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.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
Tax calculation will be finalised during checkout.
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.
R.L. Pressey, The first reserve selection algorithm – a retrospective on Jamie Kirkpatrick's 1983 paper, Prog. Phys. Geogr. 26(3) (2002) 434–441.
M. Cabeza and A. Moilanen, Design of reserve networks and the persistence of biodiversity, Trends Ecol. Evol. 16(5) (2001) 242–248.
J.M. Diamond, The island dilemma: lessons of modern biogeographic studies for the design of nature reserves, Biol. Conserv. 7 (1975) 129–146.
C. Margules, A. Nichols and R. Pressey, Selecting networks of reserves to maximize biological diversity, Biol. Conserv. 43 (1988) 63–76.
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.
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.
L. Underhill, Optimal and suboptimal reserve selection algorithms, Biol. Conserv. 35 (1994) 85–87.
C. Toregas, R. Swain, C. ReVelle and L. Bergman, The location of emergency service facilities, Oper. Res. 19 (1971) 1363–1373.
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.
R.L. Church, D.M. Stoms and F.W. Davis, Reserve selection as a maximal covering location problem, Biol. Conserv. 76 (1996) 105–112.
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.
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.
S. Levin, Fragile Dominion (Perseus Books, Reading, MA, 1999).
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.
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.
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.
M. Cabeza and A. Moilanen, Site-selection algorithms and habitat loss, Conserv. Biol. 17(5) (2003) 1402–1413.
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.
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.
R.J. Lambeck, Focal species: a multi-species umbrella for nature conservation, Conserv. Biol. 11(4) (1997) 849–856.
L. Fahrig, How much habitat is enough?, Biol. Conserv. 100 (2001) 65–74.
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.
D. Simberloff and L.G. Abele, Refuge design and island biogeographic theory: effects of fragmentation, Am. Nat. 120(1) (1982) 41–50.
I. Hanski, Metapopulation dynamics, Nature 396 (1998) 41–49.
C.L. Shafer, Inter-reserve distance, Biol. Conserv. 100 (2001) 215–227.
R.A. Briers, Incorporating connectivity into reserve selection procedures, Biol. Conserv. 103 (2002) 77–83.
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.
L. Tischendorf and L. Fahrig, On the usage and measurement of landscape connectivity, Oikos 90 (2000) 7–19.
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.
D. Urban and T. Keitt, Landscape connectivity: a graph–theoretic perspective, Ecology 82(5) (2001) 1205–1218.
D. Simberloff and J. Cox, Consequences and costs of conservation corridors, Conserv. Biol. 1(1) (1987) 63–71.
R.F. Noss, Corridors in real landscapes: a reply to Simberloff and Cox, Conserv. Biol. 1(2) (1987) 159–164.
R.J. Hobbs, The role of corridors in conservation: solution or bandwagon?, Trends Ecol. Evol. 7(11) (1992) 389–392.
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.
G.R. Hess, Conservation corridors and contagious disease: a cautionary note, Conserv. Biol. 8(1) (1994) 256–262.
D.J.D. Earn, S.A. Levin and P. Rohani, Coherence and conservation, Science 290 (2000) 1360–1364.
P. Beier and R.F. Noss, Do habitat corridors provide connectivity?, Conserv. Biol. 12(6) (1998) 1241–1252.
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.
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.
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.
W.E. Kunin, Sample shape, spatial scale and species counts: implications for reserve design, Biol. Conserv. 82 (1997) 369–377.
M. Game, Best shape for nature reserves, Nature 287 (1980) 630–632.
E.J. Gustafson, Quantifying landscape spatial pattern: what is the state of the art?, Ecosystems 1 (1998) 143–156.
R.H. Giles and M.G. Trani, Key elements of landscape pattern measures, Environ. Manag. 23(4) (1999) 477–481.
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.
F. Medda, P. Nijkamp and P. Rietveld, Recognition and classification of urban shapes, Geogr. Anal. 30(3) (1998) 304–314.
M. Batisse, The relevance of MAB, Environ. Conserv. 7 (1980) 179–184.
M. Batisse, The biosphere reserve: a tool for environmental conservation and management, Environ. Conserv. 9 (1982) 101–111.
M. Batisse, Development and implementation of the biosphere reserve concept and its applicability to coastal regions, Environ. Conserv. 17 (1990) 111–116.
M. Batisse, A challenge for biodiversity conservation and regional development, Environment 39(5) (1997) 7–15, 31–33.
M.W. Schwartz, Choosing the appropriate scale of reserves for conservation, Ann. Rev. Ecolog. Syst. 30 (1999) 83–108.
C.C. Mann and M.L. Plummer, The high cost of biodiversity, Science 260 (1993) 1868–1871.
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.
A.O. Nicholls and C.R. Margules, An upgraded reserve selection algorithm, Biol. Conserv. 64 (1993) 165–169.
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.
P. Siitonen, A. Tanskanen and A. Lehtinen, Method for selection of old-forest reserves, Conserv. Biol. 16(5) (2002) 1398–1408.
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.
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.
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.
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.
S. Snyder and C. ReVelle, Multiobjective grid packing model: an application in forest management, Location Sci. 5(3) (1997) 165–180.
A.T. Murray and S. Snyder, Spatial modeling in forest management and natural resources planning, For. Sci. 46(2) (2000) 153–156.
K.D. Rothley, Designing bioreserve networks to satisfy multiple, conflicting demands, Ecol. Appl. 9(3) (1999) 741–750.
M. McDonnell, H. Possingham, I. Ball and E. Cousins, Mathematical methods for spatially cohesive reserve design, Environ. Model. Assess. 7(2) (2002) 107–114.
