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Using a GIS to select priority areas for conservation
Computers, Environment and Urban Systems 24 (2000) 79±93 www.elsevier.com/locate/compenvurbsys
Using a GIS to select priority areas for conservation S. Woodhousea,*, A. Lovetta, P. Dolmana, R. Fullerb a
School of Environmental Sciences, University of East Anglia, Norwich NR4 7TJ, UK b British Trust for Ornithology, The Nunnery, Nunnery Place, Thetford, UK
Abstract Species richness and species rarity have been identi®ed as important criteria when selecting conservation areas. Traditional approaches that choose sites based solely on local species richness often fail to protect those species most at risk. By assessing the representation of species across a network of sites, the protection of all species is more likely to be assured. A GIS approach based on the Maximal Covering Location Problem (MCLP) is compared to existing complementarity algorithms using data collected by the British Trust for Ornithology on the distribution of birds in Wales, UK. Despite a range of solutions depending on the algorithm used, the results presented here suggest that the overall pattern of species and the habitats with which they are associated remain largely unchanged. Community ordination is used to examine the species composition of sample units and to relate this to habitat composition. This shows that key marine, coastal and moorland sites are selected by most solutions while there is a greater degree of substitutability for sites that are predominantly woodland and farmland. The GIS-based MCLP approach is then extended by incorporating various priority weightings, considered in terms of conservation criteria relevant to birds in Wales. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: GIS; Priority weightings; Conservation; Reserve selection; DCA; MCLP
1. Introduction The combined eect of habitat loss and fragmentation, ecosystem disruption and global warming severely threatens the diversity of species on our planet (Dolman, 2000). Consequently, it is estimated that many hundreds of thousands, perhaps millions, of species are threatened with extinction (Reaka-Kudla, Wilson & Wilson, * Corresponding author. Tel.: +44-1603-456161; fax: +44-1603-57719. E-mail addresses: [email protected] (S. Woodhouse), [email protected] (A. Lovett), p.dolman @uea.uk (P. Dolman), [email protected] (R. Fuller). 0198-9715/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0198-9715(99)00046-0
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1996). Although many other approaches are important, conservation of biodiversity will primarily be achieved by selecting and protecting key areas of habitat (Primack, 1993). Unfortunately, due to the demands of human populations, only a very small proportion of the Earth's surface can be managed for conservation alone. Therefore, biologists are forced to prioritise in the selection of protected areas in order to maximise potential biodiversity gains. An initial attempt to resolve this problem might be to select the most species rich locations. At a global scale, this kind of approach has proved very successful. This is because much biodiversity is unique to speci®c `biogeographic regions' and so choosing between such areas results in minimal overlap of species composition. However, when the sizes of the areas under scrutiny are substantially smaller than biogeographic regions, selecting richness hotspots may result in a high degree of species replication. Also, simply selecting areas with the highest number of taxa may do little to aid the conservation of rare species; as many species have unique habitat preferences and so do not necessarily occur in the most species-rich sites (Curnutt, Lockwood, Luh, Nott & Russell, 1994; Prendergast, Quinn, Lawton, Eversham & Gibbons, 1993; Williams, Gibbons, Margules, Rebelo, Humphries & Pressey, 1996). A far better approach, therefore, is to consider areas of complementary richness (i.e. areas that together contribute a large number of species). Identifying the best set of sites to conserve can prove to be a dicult task, particularly where the species composition of sites is similar. For example, Britain can be approximately divided into 3000 10-km squares containing some 200 dierent bird species (Gibbons, Reid & Chapman, 1993). Suppose that 150 (5%) of these squares are to be protected in order to conserve as many of the 200 species as possible. Finding the best (optimal) set of squares by testing every conceivable con®guration would require 1.4710257 separate calculations; a problem beyond the capabilities of even the most powerful computer. Consequently, problems of this type are solved using an algorithm or heuristic (Church, 1999). As such, numerous algorithms have been developed over the past decade to select conservation areas (Cocks & Baird, 1989; Margules, Nicholls & Pressey, 1988; Nicholls & Margules, 1993; Pressey, Humphries, Margules, Vanewright & Williams, 1993; Rebelo & Siegfried, 1990; Vane-Wright, Humphries & Williams, 1991; Sñtersdal, Line & Birks, 1993); examples of which are described and evaluated in the following sections of this paper. The primary objective of this study is to review and extend a GIS approach adopted by Gerrard, Church, Stoms and Davis (1997) based on the Maximal Covering Location Problem (MCLP). Two disadvantages of previous algorithms have been their inability to ®nd an optimal solution (Underhill, 1994) and the diculties encountered while trying to use procedures that are computationally complex (Church, 1999). Initially, the MCLP model is compared to the richness hotspot approach using atlas data collected by the British Trust for Ornithology (BTO; Gibbons et al., 1993). The same dataset is also used to assess the validity of the GIS-based MCLP approach relative to more widely used complementarity algorithms. Finally, the impact of a variety of priority weightings in a GIS approach are explored and an assessment made of the future role of GIS in selecting priority areas.
