Abstract
The problem of selecting nature reserves has received increased attention in the literature during the past decade, and a variety of approaches have been promoted for selecting those sites to include in a reserve network. One set of techniques employs heuristic algorithms and thus provides possibly sub-optimal solutions. Another set of models and accompanying algorithms uses an integer programming formulation of the problem, resulting in an optimization problem known as the Maximal Covering Problem, or MCP. Solution of the MCP provides an optimal solution to the reserve site selection problem, and while various algorithms can be employed for solving the MCP they all suffer from the disadvantage of providing a single optimal solution dictating the selection of areas for conservation. In order to provide complete information to decision makers, the determination of all alternate optimal solutions is necessary. This paper explores two procedures for finding all such solutions. We describe the formulation and motivation of each method. A computational analysis on a data set describing native terrestrial vertebrates in the state of Oregon illustrates the effectiveness of each approach.
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Camm, J.D. and Sweeney, D.J. (1994) Row reduction in the maximal set covering problem. Working paper QA-1994-005, Department of Quantitative Analysis and Operations Management, University of Cincinnati, Cincinnati, OH.
Camm, J.D., Polasky, S., Solow, A. and Csuti, B. (in press) A note on optimization models for reserve site selection. Biological Conservation.
Church, R.L., Stoms, D.M. and Davis, F.W. (1996) Reserve selection as a maximal covering location problem. Biological Conservation, 76, 105–12.
Csuti, B., Polasky, S., Williams, P.H., Pressey, R.L., Camm, J.D., Kershaw, M., Kiester, A.R., Downs, B.
Hamilton, R., Huso, M. and Sahr, K. (in press) A comparison of reserve selection algorithms using data on terrestrial vertebrates in Oregon. Biological Conservation.
Downs, B.T. and Camm, J.D. (1996) An exact algorithm for the maximal covering problem. Naval Research Logistics, 34, 435–61
Garfinkel, R.S. and Nemhauser, G.L. (1972) Integer programming. Wiley, New York.
Gerrard, R.A. and Church, R.L. (1995) A general construct for the zonally constrained p-median problem. Environment and Planning B: Planning and Design, 22, 213–36.
IBM (1992) Optimization Subroutine Library (OSL), Guide and Reference, Release 2. Fourth edition. IBM Corporation, Kingston, New York.
Kershaw, M., Williams, P.H. and Mace, G.C. (1994) Conservation of Afrotropical antelopes: consequences and efficiency of using different site selection methods and diversity criteria. Biodiversity and Conservation, 3, 354–72.
Land, A.H. and Doig, A.G. (1960) An automatic method of solving discrete programming problems. Econometrica, 28, 497–520.
Margules, C.R., Nicholls, A.O. and Pressey, R.L. (1988) Selecting networks of reserves to maximize biological diversity. Biological Conservation, 43, 63–76.
Nicholls, A.O. and Margules, C.R. (1993) An upgraded reserve selection algorithm. Biological Conservation, 41, 11–37.
Polasky, S., Jaspin, M., Szenfandrasi, S., Bergeron, N. and Berrens, R. (1995) Bibliography on the Conservation of Biological Diversity: Biological/Ecological, Economic, and Policy Issues. Unpublished report. Department of Agricultural and Resource Economics, Oregon State University, Corvallis, OR.
Pressey, R.L. and Nicholls, A.O. (1989) Application of a numerical algorithm to the selection of reserves in semi-arid New South Wales. Biological Conservation, 50, 263–78.
Pressey, R.L., Possingham, H.P. and Margules, C. R. (1996) Optimality in reserve selection algorithms: when does it matter and how much? Biological Conservation, 76, 259–67.
Pressey, R.L., Humphries, C.J., Margules, C.R., Vane-Wright, R.I. and Williams, P.H. (1993) Beyond opportunism: key principles for systematic reserve selection. Trends in Ecology and Evolution, 8, 124–8.
Underhill, L.G. (1994) Optimal and suboptimal reserve selection algorithms. Biological Conservation, 70, 85–7.
Vane-Wright, R.I., Humphries, C.J. and Williams, P.H. (1991) What to protect? systematics and the agony of choice. Biological Conservation, 55, 235–54.
White, D., Kimerling, A.J. and Overton, W.S. (1992) Cartographic and geometric components of a global sampling design for environmental monitoring. Cartography and Geographic Information Systems, 19, 5–22.
Williams, P.H., Vane-Wright, R.I. and Humphries, C.J. (1993) Measuring biodiversity for choosing conservation areas. In Hymenoptera and Biodiversity, J. LaSalle and I Gauld (eds) CAB International: Wallingford, U
Williams, P., Gibbons, C., Margules, C., Rebelo, A., Humphries, C. and Pressey, R. (in press) A comparison of richness hotspots, rarity hotspots, and complementary areas of conserving diversity using British birds. Biological Conservation.
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Arthur, J.L., Hachey, M., Sahr, K. et al. Finding all optimal solutions to the reserve site selection problem: formulation and computational analysis. Environmental and Ecological Statistics 4, 153–165 (1997). https://doi.org/10.1023/A:1018570311399
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DOI: https://doi.org/10.1023/A:1018570311399