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.
K.D. Rothley, Dynamically-based criteria for the identification of optimal bioreserve networks, Environ. Model. Assess. 7(2) (2002) 123–128.
J.C. Williams and C.S. ReVelle, A 0–1 programming approach to delineating protected reserves, Environ. Plann. B 23 (1996) 607–624.
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.
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.
M.A. Clemens, C.S. ReVelle and J.C. Williams, Reserve design for species preservation, Eur. J. Oper. Res. 112 (1999) 273–283.
J. Sessions, Solving for habitat connections as a Steiner network problem, For. Sci. 38 (1992) 203–207.
J.C. Williams, Delineating protected wildlife corridors with multi-objective programming, Environ. Model. Assess. 3 (1998) 77–86.
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.
J.C. Williams, A zero–one programming model for contiguous land acquisition, Geogr. Anal. 34(4) (2002) 330–349.
R.S. Garfinkel and G.L. Nemhauser, Optimal political districting by implicit enumeration techniques, Manag. Sci. 16B (1970) 495–508.
J.T. Diamond and J.R. Wright, An implicit enumeration technique for the land acquisition problem, Civ. Eng. Syst. 8 (1991) 101–114.
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.
H. Onal and R.A. Briers, Incorporating spatial criteria in optimum reserve network selection, Proc. R. Soc. Lond., B 269 (2002) 2437–2441.
S.A. Malcolm and C. ReVelle, Rebuilding migratory flyways using directed conditional covering, Environ. Model. Assess. 7(2) (2002) 129–138.
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.
T.J. Cova and R.L. Church, Contiguity constraints for single-region site search problems, Geogr. Anal. 32(4) (2000) 306–329.
J.C. Williams, Convex land acquisition with zero–one programming, Environ. Plann. B 30 (2003) 255–270.
F. Jordan, A reliability-theory approach to corridor design, Ecol. Model. 128 (2000) 211–220.
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.
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.
S. Benabdallah and J.R. Wright, Shape considerations in spatial optimization, Civ. Eng. Syst. 8 (1991) 145–152.
I.H. Osman and J.P. Kelly, Meta-Heuristics: Theory and Applications (Kluwer Academic Publishers, Boston, 1996).
K. Rosing and C. ReVelle, Heuristic concentration: two stage solution construction, Eur. J. Oper. Res. 97 (1997) 75–86.
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.
A.S.L. Rodrigues and K.J. Gaston, Optimization in reserve selection procedures – why not?, Biol. Conserv. 107 (2002) 123–129.
H. Onal, First-best, second-best, and heuristic solutions in conservation reserve site selection, Biol. Conserv. 115 (2003) 55–62.
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.
C.S. ReVelle, Facility siting and integer-friendly programming, Eur. J. Oper. Res. 65 (1993) 147–158.
J.G. Skellam, Random dispersal in theoretical populations, Biometrika 38 (1951) 196–218.
A. Okubo and S.A. Levin, Diffusion and Ecological Problems: Modern Perspectives, second edition (Springer, Berlin Heidelberg New York, 2001).
R. Levins, Some demographic and genetic consequences of environmental heterogeneity for biological control, Bull. Entomol. Soc. Am. 15 (1969) 237−240.
R. Levins, Extinction, in: Some Mathematical Problems in Biology, ed. M. Gesternhaber (Amercian Mathematical Society, Providence, RI, 1970) pp. 77–107.
S.A. Levin, Population dynamic models in heterogeneous environments, Ann. Rev. Ecolog. Syst. 7 (1976) 287–311.
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.
D.S. DeAngelis and L.J. Gross, Individual-Based Models and Approaches in Ecology: Populations, Communities and Ecosystems (Chapman & Hall, New York, 1992).
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.
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.
P. Kareiva and U. Wennergren, Connecting landscape patterns to ecosystem and population processes, Nature 373 (1995) 299–302.
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.
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.
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.
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.
F.R. Adler and B. Nuernberger, Persistence in patchy irregular landscapes, Theor. Popul. Biol. 45 (1994) 41–75.
J. Chave, K. Wiegand and S. Levin, Spatial and biological aspects of reserve design, Environ. Model. Assess. 7(2) (2002) 115–122.
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.
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.
J. Hof and M. Bevers, Spatial Optimization for Managed Ecosystems (Columbia University Press, New York, 1998).
J. Hof and M. Bevers, Spatial Optimization in Ecological Applications (Columbia University Press, New York, 2002).
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.
A. Moilanen and M. Cabeza, Single-species dynamic site selection, Ecol. Appl. 12(3) (2002) 913–926.
R. Haight, C. ReVelle and S. Snyder, An integer optimization approach to a probabilistic reserve site selection problem, Oper. Res. 48 (2000) 697–708.
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.
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.
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.
M.B. Araujo and P.H. Williams, Selecting areas for species persistence using occurrence data, Biol. Conserv. 96 (2000) 331–345.
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.
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.
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.
C. Costello and S. Polasky, Dynamic reserve site selection, Res. Energy Econ. 26 (2004) 157–174.
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.
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.
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.
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.
S.A. Levin, The problem of pattern and scale in ecology, Ecology 73(6) (1992) 1943–1967.
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.
D. Memtsas, Multiobjective programming methods in the reserve selection problem. Eur. J. Oper. Res. 150 (2003) 640–652.
J. Cohon, Multiobjective Programming and Planning (Academic Press, New York, 1978).
R.E. Steuer, Multiple Criteria Optimization: Theory, Computation, and Application (John Wiley & Sons, New York, 1986).
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.
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
- reserve design
- biological conservation
- spatial optimization
- mathematical modeling