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2. Complementarity as a facility location problem The MCLP is an example of a facility location problem (i.e. the placement of a facility or facilities to meet a pre-determined set of objectives). Speci®cally, it is the quest to locate a set number of facilities to maximise the population served within a predetermined distance or travel time. For example, in Baltimore, MD, the MCLP model was used to determine the location of ®re stations to achieve response times of 30 min or less in rural areas and 10 min or less in urban areas (ReVelle, Bigman, Schilling, Cohon & Church, 1977). By treating species as demand centres and potential reserve sites as facility locations, Gerrard et al. (1997) showed that the MCLP model could also be used to locate conservation areas. In particular, they showed how this could be achieved using algorithms available within a GIS. ARC/INFO includes two heuristic algorithms with the ability to solve the MCLP: GRIA (global/regional interchange algorithm); (Densham & Rushton, 1992) and TEITZBART (Teitz & Bart, 1968). On the whole TEITZBART has proved to be more robust than GRIA, despite the greater sophistication of the latter. In trying to locate conservation reserves in southwestern California, Gerrard et al. (1997) found that TEITZBART outperformed GRIA once the number of reserves selected rose above four. This was attributed to the fact that the demand nodes and candidate site nodes are mutually exclusive when applying the MCLP model to reserve selection. When applied to a more conventional MCLP, however, the two heuristics were found to perform comparably, with TEITZBART ®nding the optimal solution in 54 out of 115 trials, whilst GRIA managed 56 (Church & Sorensen, 1996). Both GRIA and TEITZBART, however, were originally developed as ways of solving a slightly dierent problem: the p-median problem. Rather than seeking to maximise the population covered within a predetermined service distance, the pmedian algorithm attempts to minimise the average distance travelled between each demand node and its closest facility. Since the MCLP arose as a direct consequence of the p-median problem, algorithms to solve the p-median problem were already in place (Maranzana, 1964; Teitz & Bart, 1968). In 1976, Church and ReVelle showed that p-median algorithms could be used to solve the MCLP. This was achieved by replacing each distance in the p-median problem by zero if it was less than the maximal service distance (S) and one otherwise. Minimising the average distance travelled between each demand node and its closest facility in this instance is equivalent to minimising the amount of population served outside S (an equivalent statement to the MCLP). In addition to the two GIS heuristics described earlier, the MCLP can also be solved directly using algorithms from the ®eld of operational research (e.g. SIMPLEX [ChvaÂtal, 1983]). These can be found in both specialised optimisation packages (e.g. LINDO [Schrage, 1989]) but also in more general mathematical software such as MAPLE (Char, Geddes, Gonnet, Leong, Monagen & Watt, 1991). Unlike TEITZBART and GRIA, linear programming algorithms such as SIMPLEX will always locate an optimal solution where one exists. Whilst this is clearly a favourable property for an algorithm to hold, both the MCLP and the p-median problem are notoriously dicult to solve using standard integer programming techniques
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(Church, 1999). In locating conservation areas, where there are often a high number of site-species combinations to consider, ®nding an optimal con®guration of sites can prove to be a less than trivial task. Also, trying to solve the MCLP using linear programming is often dicult due to the integer constraints placed on the variables within the optimisation process. Although in 80% of cases a slight modi®cation to the MCLP model will produce zero-one solutions, in instances where a fractional solution is returned, a method of inspection or a Branch and Bound technique needs to be employed to obtain an optimal integer solution (Church & ReVelle, 1974). 3. Data sources and methods 3.1. Species data The species data used here derive from a nationwide survey conducted by the BTO between 1988 and 1991. The methodology employed during the survey is detailed in Gibbons et al. (1993) and is summarised here. Observers were asked to record the presence/absence (abundance in some cases) as well as the breeding status of each species within 10-km squares across Britain and Ireland. Rather than attempting to cover the entire 10-km square, each was subdivided into 25 tetrads (i.e. 22 km), of which observers were asked to spend 2 h in at least eight. Where the same 10-km square was visited in subsequent years, volunteers were encouraged to visit tetrads that had not been previously surveyed. As well as observations during timed visits, volunteers were required to submit supplementary record forms detailing additional `sightings' along with the grid reference of the 10-km square in which they occurred. This was to ensure that species undetected during timed visits would not be overlooked for the purpose of compiling the BTO Breeding Bird Atlas. For the analyses presented here, the presence or absence of each bird species at the 10-km level is based on whether or not there was evidence of breeding within that square. Also, data collected outside of timed visits are excluded to prevent further bias arising from dierential survey eort. Only 10-km squares containing visited tetrads within Wales are considered as a comparative exercise to evaluate the performance of the GIS-based MCLP approach against other selection algorithms. Timed visits during the BTO survey recorded 151 species of breeding bird across 267 10-km squares within Wales. Fig. 1a shows abundance (number of 10-km squares in which each species was found to be breeding during timed visits) plotted against species rank. It is worth noting the high number of rare species contained within the BTO dataset for Wales (characterised by the distribution's long tail), a factor that could potentially in¯uence site selection analyses. The frequency distribution of species richness across Wales is given in Fig. 1b and depicts a positively skewed pattern with a modal peak around 50 species per square. Whilst these two ®gures are primarily included to assist the reader's appreciation of the underlying dataset, both highlight interesting facets of the data worthy of consideration in future studies.
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Fig. 1. (a) The abundance of breeding bird species in Wales ranked according to their range size (1=commonest species, 151=rarest species). (b) The frequency distribution of species richness within 10km squares in Wales.
