Skip to main content

Spatial attributes and reserve design models: A review

Environmental Modeling & Assessment volume 10, pages 163–181 (2005)Cite this article

A variety of decision models have been formulated for the optimal selection of nature reserve sites to represent a diversity of species or other conservation features. Unfortunately, many of these models tend to select scattered sites and do not take into account important spatial attributes such as reserve shape and connectivity. These attributes are likely to affect not only the persistence of species but also the general ecological functioning of reserves and the ability to effectively manage them. In response, researchers have begun formulating reserve design models that improve spatial coherence by controlling spatial attributes. We review the spatial attributes that are thought to be important in reserve design and also review reserve design models that incorporate one or more of these attributes. Spatial modeling issues, computational issues, and the trade-offs among competing optimization objectives are discussed. Directions for future research are identified. Ultimately, an argument is made for the development of models that capture the dynamic interdependencies among sites and species populations and thus incorporate the reasons why spatial attributes are important.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

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

Figure 1
Figure 2
Figure 3

References

  1. J.B. Kirkpatrick, An iterative method for establishing priorities for the selection of nature reserves: an example from Tasmania, Biol. Conserv. 25 (1983) 127–134.

    Article  Google Scholar 

  2. R.L. Pressey, The first reserve selection algorithm – a retrospective on Jamie Kirkpatrick's 1983 paper, Prog. Phys. Geogr. 26(3) (2002) 434–441.

    Article  Google Scholar 

  3. M. Cabeza and A. Moilanen, Design of reserve networks and the persistence of biodiversity, Trends Ecol. Evol. 16(5) (2001) 242–248.

    Article  PubMed  Google Scholar 

  4. J.M. Diamond, The island dilemma: lessons of modern biogeographic studies for the design of nature reserves, Biol. Conserv. 7 (1975) 129–146.

    Article  Google Scholar 

  5. C. Margules, A. Nichols and R. Pressey, Selecting networks of reserves to maximize biological diversity, Biol. Conserv. 43 (1988) 63–76.

    Article  Google Scholar 

  6. R.L. Pressey, H.P. Possingham and J.R. Day, Effectiveness of alternative heuristic algorithms for identifying indicative minimum requirements for conservation reserves, Biol. Conserv. 80 (1997) 207–219.

    Article  Google Scholar 

  7. H. Possingham, J. Day, M. Goldfinch, F. Salzborn, The mathematics of designing a network of protected areas for conservation, in: Decision Sciences, Tools for Today, eds. D. Sutton, E. Cousins and C. Pierce (Proceedings of the 12th Australian Operations Research Conference, ASOR, Adelaide, 1993) pp. 536–545.

  8. L. Underhill, Optimal and suboptimal reserve selection algorithms, Biol. Conserv. 35 (1994) 85–87.

    Article  Google Scholar 

  9. C. Toregas, R. Swain, C. ReVelle and L. Bergman, The location of emergency service facilities, Oper. Res. 19 (1971) 1363–1373.

    Google Scholar 

  10. J.D. Camm, S. Polasky, A. Solow and B. Csuti, A note on optimal algorithms for reserve site selection, Biol. Conserv. 78 (1996) 353–355.

    Article  Google Scholar 

  11. R.L. Church, D.M. Stoms and F.W. Davis, Reserve selection as a maximal covering location problem, Biol. Conserv. 76 (1996) 105–112.

    Article  Google Scholar 

  12. A.S. Rodrigues, J.O. Cerdeira and K.J. Gaston, Flexibility, efficiency, and accountability: adapting reserve selection algorithms to more complex conservation problems, Ecography 23 (2000) 565–574.

    Article  Google Scholar 

  13. C.S. ReVelle, J.C. Williams and J.J. Boland, Counterpart models in facility location science and reserve selection science, Environ. Model. Assess. 7(2) (2002) 71–80.

    Google Scholar 

  14. S. Levin, Fragile Dominion (Perseus Books, Reading, MA, 1999).

    Google Scholar 

  15. C.R. Margules, A.O. Nicholls and M.B. Usher, Apparent species turnover, probability of extinction and the selection of nature reserves: a case study of the Ingleborough limestone pavements, Conserv. Biol. 8(2) (1994) 398–409.

