This article was downloaded by: [UNSW Library] On: 30 June 2011, At: 20:36 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
International Journal of Geographical Information Science Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tgis20
Incorporating a distance cost in systematic reserve design Kun Zhang
a b
b
b
, Shawn W. Laffan , Daniel Ramp & Evan Webster
b a
Lab of Geographic Information Science, East China Normal University, Shanghai, China b
School of Biological, Earth and Environmental Sciences, University of New South Wales, Sydney, NSW, Australia Available online: 23 May 2011
To cite this article: Kun Zhang, Shawn W. Laffan, Daniel Ramp & Evan Webster (2011): Incorporating a distance cost in systematic reserve design, International Journal of Geographical Information Science, 25:3, 393-404 To link to this article: http://dx.doi.org/10.1080/13658816.2010.517753
PLEASE SCROLL DOWN FOR ARTICLE Full terms and conditions of use: http://www.tandfonline.com/page/terms-andconditions This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan, sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.
International Journal of Geographical Information Science Vol. 25, No. 3, March 2011, 393–404
Incorporating a distance cost in systematic reserve design Kun Zhanga,b*, Shawn W. Laffanb, Daniel Rampb and Evan Websterb a
Lab of Geographic Information Science, East China Normal University, Shanghai, China; bSchool of Biological, Earth and Environmental Sciences, University of New South Wales, Sydney, NSW, Australia
Downloaded by [UNSW Library] at 20:36 30 June 2011
(Received 2 July 2009; final version received 18 August 2010) The selection of parcels of land to incorporate into reserve systems necessitates trade-offs among biodiversity targets, costs such as land area and spatial compactness. There are well-established systematic reserve design algorithms that incorporate these trade-offs to assist decision-makers in this process. One cost that has received little attention is the proximity of new land parcels to the existing reserve network: the ability of environmental managers to effectively maintain and protect additional land units is often constrained by their proximity to existing reserve networks. The selection of parcels of land close to existing reserves makes them logistically easier to deploy infrastructure to and can also improve the spatial contiguity of the existing reserve network. Previous research has been limited to using distance from the centroids of existing reserves, which significantly biases algorithms when reserves are irregularly shaped. Here we describe a new approach that overcomes this limitation by using the existing reserve boundary to determine proximity. We provide an example of this approach by implementing it as an additional constraint in an analysis of biodiversity targets within the Greater Blue Mountains World Heritage Area, Australia, via the Marxan reserve design software. The incorporation of the distance cost in the analysis was effective in selecting parcels near to the existing reserve system and can be combined with other variables in the algorithm to improve spatial compactness while meeting biodiversity and other targets. It provides alternative solutions for use by reserve planners when extending reserve systems. Keywords: systematic reserve design; biodiversity; distance cost; Marxan; Greater Blue Mountains World Heritage Area
1. Introduction The establishment of reserve systems dedicated to the conservation of biodiversity is the cornerstone of most national, regional and state conservation strategies (McDonnell et al. 2002). For the most part, reserves have historically been selected opportunistically (Pressey 1994). Reserve boundaries are typically shaped by conservation, economic and political pressures, relying heavily on expert opinion and qualitative assessments to help prioritise sites (Prendergast et al. 1999). Large reserve systems are almost always developed incrementally and are often comprised of areas with different land use and tenure histories (Foster et al. 2003). Current attempts to improve species representation in existing reserves to create resilience from threatening processes, for example climate change and invasive weeds, are constrained by existing boundaries. Strategic and systematic approaches to *Corresponding author. Email:
[email protected] ISSN 1365-8816 print/ISSN 1362-3087 online # 2011 Taylor & Francis DOI: 10.1080/13658816.2010.517753 http://www.informaworld.com