3.2. Evaluating the performance of the MCLP model and other algorithms A network representing the species' distributions and potential reserve sites was constructed following the procedure documented by Gerrard et al. (1997). Initially,
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the performances of the richness hotspot and complementarity approaches (represented by the MCLP model) were compared by considering the total number of bird species and the number of rare species contained within a network of 13 squares (5% of the total number) as selected by each of the two methods; `rare' in this instance being de®ned as a species breeding in no more than two 10-km squares within Wales [based on the same proportion as that used by Prendergast et al. (1993) and Curnutt et al. (1994)]. Secondly, the MCLP model was compared to three contrasting algorithms according to how eciently it selected squares in order to conserve all species within a given area. Mathematically: Minimise
267 i1
Yi
267 s:t: Yi xij 51 i1
j 1; . . . ; 151
where xij=1 if square i (i=1,. . .,267) conserves species j ( j=1,. . .,151); and xij=0 otherwise. The ®rst of these is an iterative or `adding' algorithm, the simplest and most widely used algorithm of its kind. This begins by selecting the most species-rich square, then the square that provides the most additional species and so on until all species have been selected. The second is an example of a more advanced iterative approach (an example of a `greedy' heuristic algorithm) adapted from Margules et al. (1988) and Nicholls and Margules (1993). It can be summarised in the following four stages: 1. Select all squares with unique occurrences of species. 2. From the squares containing the next rarest species, select the square that also adds the greatest number of additional species (i.e. species not represented in the squares already selected). 3. Where more than one square contains an equal number of unrepresented species, select the ®rst square in the list. 4. Go to Step 2. The third approach solves the reserve selection problem directly using the SIMPLEX algorithm (i.e. ®nds the minimum number of squares needed to conserve all 151 breeding bird species). This is essentially equivalent to running the MCLP model having set the number of squares required to 17 (the number needed to conserve all species). 3.3. Detrended correspondence analysis With algorithms of the type described earlier, there often exist several dierent ways of representing all species in the same number of squares; an important con-
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sideration when adopting their ®ndings to reserve selection in practice. Even in instances where a solution is known to be optimal, there may be many other combinations of sites that are also optimal, depending on the size of the area under examination and the degree of species variability that it contains. As such, it is often more interesting to study the type of squares selected and the habitat characteristics that they exhibit, rather than focusing immediately on their location. Ordination techniques such as detrended correspondence analysis (DCA) are an eective way of identifying underlying patterns in large datasets. In this instance, a DCA enabled comparisons to be made between the species composition of squares, in order to arrange species in multi-dimensional `ordination' space such that co-occurring species were in close proximity. `Site' scores on the axes of the DCA were then calculated as a weighted average of the co-ordinates of those species occurring in each 10km square. Therefore, squares with a similar location in ordination space had a similar species composition, while dissimilar squares were located in dierent parts of the ordination. The multivariate species composition of squares was then examined by locating each square on the ®rst two DCA axes, greatly reducing the number of dimensions involved (i.e. from 151 dimensions!). Bird species-habitat associations, superimposed on a DCA ordination, were subsequently used to investigate the equivalence or dissimilarity of alternative solutions obtained from the diering algorithms. These associations were primarily derived from lists given in Tucker and Evans' (1997) book Habitats for Birds in Europe, supplemented by other sources (Fuller, 1995; Fuller et al., 1995; Lovegrove, Williams & Williams, 1994). 4. Results The performance of the complementarity approach (in this case the MCLP model) is compared to the solution obtained from the richness hotspot approach in Table 1. Only four of the 13 hotspots selected contained at least one rare species and just three of the 19 rare species were represented somewhere in the network of 10-km squares. From this it is clear that complementarity is better than the richness hotspot approach both in terms of the total number of species covered and the extent to which rare species are also protected; a similar conclusion to that reached
Table 1 Richness hotspots versus complementary areas: a summary of the eectiveness of two approaches in covering rare bird species distributions in Wales Number of squares containing at least one of the 19 rare species (% of 13 squares) Richness hotspots 4 (31) Complementary areas 10 (77)
Number of rare species Total number of species contained within network represented in the network of 10-km squares (% of all 151 species) (% of all 19 rare species) 3 (16) 16 (84)
116 (77) 147 (97)
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by Prendergast et al. (1993) and Curnutt et al. (1994). The performance of the MCLP model is compared to other widely used complementarity algorithms in Table 2. The MCLP is solved both optimally as well as heuristically using the TEITZBART and GRIA algorithms available within a GIS. Despite failing to ®nd an optimal solution, the GIS heuristics perform better than the more widely used iterative approaches. For each of the six solutions in Table 2, the degree of complementarity can be assessed by considering the locations of each set of squares on the ®rst two axes of the site ordination as obtained from the DCA of the bird distribution data. These two axes combined explain 26.5% of the variation in the species data. As bird species' distributions are often determined by habitat availability at a scale below that of the 10-km square study unit, being able to explain just over a quarter of the variation at such a spatial resolution is ecologically pleasing; whilst the inclusion of further ordination axes inevitably increases the total variance explained (36% by the ®rst four axes), the simplicity and clarity of representation is lost. Also, as the number of DCA axes increases, diculties associated with attaching biological meaning to axes lower down the order increase. For this reason, results presented here are restricted to the ®rst two DCA axes. In addition, the option to exclude certain species and downweight others was rejected as the overall distribution of species remains relatively unchanged, whilst the variance explained is substantially reduced. Fig. 2 shows the positions of ®ve groups of birds on the species ordination diagram categorised according to their principal habitat. These habitats are de®ned as marine, coastal, farmland, woodland and moorland. The species plotted here represent the subset of all breeding birds in Wales where a principal habitat was easily identi®able; birds falling evenly into two or more categories (e.g. woodland/farmland) are excluded. It is not surprising that those species with similar habitat preferences (as shown in Fig. 2) are closely clustered on the ordination axes and are likely to be indicative of the species variation accounted for by the DCA. Since each site ordination score is calculated as the weighted average of the species ordination scores, as well as being able to compare the dierent solutions, the relative positions of 10-km squares in the ordination can be related back to the species that they contain. By calculating centroids for each habitat group using
Table 2 The number of 10-km squares needed to represent all breeding bird species in Wales using six complementarity algorithms Algorithm
O/Sa
Number of 10-km squares required
Algorithm
O/Sa
Number of 10-km squares required
Iterative Greedy SIMPLEX
S S O
19 18 17
MCLP (GRIA) MCLP (TEITZBART) MCLP (SIMPLEX)
S S O
18 18 17
a
O, optimal; S, suboptimal; MCLP, Maximal Covering Location Problem.
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Fig. 2. Species ordination scores for the ®rst two axes of a detrended correspondence analysis of the British Trust for Ornithology (BTO) breeding bird survey data, grouped according to principal habitat.
the species ordination scores, it is possible to determine the in¯uence of each habitat type on the position of squares. Each habitat centroid diers in its position relative to the overall mean and this dierence can therefore be plotted as a vector. Site ordination diagrams showing the positions of squares selected by each algorithm
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Fig. 3. Site ordination scores from a detrended correspondence analysis for six alternative algorithms for the prioritisation of conservation areas.
overlaid with these vectors are displayed in Fig. 3. From these it is clear that certain squares occur in each of the six solutions (irreplaceable) while others tend to appear more sporadically (substitutable). This re¯ects the number of rare species in the Welsh dataset (see Fig. 1a). The fact that ®ve squares contain unique occurrences of species immediately reduces the number of substitutable squares available for selection. Despite this, the overall distributions of squares selected by the six algorithms are similar in terms of their location on the ®rst two ordination axes. This suggests that where there is a choice between squares, although the location may dier, the underlying habitat characteristics are consistent regardless of the algorithm used.