    Article  Google Scholar 

  16. K.M. Virolainen, T. Virola, J. Suhonen, M. Kuitunen, A. Lammi and P. Siikamaki, Selecting networks of nature reserves: methods do affect the long-term outcome, Proc. R. Soc. Lond., B 266 (1999) 1141–1146.

    Google Scholar 

  17. A.S.L. Rodrigues, R.D. Gregory and K.J. Gaston, Robustness of reserve selection procedures under temporal species turnover, Proc. R. Soc. Lond., B 267 (2000) 49–55.

    CAS  Google Scholar 

  18. M. Cabeza and A. Moilanen, Site-selection algorithms and habitat loss, Conserv. Biol. 17(5) (2003) 1402–1413.

    Article  Google Scholar 

  19. C.R. Margules, A.J. Higgs and R.W. Rafe, Modern biogeographic theory: are there any lessons for nature reserve design?, Biol. Conserv. 24 (1982) 115–128.

    Article  Google Scholar 

  20. M.E. Soule and D. Simberloff, What do genetics and ecology tell us about the design of nature reserves?, Biol. Conserv. 35 (1986) 19–40.

    Article  Google Scholar 

  21. R.J. Lambeck, Focal species: a multi-species umbrella for nature conservation, Conserv. Biol. 11(4) (1997) 849–856.

    Article  Google Scholar 

  22. L. Fahrig, How much habitat is enough?, Biol. Conserv. 100 (2001) 65–74.

    Article  Google Scholar 

  23. R.S. Etienne and J.A.P. Heesterbeek, On optimal size and number of reserves for metapopulation persistence, J. Theor. Biol. 203 (2000) 33–50.

    Article  PubMed  CAS  Google Scholar 

  24. D. Simberloff and L.G. Abele, Refuge design and island biogeographic theory: effects of fragmentation, Am. Nat. 120(1) (1982) 41–50.

    Article  Google Scholar 

  25. I. Hanski, Metapopulation dynamics, Nature 396 (1998) 41–49.

    Article  CAS  Google Scholar 

  26. C.L. Shafer, Inter-reserve distance, Biol. Conserv. 100 (2001) 215–227.

    Article  Google Scholar 

  27. R.A. Briers, Incorporating connectivity into reserve selection procedures, Biol. Conserv. 103 (2002) 77–83.

    Article  Google Scholar 

  28. F. van Langevelde, W.G.M. van der Knaap and G.D.H. Classen, Comparing connectivity in landscape networks, Environ. Plann. B 25 (1998) 849–863.

    Google Scholar 

  29. L. Tischendorf and L. Fahrig, On the usage and measurement of landscape connectivity, Oikos 90 (2000) 7–19.

    Article  Google Scholar 

  30. A.G. Bunn, D.L. Urban and T.H. Keitt, Landscape connectivity: a conservation application of graph theory, J. Environ. Manag. 59 (2000) 265–278.

    Google Scholar 

  31. D. Urban and T. Keitt, Landscape connectivity: a graph–theoretic perspective, Ecology 82(5) (2001) 1205–1218.

    Article  Google Scholar 

  32. D. Simberloff and J. Cox, Consequences and costs of conservation corridors, Conserv. Biol. 1(1) (1987) 63–71.

    Article  Google Scholar 

  33. R.F. Noss, Corridors in real landscapes: a reply to Simberloff and Cox, Conserv. Biol. 1(2) (1987) 159–164.

    Article  Google Scholar 

  34. R.J. Hobbs, The role of corridors in conservation: solution or bandwagon?, Trends Ecol. Evol. 7(11) (1992) 389–392.

    Article  Google Scholar 

  35. D. Simberloff, J.A. Farr, J. Cox and D.W. Mehlman, Movement corridors: conservation bargains or poor investments?, Conserv. Biol. 6(4) (1992) 493–504.