Downloaded by [UNSW Library] at 20:36 30 June 2011
394
K. Zhang et al.
increasing reserve areas are required to successfully complement existing levels of representation with biodiversity from surrounding landscapes. A complicating factor is that the spatial form of the reserve system has a large bearing on a reserve’s capacity to confer representation and resilience. Reserve design theory has highlighted the role that shape, size and connectivity play in dictating the effectiveness of reserve clusters (Fischer and Church 2003, Williams et al. 2005). By considering existing reserve clusters as part of a reserve portfolio, additions to the existing portfolio can take on many spatial forms: evenly contiguous with an existing boundary, unattached to the existing boundary or a mixture of both. The benefit of the systematic approach to the selection of land for setting aside as reserves is that the process can explicitly deal with spatial problems. Systematic approaches to reserve design utilise the concept of conservation planning units (parcels of land at predefined scales, often related to management actions), where planning units selected in the design process are those that best contribute to the overall representation of biodiversity. In its simplest form, systematic selection incurs no additional costs associated with selecting a particular unit, regardless of its proximity to other selected units or the existing reserve system. Yet the selection of land parcels for reserve acquisition is constrained by additional factors other than biodiversity values. One important constraint is the proximity of new acquisitions to the existing portfolio. Common sense suggests that selection of a portfolio of planning units within close proximity to the existing system will have benefits through improving the capacity of management authorities to employ existing infrastructure and personnel, for example for fire and weed control and infrastructure development. One way to incorporate proximity into the reserve design problem is to include a distance cost into the optimisation formulation. Nalle et al. (2002) used a model which minimised the distance of each planning unit from the centroid of the existing reserves. Although this approach has merit, centroids are greatly affected by the size and shape of the reserves they represent. The centroid of the existing reserve will not adequately represent the mean distance to the reserve boundary for irregularly shaped planning units or clusters of units that are common within existing reserve systems. Planning units near the extremes of elongated reserve systems will be assigned less weight than those near the centre, even if they are an equal distance from the boundary. Similarly, the centroid of a large parcel will necessarily be further away from candidate planning units than the centroid of a similarly shaped but smaller parcel, thereby receiving less weight in the solution. Clearly, a distance cost that avoids these biases is needed. In this article, we describe a method to select parcels of land for addition to an existing reserve that are close to the existing reserve system, while simultaneously satisfying other standard criteria such as biodiversity representation and spatial compactness. This requirement is implemented by introducing a distance cost into the minimum-set-covering model used as the basis of systematic reserve design. We contend that by implementing distance from the boundary of the existing reserve network, rather than distance to the centroid, we overcome many of the drawbacks of the centroid approach. Our method is affected by neither the shape nor the size of the existing reserve portfolio. This article is structured as follows. First, we describe the minimum-set-covering problem, including the incorporation of a distance cost component and its weighting. Second, we demonstrate the application of the distance cost to a large reserve network in south-eastern Australia, assessing a set of combinations. Finally, we consider methods to select the optimal weighting for the distance component.
International Journal of Geographical Information Science
Downloaded by [UNSW Library] at 20:36 30 June 2011
2.
395
The minimum-set-covering problem and the distance cost
A primary objective of reserve design and establishment is to use limited resources to achieve conservation goals. This problem can be formulated as a minimum-set-covering problem (Possingham et al. 2000, McDonnell et al. 2002, Nalle et al. 2002, Wilson et al. 2005), which for species conservation has the aim of minimising the cost of a reserve system while achieving a comprehensive representation of species requiring conservation (the biodiversity constraint). Cost is commonly the area of the planning units, but can be a function of economic, heritage or other relevant values. Implementation of the minimum-set-covering formulation is made via specialist software. Here we use version 2.0.2 of the Marxan reserve design software (Ball and Possingham 2000). Marxan uses a simulated annealing algorithm to obtain a range of solutions to the minimum-set-covering formulation. This means that an analysis is not guaranteed to find the optimal solution, although it should be near optimal. This approach makes a trade-off between infinite solution times and solutions that are good enough in practise, as other considerations will also influence the final determination of reserve boundaries (Cook and Auster 2005). The planning units in the study area act as the building blocks of the final reserve system (portfolio) in the simulated annealing algorithm. The final portfolio consists of the existing conservation area plus newly selected planning units. The cost of the reserve system in Marxan can be represented as M X