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This is emphasised by the ®ve habitat vectors, which provide some insight into the principal habitat of each of the selected squares. These would also seem to suggest that there is a greater choice between predominantly woodland and farmland squares than between those squares that are primarily marine, coastal and moorland. This is not particularly surprising bearing in mind that 80% of the total land area of Wales is classed as agricultural and 12% as woodland (Welsh Oce, 1996). 5. Incorporating priority weightings within a GIS analysis It is often of greater practical value to attempt to maximise the number of species within a given area than to determine the smallest area within which every species can be represented (Underhill, 1994). Clearly, the MCLP is better placed to solve a problem of this type than algorithms forced to represent the full complement of species. A further advantage of the GIS-based MCLP approach is its adaptability, particularly its ability to incorporate priority weightings. For instance, Gerrard et al. (1997) ran the MCLP model within ARC/INFO having applied a weighting to favour endemic species, an approach extendable to a whole range of conservation criteria. Rather than simply aiming to maximise the total number of species represented in a given total area, it would be more useful to attach a higher priority to those species of greater conservation concern. Three alternative criteria are the relative abundance of each species within Wales (as de®ned by range size), the relative contribution of the Welsh population to the total UK range of the species, and the extent to which species are already considered at risk, as de®ned by published lists of Birds of Conservation Concern (the `Red' and `Amber' lists; Gibbons et al., 1996). Fig. 4 shows the distribution of squares selected when applying these criteria, via the GIS MCLP model, to the BTO dataset for Wales. For comparison, the set of squares selected where no weightings are applied is also given. Whilst further analyses would be required before presenting such results to conservation organisations, it is evident which squares should be given priority in the ®rst instance. 6. Discussion and conclusions The results presented in this paper suggest that when selecting priority areas for conservation, it is far better to consider the coverage of species across an entire network of protected areas than to select sites based solely on individual merit. The MCLP model is an eective way of doing this. The MCLP can be solved both optimally (via traditional integer programming techniques) as well as heuristically via a whole host of existing algorithms. In cases where an optimal solution is essential and providing the requirements of optimality are met, then an integer programming technique should be adopted. However, where the size of the dataset being analysed makes linear optimisation infeasible, heuristic approaches available within a GIS are ecient, easily applied and result in solutions comparable to those obtained using alternative algorithms. Also, the use of inbuilt GIS procedures to
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Fig. 4. Maps showing the 10-km squares selected in Wales using the GIS MCLP model with: (i) no weightings applied; (ii) species weighted by the reciprocal of the number of squares in which they are known to be breeding; (iii) species weighted by the proportion of Welsh squares in their UK distribution as a whole; (iv) only bird species on the red and amber lists included.
solve the MCLP enables weightings for a wide range of conservation criteria to be easily incorporated. This considerably increases the practical potential of the GIS MCLP model in prioritising areas for conservation investment. In addition, as well as being able to display results as maps (as in Fig. 4) without the need for any additional software, GIS allows for the integration of other spatially referenced datasets; a very useful property when analysing ecological data. For example, a natural progression to the analyses presented here is to consider the environmental attributes of the grid squares selected by each of the complementarity algorithms. What causes one square to be selected over another? Why do two adjacent squares
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vary considerably in terms of the number of species that they contain, despite having almost identical habitat characteristics? What other factors in¯uence the distribution and abundance of species? These kinds of questions are perfectly suited to analysis within a GIS (Johnston, 1998; Wadsworth & Treweek, 1999). Conservation biologists are constantly striving to ®nd more ecient ways of allocating protected areas. Much of this has stemmed from the Gap Analysis Program in the US where the aim has been to assess the distribution and protection status of plants and terrestrial vertebrates (Scott et al., 1993). Clearly, such an approach requires knowledge of areas of high complementary richness and of existing protected areas. GIS enables both of these operations to be carried out simultaneously in an integrated computer environment. A further extension to the GISbased MCLP approach would be to consider phylogenetic diversity rather than species richness (Walker & Faith, 1995). Although areas of high species richness generally contain more genetic variation (Williams & Humphries, 1996), the incorporation of more complex measures of diversity could prove to be an interesting and worthwhile enhancement of the methods discussed in this paper. Acknowledgements Simon Woodhouse is supported by a NERC Case studentship (collaborating partner ITE Bangor, Wales). We are also grateful to Dr. David Martin and two anonymous referees for helpful comments on an earlier version of this paper. References Char, B. W., Geddes, K. O., Gonnet, G. H., Leong, B. L., Monagan, M. B., & Watt, S. M. (1991). Maple V library reference manual. New York: Springer-Verlag: Waterloo Maple Publishing. Church, R. L. (1999). Location modelling and GIS. In P. A. Longley, M. F. Goodchild, D. J. Maguire, & D. W. Rhind, Geographical information systems: vol. 1. Principles and technical issues (2nd ed.) (pp. 293±303). Chichester, UK: John Wiley. Church, R. L., & ReVelle, C. S. (1974). The maximal covering location problem. Papers of the Regional Science Association, 32, 101±118. Church, R. L., & ReVelle, C. S. (1976). Theoretical and computational links between the p-median, location set-covering and the maximal covering location problem. Geographical Analysis, 8, 406±415. Church, R. L., & Sorensen, P. (1996). Integrating normative location models into GIS: problems and prospects with the p-median model. In P. A. Longley, & M. Batty, Spatial analysis: modelling in a GIS environment (pp. 167±184). New York: John Wiley. ChvaÂtal, V. (1983). Linear programming. New York: W.H. Freeman and Company. Cocks, K. D., & Baird, I. A. (1989). Using mathematical programming to address the multiple reserve selection problem: an example from the Eyre Peninsula, South Australia. Biological Conservation, 49, 113±130. Curnutt, J., Lockwood, J., Luh, H., Nott, P., & Russell, G. (1994). Hotspots and species diversity. Nature, 367, 326±327. Densham, P. J., & Rushton, G. (1992). A more ecient heuristic for solving large p-median problems. Papers in Regional Science, 71, 307±329. Dolman, P. (2000). Biodiversity and ethics. In T. O'Riordan, Environmental science for environmental management (pp. 119±148). Harlow, UK: Prentice Hall.