    Article  Google Scholar 

  36. G.R. Hess, Conservation corridors and contagious disease: a cautionary note, Conserv. Biol. 8(1) (1994) 256–262.

    Article  Google Scholar 

  37. D.J.D. Earn, S.A. Levin and P. Rohani, Coherence and conservation, Science 290 (2000) 1360–1364.

    CAS  Google Scholar 

  38. P. Beier and R.F. Noss, Do habitat corridors provide connectivity?, Conserv. Biol. 12(6) (1998) 1241–1252.

    Article  Google Scholar 

  39. M.E. Soule, and M.E. Gilpin, The theory of wildlife corridor capability, in: Nature Conservation 2: The Role of Corridors, eds. D.A. Saunders and R.J. Hobbs (Surrey Beatty & Sons, New South Wales, 1991) pp. 3–8.

    Google Scholar 

  40. R.T.T. Forman, Landscape corridors: from theoretical foundations to public policy, in: Nature Conservation 2: The Role of Corridors, eds. D.A. Saunders and R.J. Hobbs (Surrey Beatty & Sons, New South Wales, 1991) pp. 71–84.

    Google Scholar 

  41. C.M. Schonewald-Cox and J.W. Bayless, The boundary model: a geographic analysis of design and conservation of nature reserves, Biol. Conserv. 38 (1986) 305–322.

    Article  Google Scholar 

  42. W.E. Kunin, Sample shape, spatial scale and species counts: implications for reserve design, Biol. Conserv. 82 (1997) 369–377.

    Article  Google Scholar 

  43. M. Game, Best shape for nature reserves, Nature 287 (1980) 630–632.

    Article  Google Scholar 

  44. E.J. Gustafson, Quantifying landscape spatial pattern: what is the state of the art?, Ecosystems 1 (1998) 143–156.

    Article  Google Scholar 

  45. R.H. Giles and M.G. Trani, Key elements of landscape pattern measures, Environ. Manag. 23(4) (1999) 477–481.

    Article  Google Scholar 

  46. R.F. Austin, Measuring and comparing two-dimensional shapes, in: Spatial Statistics and Models, eds. G.L. Gaile and C.J. Willmott (D. Reidel Publishing Co., Dordrecht, 1984) pp. 293–312.

    Google Scholar 

  47. F. Medda, P. Nijkamp and P. Rietveld, Recognition and classification of urban shapes, Geogr. Anal. 30(3) (1998) 304–314.

    Google Scholar 

  48. M. Batisse, The relevance of MAB, Environ. Conserv. 7 (1980) 179–184.

    Google Scholar 

  49. M. Batisse, The biosphere reserve: a tool for environmental conservation and management, Environ. Conserv. 9 (1982) 101–111.

    Google Scholar 

  50. M. Batisse, Development and implementation of the biosphere reserve concept and its applicability to coastal regions, Environ. Conserv. 17 (1990) 111–116.

    Article  Google Scholar 

  51. M. Batisse, A challenge for biodiversity conservation and regional development, Environment 39(5) (1997) 7–15, 31–33.

    Google Scholar 

  52. M.W. Schwartz, Choosing the appropriate scale of reserves for conservation, Ann. Rev. Ecolog. Syst. 30 (1999) 83–108.

    Article  Google Scholar 

  53. C.C. Mann and M.L. Plummer, The high cost of biodiversity, Science 260 (1993) 1868–1871.

    CAS  Google Scholar 

  54. M.E. Soule and J. Terborgh, The policy and science of regional conservation, in: Continental Conservation, eds. M.E. Soule and J. Terborgh (Island Press, Washington, DC, 1999) pp.1–17.

    Google Scholar 

  55. A.O. Nicholls and C.R. Margules, An upgraded reserve selection algorithm, Biol. Conserv. 64 (1993) 165–169.

    Article  Google Scholar 

  56. M. Bedward, R.L. Pressey and D.A. Keith, A new approach for selecting fully representative reserve networks: addressing efficiency, reserve design and land suitability with an iterative analysis, Biol. Conserv. 62 (1992) 115–125.

    Article  Google Scholar 

  57. P. Siitonen, A. Tanskanen and A. Lehtinen, Method for selection of old-forest reserves, Conserv. Biol. 16(5) (2002) 1398–1408.

    Article  Google Scholar 

  58. J. Wright, C. ReVelle and J. Cohon, A multiobjective integer programming model for the land acquisition problem, Reg. Sci. Urban Econ. 13 (1983) 31–53.