ci xi þ BLM
X
boundary:
(1)
i¼1
where xi is a control variable indicating whether planning unit i is included in the reserve; xi is 1 when planning unit i is included, and 0 otherwise; ci the cost of including P site i (in this case area); M the total number of sites available for inclusion in the reserve; boundary the length of the reserve system boundary; and BLM the boundary length modifier, used to achieve a more spatially compact portfolio by minimising its overall boundary length (Possingham et al. 2000). The minimum-set-covering model attempts to simultaneously minimise the cost and satisfy the biodiversity constraint: M X
aij xi tj
i¼1
M X
aij
j ¼ 1; . . . ; N:
(2)
i¼1
where aij represents the amount of species j in planning unit i; N the total number of species; and tj the protection target for species j. The value of tj is typically set between 20% and 50% (Stewart and Possingham 2005). The cost function in Equation (1), however, does not guarantee that the solution will be proximal to the existing reserve system. Here, we introduce a distance cost to the solution by modifying the first term in Equation (1) to be a combination of both area and distance: M X
ðð1 aÞsi þ adi Þxi
(3)
i¼1
where di is the distance of planning unit i from the closest boundary of the existing reserve system; si the area of planning unit i; and a a weight factor with values in the interval [0,1]. When a is 1, the cost of planning unit i is solely determined by di, and the cost of including a planning unit in the solution increases with distance from the existing reserve. When a is 0, the cost of planning unit i is solely determined by its area. Note that the distance metric used
396
K. Zhang et al.
in this research is Euclidean, but any appropriate metric can be used. For example, one could incorporate travel times associated with vehicle access to planning units or alternately ecologically based distances such as patch contiguity for fauna movements. One issue with Equation (3) is that si and di are in different units (one is in the units of area, whereas the other is in the units of distance). We therefore apply a standardisation to these two variables by dividing them by the sum of all their respective values over M, such that the value of si and di are between 0 and 1: ! M X si di ð 1 aÞ PM þ a PM (4) xi i¼1 i¼1 si i¼1 di
Downloaded by [UNSW Library] at 20:36 30 June 2011
In some cases, one might wish to adjust the relative cost of distances so that shorter distances have a much lower cost than further distances. Functions such as the square of the distance can be used in these cases: M X i¼1
si
ð 1 aÞ PM
i¼1 si
!
di2
þ a PM
i¼1
di2
xi
(5)
3. Methods To demonstrate the incorporation of distance we describe a series of scenarios for a hypothetical expansion of the Greater Blue Mountains World Heritage Area (GBMWHA) reserve network, using the spatial distribution of 103 plant species in the family Myrtaceae.
3.1.
Study area
The GBMWHA is situated in New South Wales, Australia (Figure 1). It was inscribed onto the World Heritage List in 2000 on the basis of its outstanding natural values. The GBMWHA contains highly diverse ecosystems and communities of plants and animals, particularly eucalypt-dominated ecosystems. The GBMWHA consists of approximately 1.03 million ha of mostly forested landscape on a sandstone plateau extending from 60 to 180 km inland from central Sydney (Department of the Environment and Heritage 2005). Although the GBMWHA captures a significant portion of the region’s diverse biota, the reserve boundaries were not established using a systematic process. Hence, management agencies are interested in acquiring additions to the GBMWHA to capture increasing representation and to create resilience (Department of the Environment and Heritage 2005). Given the long (,5000 km) and complex boundary, additions to the reserve that are close to the existing system will potentially be easier to manage than those further away. We restricted our analyses to all land areas within a 100 km buffer of the existing GBMWHA boundary, truncated at the west by the boundary between UTM zones 55 and 56. This buffer includes many built-up urban and peri-urban areas, including the cities of Sydney, Newcastle and Wollongong. There are also other protected areas within the buffer region that are not included as part of the GBMWHA (Figure 1). The buffer region was divided into 22,568 square planning units, each being 2 · 2 km in size. Planning units with more than 50% of their area being urban were excluded from consideration (468 planning units, most of which were located in Sydney). Planning units with 50% or more of their area occurring in the GBMWHA, national parks and state forests
Downloaded by [UNSW Library] at 20:36 30 June 2011
International Journal of Geographical Information Science
397
Figure 1. The study region includes land areas within a 100 km radius around the GBMWHA in Australia.