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Williams, P., Gibbons, D., Margules, C., Rebelo, A., Humphries, C., & Pressey, R. (1996). A comparison of richness hotspots, rarity hotspots, and complementary areas for conserving diversity of British birds. Conservation Biology, 10, 155±174. Williams, P. H., & Humphries, C. J. (1996). Comparing character diversity among biotas. In K. J. Gaston, Biodiversity: a biology of numbers and dierence (pp. 54±76). Oxford: Blackwell Science.
Using a GIS to select priority areas for conservation S. Woodhousea,*, A. Lovetta, P. Dolmana, R. Fullerb a
School of Environmental Sciences, University of East Anglia, Norwich NR4 7TJ, UK b British Trust for Ornithology, The Nunnery, Nunnery Place, Thetford, UK
Abstract Species richness and species rarity have been identi®ed as important criteria when selecting conservation areas. Traditional approaches that choose sites based solely on local species richness often fail to protect those species most at risk. By assessing the representation of species across a network of sites, the protection of all species is more likely to be assured. A GIS approach based on the Maximal Covering Location Problem (MCLP) is compared to existing complementarity algorithms using data collected by the British Trust for Ornithology on the distribution of birds in Wales, UK. Despite a range of solutions depending on the algorithm used, the results presented here suggest that the overall pattern of species and the habitats with which they are associated remain largely unchanged. Community ordination is used to examine the species composition of sample units and to relate this to habitat composition. This shows that key marine, coastal and moorland sites are selected by most solutions while there is a greater degree of substitutability for sites that are predominantly woodland and farmland. The GIS-based MCLP approach is then extended by incorporating various priority weightings, considered in terms of conservation criteria relevant to birds in Wales. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: GIS; Priority weightings; Conservation; Reserve selection; DCA; MCLP
1. Introduction The combined eect of habitat loss and fragmentation, ecosystem disruption and global warming severely threatens the diversity of species on our planet (Dolman, 2000). Consequently, it is estimated that many hundreds of thousands, perhaps millions, of species are threatened with extinction (Reaka-Kudla, Wilson & Wilson, * Corresponding author. Tel.: +44-1603-456161; fax: +44-1603-57719. E-mail addresses: [email protected] (S. Woodhouse), [email protected] (A. Lovett), p.dolman @uea.uk (P. Dolman), [email protected] (R. Fuller). 0198-9715/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0198-9715(99)00046-0
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1996). Although many other approaches are important, conservation of biodiversity will primarily be achieved by selecting and protecting key areas of habitat (Primack, 1993). Unfortunately, due to the demands of human populations, only a very small proportion of the Earth's surface can be managed for conservation alone. Therefore, biologists are forced to prioritise in the selection of protected areas in order to maximise potential biodiversity gains. An initial attempt to resolve this problem might be to select the most species rich locations. At a global scale, this kind of approach has proved very successful. This is because much biodiversity is unique to speci®c `biogeographic regions' and so choosing between such areas results in minimal overlap of species composition. However, when the sizes of the areas under scrutiny are substantially smaller than biogeographic regions, selecting richness hotspots may result in a high degree of species replication. Also, simply selecting areas with the highest number of taxa may do little to aid the conservation of rare species; as many species have unique habitat preferences and so do not necessarily occur in the most species-rich sites (Curnutt, Lockwood, Luh, Nott & Russell, 1994; Prendergast, Quinn, Lawton, Eversham & Gibbons, 1993; Williams, Gibbons, Margules, Rebelo, Humphries & Pressey, 1996). A far better approach, therefore, is to consider areas of complementary richness (i.e. areas that together contribute a large number of species). Identifying the best set of sites to conserve can prove to be a dicult task, particularly where the species composition of sites is similar. For example, Britain can be approximately divided into 3000 10-km squares containing some 200 dierent bird species (Gibbons, Reid & Chapman, 1993). Suppose that 150 (5%) of these squares are to be protected in order to conserve as many of the 200 species as possible. Finding the best (optimal) set of squares by testing every conceivable con®guration would require 1.4710257 separate calculations; a problem beyond the capabilities of even the most powerful computer. Consequently, problems of this type are solved using an algorithm or heuristic (Church, 1999). As such, numerous algorithms have been developed over the past decade to select conservation areas (Cocks & Baird, 1989; Margules, Nicholls & Pressey, 1988; Nicholls & Margules, 1993; Pressey, Humphries, Margules, Vanewright & Williams, 1993; Rebelo & Siegfried, 1990; Vane-Wright, Humphries & Williams, 1991; Sñtersdal, Line & Birks, 1993); examples of which are described and evaluated in the following sections of this paper. The primary objective of this study is to review and extend a GIS approach adopted by Gerrard, Church, Stoms and Davis (1997) based on the Maximal Covering Location Problem (MCLP). Two disadvantages of previous algorithms have been their inability to ®nd an optimal solution (Underhill, 1994) and the diculties encountered while trying to use procedures that are computationally complex (Church, 1999). Initially, the MCLP model is compared to the richness hotspot approach using atlas data collected by the British Trust for Ornithology (BTO; Gibbons et al., 1993). The same dataset is also used to assess the validity of the GIS-based MCLP approach relative to more widely used complementarity algorithms. Finally, the impact of a variety of priority weightings in a GIS approach are explored and an assessment made of the future role of GIS in selecting priority areas.