    Article  Google Scholar 

  59. K.C. Gilbert, D.D. Holmes and R.E. Rosenthal, A multiobjective discrete optimization model for land allocation, Manag. Sci. 31(12) (1985) 1509–1522.

    Google Scholar 

  60. S.D. Minor and T.L. Jacobs, Optimal land allocations for solid- and hazardous-waste landfill siting, J. Environ. Eng. 120(5) (1994) 1095–1108.

    Google Scholar 

  61. J.G. Hof and L.A. Joyce, A mixed-integer linear programming approach for spatially optimizing wildlife and timber in managed forest ecosystems, For. Sci. 39(4) (1993) 816–834.

    Google Scholar 

  62. S. Snyder and C. ReVelle, Multiobjective grid packing model: an application in forest management, Location Sci. 5(3) (1997) 165–180.

    Article  Google Scholar 

  63. A.T. Murray and S. Snyder, Spatial modeling in forest management and natural resources planning, For. Sci. 46(2) (2000) 153–156.

    Google Scholar 

  64. K.D. Rothley, Designing bioreserve networks to satisfy multiple, conflicting demands, Ecol. Appl. 9(3) (1999) 741–750.

    Google Scholar 

  65. M. McDonnell, H. Possingham, I. Ball and E. Cousins, Mathematical methods for spatially cohesive reserve design, Environ. Model. Assess. 7(2) (2002) 107–114.

    Google Scholar 

  66. D.T. Fischer and R.L. Church, Clustering and compactness in reserve site selection: an extension of the biodiversity management area selection model, For. Sci. 49(4) (2003) 555–565.

    Google Scholar 

  67. K.D. Rothley, Dynamically-based criteria for the identification of optimal bioreserve networks, Environ. Model. Assess. 7(2) (2002) 123–128.

    Google Scholar 

  68. J.C. Williams and C.S. ReVelle, A 0–1 programming approach to delineating protected reserves, Environ. Plann. B 23 (1996) 607–624.

    Google Scholar 

  69. D.J. Nalle, J.L. Arthur and J. Sessions, Designing compact and contiguous reserve networks with a hybrid heuristic algorithm, For. Sci. 48(1) (2002) 59–68.

    Google Scholar 

  70. J.C. Williams and C.S. ReVelle, Reserve assemblage of critical areas: a zero–one programming approach, Eur. J. Oper. Res. 104 (1998) 497–509.

    Article  Google Scholar 

  71. M.A. Clemens, C.S. ReVelle and J.C. Williams, Reserve design for species preservation, Eur. J. Oper. Res. 112 (1999) 273–283.

    Article  Google Scholar 

  72. J. Sessions, Solving for habitat connections as a Steiner network problem, For. Sci. 38 (1992) 203–207.

    Google Scholar 

  73. J.C. Williams, Delineating protected wildlife corridors with multi-objective programming, Environ. Model. Assess. 3 (1998) 77–86.

    Google Scholar 

  74. J. Hof and C.H. Flather, Accounting for connectivity and spatial correlation in the optimal placement of wildlife habitat, Ecol. Model. 88 (1996) 143–155.

    Article  Google Scholar 

  75. J.C. Williams, A zero–one programming model for contiguous land acquisition, Geogr. Anal. 34(4) (2002) 330–349.

    Google Scholar 

  76. R.S. Garfinkel and G.L. Nemhauser, Optimal political districting by implicit enumeration techniques, Manag. Sci. 16B (1970) 495–508.

    Google Scholar 

  77. J.T. Diamond and J.R. Wright, An implicit enumeration technique for the land acquisition problem, Civ. Eng. Syst. 8 (1991) 101–114.

    Google Scholar 

  78. D.J. Nalle, J.L. Arthur, C.A. Montgomery and J. Sessions, Economic and spatial impacts of an existing reserve network on future augmentation, Environ. Model. Assess. 7(2) (2002) 99–105.

    Google Scholar 

  79. H. Onal and R.A. Briers, Incorporating spatial criteria in optimum reserve network selection, Proc. R. Soc. Lond., B 269 (2002) 2437–2441.

    Google Scholar 

  80. S.A. Malcolm and C. ReVelle, Rebuilding migratory flyways using directed conditional covering, Environ. Model. Assess. 7(2) (2002) 129–138.