(5399 planning units) were marked as already reserved. This left a total of 16,701 planning units available for selection in the reserve design solution.
3.2.
Distribution of Myrtaceae species
We used predicted distributions for 103 Myrtaceae species as the input biodiversity data. The diversity of the Myrtaceae in the region is one of the reasons for the world heritage status of the GBMWHA. Surveyed distribution information was not available for every planning unit, as is often the case (Wilson et al. 2005), so we developed generalised additive models (GAMs) to predict the distribution of each of the 103 species. We used data from a total of 8673 floristic survey sites located within the study area and maintained in the NSW Department of Environment and Climate Change corporate vegetation database (YETI). The 103 species represented those species in the Myrtaceae that were recorded as having presences in more than 50 of the survey sites. Environmental information used to develop predictive models included the mean annual minimum temperature ( C), mean annual maximum temperature ( C), mean annual yearly rainfall (mm), annual radiation, a terrain
398
K. Zhang et al.
variable, slope gradient, wetness and fire frequency since 1943. Binomial GAMs using the full set of predictors were used to predict all cells within the 100 km buffered region to produce a surface of probability of presence for each Myrtaceae species. The predictions were applied to a regular lattice of square cells 25 m on a side, resulting in 6400 such cells per 2 km planning unit. The spatial distribution of the species predictions is given in the supplementary material (available online). The results of the predictive models are probabilities of each species occurring in each of the 25 m cells. The conversion of these probabilities to presence/absence maps requires the definition of arbitrary thresholds (e.g. Jime´nez-Valverde and Lobo 2007) and can potentially introduce biases into the reserve selection process. An alternative approach is to use the probabilities directly by taking the sum of the 25 m cells within each planning unit (Wilson et al. 2005). Equation (2) can then be expressed as
Downloaded by [UNSW Library] at 20:36 30 June 2011
M X X i¼1
! pjk xi tj
M X X i¼1
k2Ki
! pjk
j ¼ 1; . . . ; N
(6)
k2Ki
where pjk is the probability that species j exists in grid cell k; Ki represents the set of 25 m grid cells in planning unit i; and N equals 103. 3.3.
Site-selection scenarios
Four scenarios were used (Table 1). The first scenario compared the area and distance costs without a boundary length component. The second compared distance cost with the square of distance cost, again without considering the boundary length. The third scenario used the boundary length component in the absence of the distance cost, whereas the fourth scenario used both the BLM and square of distance costs. In each case the target conservation value, tj, was set to 20%. The selection of a = 0.917 used in scenario 4 is discussed in Section 5. Selection of an appropriate BLM value can be problematic. A suggested starting place is to scale it such that the largest boundary between planning units becomes a similar order of magnitude to the most expensive planning unit (Game and Grantham 2008). The initial value can therefore be calculated as BLM0 ¼
max ðcostÞ max ðboundaryÞ
(7)
From this initial value, it is important to explore a range of values separated by a fixed multiplier (Game and Grantham 2008). In this article, the value of BLM is increased by multiples of 2 raised to the power r, resulting in a doubling of the BLM in subsequent iterations: Table 1. Four scenarios used to explore the effectiveness of incorporating distance cost into systematic reserve design. Scenario 1 2 3 4
Aim
a values
BLM
Area cost versus distance cost Distance cost versus square of distance cost Spatially compact portfolio Spatially compact and contiguous portfolio
0, 0.5, 1 1 0 0.917
No No Yes Yes
International Journal of Geographical Information Science
Downloaded by [UNSW Library] at 20:36 30 June 2011
BLM ¼ BLM0 · 2r ;
r ¼ 0; 1; 2; 3; . . .