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2. Complementarity as a facility location problem The MCLP is an example of a facility location problem (i.e. the placement of a facility or facilities to meet a pre-determined set of objectives). Speci®cally, it is the quest to locate a set number of facilities to maximise the population served within a predetermined distance or travel time. For example, in Baltimore, MD, the MCLP model was used to determine the location of ®re stations to achieve response times of 30 min or less in rural areas and 10 min or less in urban areas (ReVelle, Bigman, Schilling, Cohon & Church, 1977). By treating species as demand centres and potential reserve sites as facility locations, Gerrard et al. (1997) showed that the MCLP model could also be used to locate conservation areas. In particular, they showed how this could be achieved using algorithms available within a GIS. ARC/INFO includes two heuristic algorithms with the ability to solve the MCLP: GRIA (global/regional interchange algorithm); (Densham & Rushton, 1992) and TEITZBART (Teitz & Bart, 1968). On the whole TEITZBART has proved to be more robust than GRIA, despite the greater sophistication of the latter. In trying to locate conservation reserves in southwestern California, Gerrard et al. (1997) found that TEITZBART outperformed GRIA once the number of reserves selected rose above four. This was attributed to the fact that the demand nodes and candidate site nodes are mutually exclusive when applying the MCLP model to reserve selection. When applied to a more conventional MCLP, however, the two heuristics were found to perform comparably, with TEITZBART ®nding the optimal solution in 54 out of 115 trials, whilst GRIA managed 56 (Church & Sorensen, 1996). Both GRIA and TEITZBART, however, were originally developed as ways of solving a slightly dierent problem: the p-median problem. Rather than seeking to maximise the population covered within a predetermined service distance, the pmedian algorithm attempts to minimise the average distance travelled between each demand node and its closest facility. Since the MCLP arose as a direct consequence of the p-median problem, algorithms to solve the p-median problem were already in place (Maranzana, 1964; Teitz & Bart, 1968). In 1976, Church and ReVelle showed that p-median algorithms could be used to solve the MCLP. This was achieved by replacing each distance in the p-median problem by zero if it was less than the maximal service distance (S) and one otherwise. Minimising the average distance travelled between each demand node and its closest facility in this instance is equivalent to minimising the amount of population served outside S (an equivalent statement to the MCLP). In addition to the two GIS heuristics described earlier, the MCLP can also be solved directly using algorithms from the ®eld of operational research (e.g. SIMPLEX [ChvaÂtal, 1983]). These can be found in both specialised optimisation packages (e.g. LINDO [Schrage, 1989]) but also in more general mathematical software such as MAPLE (Char, Geddes, Gonnet, Leong, Monagen & Watt, 1991). Unlike TEITZBART and GRIA, linear programming algorithms such as SIMPLEX will always locate an optimal solution where one exists. Whilst this is clearly a favourable property for an algorithm to hold, both the MCLP and the p-median problem are notoriously dicult to solve using standard integer programming techniques
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(Church, 1999). In locating conservation areas, where there are often a high number of site-species combinations to consider, ®nding an optimal con®guration of sites can prove to be a less than trivial task. Also, trying to solve the MCLP using linear programming is often dicult due to the integer constraints placed on the variables within the optimisation process. Although in 80% of cases a slight modi®cation to the MCLP model will produce zero-one solutions, in instances where a fractional solution is returned, a method of inspection or a Branch and Bound technique needs to be employed to obtain an optimal integer solution (Church & ReVelle, 1974). 3. Data sources and methods 3.1. Species data The species data used here derive from a nationwide survey conducted by the BTO between 1988 and 1991. The methodology employed during the survey is detailed in Gibbons et al. (1993) and is summarised here. Observers were asked to record the presence/absence (abundance in some cases) as well as the breeding status of each species within 10-km squares across Britain and Ireland. Rather than attempting to cover the entire 10-km square, each was subdivided into 25 tetrads (i.e. 22 km), of which observers were asked to spend 2 h in at least eight. Where the same 10-km square was visited in subsequent years, volunteers were encouraged to visit tetrads that had not been previously surveyed. As well as observations during timed visits, volunteers were required to submit supplementary record forms detailing additional `sightings' along with the grid reference of the 10-km square in which they occurred. This was to ensure that species undetected during timed visits would not be overlooked for the purpose of compiling the BTO Breeding Bird Atlas. For the analyses presented here, the presence or absence of each bird species at the 10-km level is based on whether or not there was evidence of breeding within that square. Also, data collected outside of timed visits are excluded to prevent further bias arising from dierential survey eort. Only 10-km squares containing visited tetrads within Wales are considered as a comparative exercise to evaluate the performance of the GIS-based MCLP approach against other selection algorithms. Timed visits during the BTO survey recorded 151 species of breeding bird across 267 10-km squares within Wales. Fig. 1a shows abundance (number of 10-km squares in which each species was found to be breeding during timed visits) plotted against species rank. It is worth noting the high number of rare species contained within the BTO dataset for Wales (characterised by the distribution's long tail), a factor that could potentially in¯uence site selection analyses. The frequency distribution of species richness across Wales is given in Fig. 1b and depicts a positively skewed pattern with a modal peak around 50 species per square. Whilst these two ®gures are primarily included to assist the reader's appreciation of the underlying dataset, both highlight interesting facets of the data worthy of consideration in future studies.
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Fig. 1. (a) The abundance of breeding bird species in Wales ranked according to their range size (1=commonest species, 151=rarest species). (b) The frequency distribution of species richness within 10km squares in Wales.