    Google Scholar 

  81. J.C. Williams, D.J. Bain and C.S. ReVelle, A decision model for selecting protected habitat areas within migratory flyways, Socio-Econ. Plann. Sci. 37 (2003) 239–268.

    Article  Google Scholar 

  82. T.J. Cova and R.L. Church, Contiguity constraints for single-region site search problems, Geogr. Anal. 32(4) (2000) 306–329.

    Article  Google Scholar 

  83. J.C. Williams, Convex land acquisition with zero–one programming, Environ. Plann. B 30 (2003) 255–270.

    Google Scholar 

  84. F. Jordan, A reliability-theory approach to corridor design, Ecol. Model. 128 (2000) 211–220.

    Article  Google Scholar 

  85. H. Possingham, I. Ball and S. Andelman, Mathematical methods for identifying representative reserve networks, in: Quantitative Methods for Conservation Biology, eds. S. Ferson and M. Burgman (Springer, Berlin Heidelberg New York, 2000) pp. 291–306.

    Google Scholar 

  86. H. Onal and R.A. Briers, Selection of a minimum-boundary reserve network using integer programming, Proc. R. Soc. Lond., B 270 (2003) 1487–1491.

    Google Scholar 

  87. S. Benabdallah and J.R. Wright, Shape considerations in spatial optimization, Civ. Eng. Syst. 8 (1991) 145–152.

    Google Scholar 

  88. I.H. Osman and J.P. Kelly, Meta-Heuristics: Theory and Applications (Kluwer Academic Publishers, Boston, 1996).

    Google Scholar 

  89. K. Rosing and C. ReVelle, Heuristic concentration: two stage solution construction, Eur. J. Oper. Res. 97 (1997) 75–86.

    Article  Google Scholar 

  90. R.L. Pressey, H.P. Possingham and C.R. Margules, Optimality in reserve selection algorithms: when does it matter and how much?, Biol. Conserv. (76) (1996) 259–267.

  91. A.S.L. Rodrigues and K.J. Gaston, Optimization in reserve selection procedures – why not?, Biol. Conserv. 107 (2002) 123–129.

    Article  Google Scholar 

  92. H. Onal, First-best, second-best, and heuristic solutions in conservation reserve site selection, Biol. Conserv. 115 (2003) 55–62.

    Article  Google Scholar 

  93. R.L. Pressey, C.J. Humphries, C.R. Margules, R.I. Vane-Wright and P.H. Williams, Beyond opportunism: key principles for systematic reserve selection, Trends Ecol. Evol. 8(4) (1993) 124–128.

    Article  Google Scholar 

  94. C.S. ReVelle, Facility siting and integer-friendly programming, Eur. J. Oper. Res. 65 (1993) 147–158.

    Article  Google Scholar 

  95. J.G. Skellam, Random dispersal in theoretical populations, Biometrika 38 (1951) 196–218.

    PubMed  CAS  Google Scholar 

  96. A. Okubo and S.A. Levin, Diffusion and Ecological Problems: Modern Perspectives, second edition (Springer, Berlin Heidelberg New York, 2001).

    Google Scholar 

  97. R. Levins, Some demographic and genetic consequences of environmental heterogeneity for biological control, Bull. Entomol. Soc. Am. 15 (1969) 237−240.

    Google Scholar 

  98. R. Levins, Extinction, in: Some Mathematical Problems in Biology, ed. M. Gesternhaber (Amercian Mathematical Society, Providence, RI, 1970) pp. 77–107.

    Google Scholar 

  99. S.A. Levin, Population dynamic models in heterogeneous environments, Ann. Rev. Ecolog. Syst. 7 (1976) 287–311.

    Article  Google Scholar 

  100. S.A. Levin, Spatial patterning and the structure of ecological communities, in: Lectures on Mathematics in the Life Sciences, Vol. 8: Some Mathematical Questions in Biology VII, ed. S.A. Levin (American Mathematical Society, Providence, RI, 1976) pp. 1–36.

    Google Scholar 

  101. D.S. DeAngelis and L.J. Gross, Individual-Based Models and Approaches in Ecology: Populations, Communities and Ecosystems (Chapman & Hall, New York, 1992).