399 (8)
where BLM0 is the initial value calculated using Equation (7). For the simulated annealing parameter, adaptive annealing was used with 1 million iterations per run over 50 runs. The run with the lowest value of the cost function was taken as the result. Although state forests and national parks external to the GBMWHA are part of an existing reserve system, the distance used was from the GBMWHA boundary, as the purpose of these analyses is for its expansion. The distance cost was calculated as the Euclidean distance between the centre of each planning unit and the nearest GBMWHA boundary. Three criteria were used to evaluate the effectiveness of the final portfolios: the number of newly added planning units, the average distance between newly added planning units and the existing GBMWHA boundary, and the boundary length of the new conservation system. The analysis was implemented using the R statistical package (R Development Core Team 2007), loosely coupled with Marxan.
4. Results For scenario 1, when a = 0 (area cost only), newly added planning units were highly fragmented (Figure 2a). When a = 1 (distance cost only), an additional 776 planning units were required to reach the same protection target as a = 0 (Table 2). However, the average distance was reduced from 49 to 36 km, with the additional planning units clearly located around the GBMWHA (Figure 2c, Table 2). When a = 0.5, the portfolio is a trade-off between minimising the number of planning units and minimising the average distance. It has an average distance of 43 km (Table 2) and results in a transitional solution between the two extremes (Figure 2b). In scenario 2, there was a clear difference between distance cost and square of distance cost when area and boundary length were not considered (Figure 3, Table 2). For the square of distance cost (Figure 3a), the average distance was reduced by 4 km, but at the cost of an additional 751 planning units compared with the unmodified distance cost (Table 2). Note that the small differences between the results for a = 1 between scenarios 1 and 2 are because
Figure 2. Portfolios for the study area for three values of a (0, 0.5 and 1). The grey-shaded areas are the current GBMWHA, whereas the black-shaded areas are the additional planning units selected by Marxan.
400 Table 2.
K. Zhang et al. Results for each scenario. a
Downloaded by [UNSW Library] at 20:36 30 June 2011
Scenario Distance power
BLM
Planning units Average distance Boundary length
1
1 1 1
0 0.5 1
0 0 0
1546 1762 2322
49 43 36
16,852 17,089 15,148
2
1 2
1 1
0 0
2365 3116
36 32
15,217 13,860
3
– – – – – –
0 0 0 0 0 0
0 499 998 1996 3992 7984
1551 1697 1860 2067 2486 3032
49 47 46 44 42 40
16,833 13,665 10,392 7428 5952 4737
4
2 2 2 2 2 2
0.917 0.917 0.917 0.917 0.917 0.917
0.000E-7 0.169E-7 0.339E-7 0.677E-7 1.350E-7 2.710E-7
2575 3757 4289 4667 5160 5154
34 30 29 29 30 31
15,234 5420 4558 3639 3345 3201
Note: The distance power, a and BLM columns contain the parameter values used. Values in the other columns summarise the Marxan results, representing the number of planning units required for the optimal solution, the average distance of planning units in that solution to the GBMWHA and the boundary length of the solution. Note that the BLM values differ between scenarios 3 and 4 because of the scaling factors used when incorporating the distance. They are, however, still calculated using Equations (7) and (8).
Figure 3. Portfolios for distance (a) and square of distance (b) costs. The grey-shaded areas are the current GBMWHA, whereas the black-shaded areas are the additional planning units selected by Marxan.
the simulated annealing algorithm used in Marxan can reach very similar objective function scores but with different portfolios (Stewart and Possingham 2005). For scenario 3, using the BLM without a distance cost resulted in spatially clustered groups of planning units (Figure 4). As specified in the Marxan formulation, clusters became
Downloaded by [UNSW Library] at 20:36 30 June 2011
International Journal of Geographical Information Science
401
Figure 4. Six portfolios resulting from different BLM values (a–f). The grey-shaded areas are the current GBMWHA, whereas the black-shaded areas are the additional planning units selected by Marxan.