3.2. Evaluating the performance of the MCLP model and other algorithms A network representing the species' distributions and potential reserve sites was constructed following the procedure documented by Gerrard et al. (1997). Initially,
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the performances of the richness hotspot and complementarity approaches (represented by the MCLP model) were compared by considering the total number of bird species and the number of rare species contained within a network of 13 squares (5% of the total number) as selected by each of the two methods; `rare' in this instance being de®ned as a species breeding in no more than two 10-km squares within Wales [based on the same proportion as that used by Prendergast et al. (1993) and Curnutt et al. (1994)]. Secondly, the MCLP model was compared to three contrasting algorithms according to how eciently it selected squares in order to conserve all species within a given area. Mathematically: Minimise
267 i1
Yi
267 s:t: Yi xij 51 i1
j 1; . . . ; 151
where xij=1 if square i (i=1,. . .,267) conserves species j ( j=1,. . .,151); and xij=0 otherwise. The ®rst of these is an iterative or `adding' algorithm, the simplest and most widely used algorithm of its kind. This begins by selecting the most species-rich square, then the square that provides the most additional species and so on until all species have been selected. The second is an example of a more advanced iterative approach (an example of a `greedy' heuristic algorithm) adapted from Margules et al. (1988) and Nicholls and Margules (1993). It can be summarised in the following four stages: 1. Select all squares with unique occurrences of species. 2. From the squares containing the next rarest species, select the square that also adds the greatest number of additional species (i.e. species not represented in the squares already selected). 3. Where more than one square contains an equal number of unrepresented species, select the ®rst square in the list. 4. Go to Step 2. The third approach solves the reserve selection problem directly using the SIMPLEX algorithm (i.e. ®nds the minimum number of squares needed to conserve all 151 breeding bird species). This is essentially equivalent to running the MCLP model having set the number of squares required to 17 (the number needed to conserve all species). 3.3. Detrended correspondence analysis With algorithms of the type described earlier, there often exist several dierent ways of representing all species in the same number of squares; an important con-
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sideration when adopting their ®ndings to reserve selection in practice. Even in instances where a solution is known to be optimal, there may be many other combinations of sites that are also optimal, depending on the size of the area under examination and the degree of species variability that it contains. As such, it is often more interesting to study the type of squares selected and the habitat characteristics that they exhibit, rather than focusing immediately on their location. Ordination techniques such as detrended correspondence analysis (DCA) are an eective way of identifying underlying patterns in large datasets. In this instance, a DCA enabled comparisons to be made between the species composition of squares, in order to arrange species in multi-dimensional `ordination' space such that co-occurring species were in close proximity. `Site' scores on the axes of the DCA were then calculated as a weighted average of the co-ordinates of those species occurring in each 10km square. Therefore, squares with a similar location in ordination space had a similar species composition, while dissimilar squares were located in dierent parts of the ordination. The multivariate species composition of squares was then examined by locating each square on the ®rst two DCA axes, greatly reducing the number of dimensions involved (i.e. from 151 dimensions!). Bird species-habitat associations, superimposed on a DCA ordination, were subsequently used to investigate the equivalence or dissimilarity of alternative solutions obtained from the diering algorithms. These associations were primarily derived from lists given in Tucker and Evans' (1997) book Habitats for Birds in Europe, supplemented by other sources (Fuller, 1995; Fuller et al., 1995; Lovegrove, Williams & Williams, 1994). 4. Results The performance of the complementarity approach (in this case the MCLP model) is compared to the solution obtained from the richness hotspot approach in Table 1. Only four of the 13 hotspots selected contained at least one rare species and just three of the 19 rare species were represented somewhere in the network of 10-km squares. From this it is clear that complementarity is better than the richness hotspot approach both in terms of the total number of species covered and the extent to which rare species are also protected; a similar conclusion to that reached
Table 1 Richness hotspots versus complementary areas: a summary of the eectiveness of two approaches in covering rare bird species distributions in Wales Number of squares containing at least one of the 19 rare species (% of 13 squares) Richness hotspots 4 (31) Complementary areas 10 (77)
Number of rare species Total number of species contained within network represented in the network of 10-km squares (% of all 151 species) (% of all 19 rare species) 3 (16) 16 (84)
116 (77) 147 (97)
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by Prendergast et al. (1993) and Curnutt et al. (1994). The performance of the MCLP model is compared to other widely used complementarity algorithms in Table 2. The MCLP is solved both optimally as well as heuristically using the TEITZBART and GRIA algorithms available within a GIS. Despite failing to ®nd an optimal solution, the GIS heuristics perform better than the more widely used iterative approaches. For each of the six solutions in Table 2, the degree of complementarity can be assessed by considering the locations of each set of squares on the ®rst two axes of the site ordination as obtained from the DCA of the bird distribution data. These two axes combined explain 26.5% of the variation in the species data. As bird species' distributions are often determined by habitat availability at a scale below that of the 10-km square study unit, being able to explain just over a quarter of the variation at such a spatial resolution is ecologically pleasing; whilst the inclusion of further ordination axes inevitably increases the total variance explained (36% by the ®rst four axes), the simplicity and clarity of representation is lost. Also, as the number of DCA axes increases, diculties associated with attaching biological meaning to axes lower down the order increase. For this reason, results presented here are restricted to the ®rst two DCA axes. In addition, the option to exclude certain species and downweight others was rejected as the overall distribution of species remains relatively unchanged, whilst the variance explained is substantially reduced. Fig. 2 shows the positions of ®ve groups of birds on the species ordination diagram categorised according to their principal habitat. These habitats are de®ned as marine, coastal, farmland, woodland and moorland. The species plotted here represent the subset of all breeding birds in Wales where a principal habitat was easily identi®able; birds falling evenly into two or more categories (e.g. woodland/farmland) are excluded. It is not surprising that those species with similar habitat preferences (as shown in Fig. 2) are closely clustered on the ordination axes and are likely to be indicative of the species variation accounted for by the DCA. Since each site ordination score is calculated as the weighted average of the species ordination scores, as well as being able to compare the dierent solutions, the relative positions of 10-km squares in the ordination can be related back to the species that they contain. By calculating centroids for each habitat group using
Table 2 The number of 10-km squares needed to represent all breeding bird species in Wales using six complementarity algorithms Algorithm
O/Sa
Number of 10-km squares required
Algorithm
O/Sa
Number of 10-km squares required
Iterative Greedy SIMPLEX
S S O
19 18 17
MCLP (GRIA) MCLP (TEITZBART) MCLP (SIMPLEX)
S S O
18 18 17
a
O, optimal; S, suboptimal; MCLP, Maximal Covering Location Problem.
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Fig. 2. Species ordination scores for the ®rst two axes of a detrended correspondence analysis of the British Trust for Ornithology (BTO) breeding bird survey data, grouped according to principal habitat.
the species ordination scores, it is possible to determine the in¯uence of each habitat type on the position of squares. Each habitat centroid diers in its position relative to the overall mean and this dierence can therefore be plotted as a vector. Site ordination diagrams showing the positions of squares selected by each algorithm
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Fig. 3. Site ordination scores from a detrended correspondence analysis for six alternative algorithms for the prioritisation of conservation areas.
overlaid with these vectors are displayed in Fig. 3. From these it is clear that certain squares occur in each of the six solutions (irreplaceable) while others tend to appear more sporadically (substitutable). This re¯ects the number of rare species in the Welsh dataset (see Fig. 1a). The fact that ®ve squares contain unique occurrences of species immediately reduces the number of substitutable squares available for selection. Despite this, the overall distributions of squares selected by the six algorithms are similar in terms of their location on the ®rst two ordination axes. This suggests that where there is a choice between squares, although the location may dier, the underlying habitat characteristics are consistent regardless of the algorithm used.