    Google Scholar 

  102. S.W. Pacala, C.D. Canham, J. Saponara, J.A. Silander, R.K. Kobe and E. Ribbens, Forest models defined by field measurements: estimation, error analysis and dynamics, Ecol. Monogr. 66(1) (1996) 1–43.

    Google Scholar 

  103. J.B. Dunning, D.J. Stewart, B.J. Danielson, B.R. Noon, T.L. Root, R.H. Lamberson and E.E. Stevens, Spatially explicit population models: current forms and future uses, Ecol. Appl. 5(1) (1995) 3–11.

    Google Scholar 

  104. P. Kareiva and U. Wennergren, Connecting landscape patterns to ecosystem and population processes, Nature 373 (1995) 299–302.

    Article  CAS  Google Scholar 

  105. S.R. Beissinger and M.I. Westphal, On the use of demographic models of population viability in endangered species management, J. Wildl. Manage. 62(3) (1998) 821–841.

    Google Scholar 

  106. J. Hof and M.G. Raphael, Optimization of habitat placement: a case study of the Northern Spotted Owl in the Olympic Peninsula, Ecol. Appl. 7(4) (1997) 1160–1169.

    Google Scholar 

  107. M. Bevers, J. Hof, D.W. Uresk and G.L. Schenbeck, Spatial optimization of prairie dog colonies for black-footed ferret recovery, Oper. Res. 45(4) (1997) 495–507.

    Article  Google Scholar 

  108. J.R. Day and H.P. Possingham, A stochastic metapopulation model with variability in patch size and position, Theor. Popul. Biol. 48 (1995) 333–360.

    Article  Google Scholar 

  109. F.R. Adler and B. Nuernberger, Persistence in patchy irregular landscapes, Theor. Popul. Biol. 45 (1994) 41–75.

    Article  Google Scholar 

  110. J. Chave, K. Wiegand and S. Levin, Spatial and biological aspects of reserve design, Environ. Model. Assess. 7(2) (2002) 115–122.

    Google Scholar 

  111. R.G. Haight, B. Cypher, P.A. Kelly, S. Phillips, H.P. Possingham, K. Ralls, A.M. Starfield, P.J. White and D. Williams, Optimizing habitat protection using demographic models of population viability, Conserv. Biol. 16(5) (2002) 1386–1397.

    Article  Google Scholar 

  112. R.G. Haight, B. Cypher, P.A. Kelly, S. Phillips, K. Ralls and H.P. Possingham, Optimizing reserve expansion for disjunct populations of San Joaquin kit fox, Biol. Conserv. 117 (2004) 61–72.

    Article  Google Scholar 

  113. J. Hof and M. Bevers, Spatial Optimization for Managed Ecosystems (Columbia University Press, New York, 1998).

    Google Scholar 

  114. J. Hof and M. Bevers, Spatial Optimization in Ecological Applications (Columbia University Press, New York, 2002).

    Google Scholar 

  115. J. Hof, M. Bevers, D.W. Uresk and G.L. Schenbeck, Optimizing habitat location for black-tailed prairie dogs in southwestern South Dakota, Ecol. Model. 147 (2002) 11–21.

    Article  Google Scholar 

  116. A. Moilanen and M. Cabeza, Single-species dynamic site selection, Ecol. Appl. 12(3) (2002) 913–926.

    Google Scholar 

  117. R. Haight, C. ReVelle and S. Snyder, An integer optimization approach to a probabilistic reserve site selection problem, Oper. Res. 48 (2000) 697–708.

    Article  Google Scholar 

  118. S. Polasky, J. Camm, A. Solow, B. Csuti, D. White and R. Ding, Choosing reserve networks with incomplete species information, Biol. Conserv. 94 (2000) 1–10.

    Article  Google Scholar 

  119. J.D. Camm, S.K. Norman, S. Polasky and A.R. Solow, Nature reserve site selection to maximize expected species covered, Oper. Res. 50(6) (2002) 946–955.

    Article  Google Scholar 

  120. J.L. Arthur, R.G. Haight, C.A. Montgomery and S. Polasky, Analysis of the threshold and expected coverage approaches to the probabilistic reserve site selection problem, Environ. Model. Assess. 7(2) (2002) 81–89.

