requirements. Computers & Operations Research, 35, 448–498.

    Article  Google Scholar 

  37. Williams, J. C., ReVelle, C. S., & Levin, S. A. (2005). Spatial attributes and reserve design models: a review. Environmental Modeling and Assessment, 10, 163–181.

    Article  Google Scholar 

Download references

Acknowledgments

The author would like to thank the anonymous reviewers for their helpful and constructive comments.

This work was supported by the Laboratory CEDRIC at the École Nationale Supérieure d’Informatique pour l’Industrie et l’Entreprise.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alain Billionnet.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Billionnet, A. Designing Connected and Compact Nature Reserves. Environ Model Assess 21, 211–219 (2016). https://doi.org/10.1007/s10666-015-9465-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10666-015-9465-3

Keywords

Navigation