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This is emphasised by the ®ve habitat vectors, which provide some insight into the principal habitat of each of the selected squares. These would also seem to suggest that there is a greater choice between predominantly woodland and farmland squares than between those squares that are primarily marine, coastal and moorland. This is not particularly surprising bearing in mind that 80% of the total land area of Wales is classed as agricultural and 12% as woodland (Welsh Oce, 1996). 5. Incorporating priority weightings within a GIS analysis It is often of greater practical value to attempt to maximise the number of species within a given area than to determine the smallest area within which every species can be represented (Underhill, 1994). Clearly, the MCLP is better placed to solve a problem of this type than algorithms forced to represent the full complement of species. A further advantage of the GIS-based MCLP approach is its adaptability, particularly its ability to incorporate priority weightings. For instance, Gerrard et al. (1997) ran the MCLP model within ARC/INFO having applied a weighting to favour endemic species, an approach extendable to a whole range of conservation criteria. Rather than simply aiming to maximise the total number of species represented in a given total area, it would be more useful to attach a higher priority to those species of greater conservation concern. Three alternative criteria are the relative abundance of each species within Wales (as de®ned by range size), the relative contribution of the Welsh population to the total UK range of the species, and the extent to which species are already considered at risk, as de®ned by published lists of Birds of Conservation Concern (the `Red' and `Amber' lists; Gibbons et al., 1996). Fig. 4 shows the distribution of squares selected when applying these criteria, via the GIS MCLP model, to the BTO dataset for Wales. For comparison, the set of squares selected where no weightings are applied is also given. Whilst further analyses would be required before presenting such results to conservation organisations, it is evident which squares should be given priority in the ®rst instance. 6. Discussion and conclusions The results presented in this paper suggest that when selecting priority areas for conservation, it is far better to consider the coverage of species across an entire network of protected areas than to select sites based solely on individual merit. The MCLP model is an eective way of doing this. The MCLP can be solved both optimally (via traditional integer programming techniques) as well as heuristically via a whole host of existing algorithms. In cases where an optimal solution is essential and providing the requirements of optimality are met, then an integer programming technique should be adopted. However, where the size of the dataset being analysed makes linear optimisation infeasible, heuristic approaches available within a GIS are ecient, easily applied and result in solutions comparable to those obtained using alternative algorithms. Also, the use of inbuilt GIS procedures to
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Fig. 4. Maps showing the 10-km squares selected in Wales using the GIS MCLP model with: (i) no weightings applied; (ii) species weighted by the reciprocal of the number of squares in which they are known to be breeding; (iii) species weighted by the proportion of Welsh squares in their UK distribution as a whole; (iv) only bird species on the red and amber lists included.
solve the MCLP enables weightings for a wide range of conservation criteria to be easily incorporated. This considerably increases the practical potential of the GIS MCLP model in prioritising areas for conservation investment. In addition, as well as being able to display results as maps (as in Fig. 4) without the need for any additional software, GIS allows for the integration of other spatially referenced datasets; a very useful property when analysing ecological data. For example, a natural progression to the analyses presented here is to consider the environmental attributes of the grid squares selected by each of the complementarity algorithms. What causes one square to be selected over another? Why do two adjacent squares
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vary considerably in terms of the number of species that they contain, despite having almost identical habitat characteristics? What other factors in¯uence the distribution and abundance of species? These kinds of questions are perfectly suited to analysis within a GIS (Johnston, 1998; Wadsworth & Treweek, 1999). Conservation biologists are constantly striving to ®nd more ecient ways of allocating protected areas. Much of this has stemmed from the Gap Analysis Program in the US where the aim has been to assess the distribution and protection status of plants and terrestrial vertebrates (Scott et al., 1993). Clearly, such an approach requires knowledge of areas of high complementary richness and of existing protected areas. GIS enables both of these operations to be carried out simultaneously in an integrated computer environment. A further extension to the GISbased MCLP approach would be to consider phylogenetic diversity rather than species richness (Walker & Faith, 1995). Although areas of high species richness generally contain more genetic variation (Williams & Humphries, 1996), the incorporation of more complex measures of diversity could prove to be an interesting and worthwhile enhancement of the methods discussed in this paper. Acknowledgements Simon Woodhouse is supported by a NERC Case studentship (collaborating partner ITE Bangor, Wales). We are also grateful to Dr. David Martin and two anonymous referees for helpful comments on an earlier version of this paper. References Char, B. W., Geddes, K. O., Gonnet, G. H., Leong, B. L., Monagan, M. B., & Watt, S. M. (1991). Maple V library reference manual. New York: Springer-Verlag: Waterloo Maple Publishing. Church, R. L. (1999). Location modelling and GIS. In P. A. Longley, M. F. Goodchild, D. J. Maguire, & D. W. Rhind, Geographical information systems: vol. 1. Principles and technical issues (2nd ed.) (pp. 293±303). Chichester, UK: John Wiley. Church, R. L., & ReVelle, C. S. (1974). The maximal covering location problem. Papers of the Regional Science Association, 32, 101±118. Church, R. L., & ReVelle, C. S. (1976). Theoretical and computational links between the p-median, location set-covering and the maximal covering location problem. Geographical Analysis, 8, 406±415. Church, R. L., & Sorensen, P. (1996). Integrating normative location models into GIS: problems and prospects with the p-median model. In P. A. Longley, & M. Batty, Spatial analysis: modelling in a GIS environment (pp. 167±184). New York: John Wiley. ChvaÂtal, V. (1983). Linear programming. New York: W.H. Freeman and Company. Cocks, K. D., & Baird, I. A. (1989). Using mathematical programming to address the multiple reserve selection problem: an example from the Eyre Peninsula, South Australia. Biological Conservation, 49, 113±130. Curnutt, J., Lockwood, J., Luh, H., Nott, P., & Russell, G. (1994). Hotspots and species diversity. Nature, 367, 326±327. Densham, P. J., & Rushton, G. (1992). A more ecient heuristic for solving large p-median problems. Papers in Regional Science, 71, 307±329. Dolman, P. (2000). Biodiversity and ethics. In T. O'Riordan, Environmental science for environmental management (pp. 119±148). Harlow, UK: Prentice Hall.
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