    Google Scholar 

  121. M.B. Araujo and P.H. Williams, Selecting areas for species persistence using occurrence data, Biol. Conserv. 96 (2000) 331–345.

    Article  Google Scholar 

  122. P.H. Williams and M.B. Araujo, Using probability of persistence to identify important areas for biodiversity conservation, Proc. R. Soc. Lond., B 267 (2000) 1959–1966.

    CAS  Google Scholar 

  123. P.H. Williams and M.B. Araujo, Apples, oranges, and probabilities: integrating multiple factors into biodiversity conservation with consistency, Environ. Model. Assess. 7(2) (2002) 139–151.

    Google Scholar 

  124. M.B. Araujo, P.H. Williams and R.J. Fuller, Dynamics of extinction and the selection of nature reserves, Proc. R. Soc. Lond. B 269 (2002) 1971–1980.

    Article  Google Scholar 

  125. C. Costello and S. Polasky, Dynamic reserve site selection, Res. Energy Econ. 26 (2004) 157–174.

    Article  Google Scholar 

  126. N.D. Burgess, C. Rahbek, F.W. Larsen, P. Williams and A. Balmford, How much of the vertebrate diversity of sub-Saharan Africa is catered for by recent conservation proposals?, Biol. Conserv. 107 (2002) 327–339.

    Article  Google Scholar 

  127. B. Csuti, S. Polasky, P.H. Williams, R.L. Pressey, J.D. Camm, M. Kershaw, A.R. Kiester, B. Downs, R. Hamilton, M. Huso and K. Sahr, A comparison of reserve selection algorithms using data on terrestrial vertebrates in Oregon, Biol. Conserv. 80 (1997) 83–97.

    Article  Google Scholar 

  128. R.L. Pressey and V.S. Logan, Size of selection units for future reserves and its influence on actual vs. targeted representation of features: a case study in western New South Wales, Biol. Conserv. 85 (1998) 305–319.

    Article  Google Scholar 

  129. S.D. Bassett and T.C. Edwards Jr., Effect of different sampling schemes on the spatial placement of conservation reserves in Utah, USA, Biol. Conserv. 113 (2003) 141–151.

    Article  Google Scholar 

  130. S.A. Levin, The problem of pattern and scale in ecology, Ecology 73(6) (1992) 1943–1967.

    Google Scholar 

  131. K. Freemark, D. Bert and M.A. Villard, Pathch-, landscape-, and regional-scale effects on biota, in: Applying Landscape Ecology in Biological Conservation, ed. K.J. Gutzwiller (Springer, Berlin Heidelberg New York, 2002) pp. 58–83.

    Google Scholar 

  132. D. Memtsas, Multiobjective programming methods in the reserve selection problem. Eur. J. Oper. Res. 150 (2003) 640–652.

    Article  Google Scholar 

  133. J. Cohon, Multiobjective Programming and Planning (Academic Press, New York, 1978).

    Google Scholar 

  134. R.E. Steuer, Multiple Criteria Optimization: Theory, Computation, and Application (John Wiley & Sons, New York, 1986).

    Google Scholar 

Download references

Acknowledgements

We thank Sharon Kingsland for her thoughtful comments on an earlier draft of this paper. We also thank two anonymous reviewers for their helpful suggestions. This research was supported by a grant from the David and Lucile Packard Foundation, Interdisciplinary Science Program. We gratefully acknowledge their support.

Author information

Authors and Affiliations

  1. Department of Geography and Environmental Engineering, Johns Hopkins University, Baltimore, MD, 21218, USA

    Justin C. Williams & Charles S. ReVelle

  2. Department of Ecology and Evolutionary Biology, Princeton University, Princeton, NJ, 08544, USA

    Simon A. Levin

Authors
  1. Justin C. Williams
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Charles S. ReVelle
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Simon A. Levin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Justin C. Williams.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Williams, J.C., ReVelle, C.S. & Levin, S.A. Spatial attributes and reserve design models: A review. Environ Model Assess 10, 163–181 (2005). https://doi.org/10.1007/s10666-005-9007-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10666-005-9007-5

Keywords

  • reserve design
  • biological conservation
  • spatial optimization
  • mathematical modeling