increasingly large as the value of the BLM increased, with the total boundary length reducing from 16,883 to 4737 km (Table 2). Additionally, the number of planning units required for the solution increased (1551 to 3032, see Table 2). Although the average distance of the selected planning units from the GBMWHA decreased over the set of BLM values used (49 to 40 km, see Table 2), the portfolio remained regionally fragmented (Figure 4). Many clusters of additional planning units were far from the existing boundary of the GBMWHA. In scenario 4, using the square of distance and a = 0.917, the selected planning units are clearly more spatially compact as the BLM increases (Figure 5), more so than in scenario 3 (Figure 4). In contrast to scenario 3, most clusters occurred within close proximity to the existing GBMWHA boundary. The portfolio of scenario 3 with the highest BLM value (Figure 4f) had the shortest boundary length of those using only the BLM (4737 km). In comparison, four portfolios in scenario 4 (Figure 5c–f) each had shorter boundary lengths than that. By using the square of distance, the average distance reduced to approximately 30 km, compared to 40 km when no distance cost was implemented (Figure 4). The improvements are, however, gained at the cost of additional planning units included in the solution.
5.
Selecting appropriate values of a and the BLM
It is clear that neither the distance cost nor the BLM alone satisfy the requirement to have both compact and proximal additions to a reserve portfolio. Some guidance is therefore
Downloaded by [UNSW Library] at 20:36 30 June 2011
402
K. Zhang et al.
Figure 5. Six portfolios for different BLM values, also using a combination of area and square of distance. a was set at 0.917. The grey-shaded areas are the current GBMWHA, whereas the black-shaded areas are the additional planning units selected by Marxan.
needed to select appropriate values for a and the BLM to use them in concert. This can be achieved using a two-step process where the value of a is first selected from a range of values, followed by that for the BLM. Here we use 13 values of a, using equally spaced increments between 0 and 1. The square of distance method is used. As a increases, an increasing number of planning units are needed to generate a portfolio that satisfies the cost and biodiversity constraints, even though the average distance from planning units to the existing reserve diminishes (Figure 6). The difference between the average distance and the median increases because the distance distribution is skewed: more planning units are selected near the existing reserve as a increases. We suggest selecting the a value that maximises avg med NPU
(9)
where avg is the average distance, med the median and NPU the number of planning units for a value of a. This formula represents a trade-off between the number of planning units near the existing reserve system and the total size of the portfolio. For the case study used here, a12 (0.917) has the maximum value using Equation (9). After selecting a, the spatial compactness of the solution can be assessed for differing values of BLM, with the BLM values incremented using Equations (7) and (8), as in scenarios 3 and 4. The results are assessed by comparing the cost and the final boundary length of the solution (Figure 7). The BLM value to use is at the inflection point of the line in
α1 α2 α3 α4 α5 α6 α7 α8
α9
α10
α11
403
α12
α13
60 40 0
20
Distance (km)
80
100
International Journal of Geographical Information Science
1500
2000
2500
3000
Figure 6. Box-plots of the distance of the additional planning units to the GBMWHA and the number of planning units (PUs) selected for a set of 13 a values (0, 0.083, 0.167, 0.250, 0.333, 0.417, 0.500, 0.583, 0.667, 0.750, 0.833, 0.917, 1). The circle symbols are the average distances, whereas the black bars are the median distances.
12,000 8000
Boundary length (km)
0.00E+00
1.69E–08 3.39E–08 4000
Downloaded by [UNSW Library] at 20:36 30 June 2011
PUs
1.35E–07 2.71E–07 6.77E–08 0.18
0.19
0.20
0.21
Cost
Figure 7. Relationship between boundary length and cost as the BLM is incrementally doubled. a is set at 0.917. The numbers adjacent to the data points are the BLM values used.
Figure 7, as this is where the increase in planning units becomes large relative to the corresponding reduction in boundary length (Game and Grantham 2008). This set of a and BLM values corresponds to the reserve portfolio displayed in Figure 5c. 6. Summary We introduced a distance cost to the minimum-set-covering problem for reserve design analyses, implementing it in combination with the area cost. The results demonstrate that such a distance cost increases the number of candidate planning units being selected near to the existing reserve system. The distance cost is simply an additional cost factor in the minimum-set-covering problem used for reserve design and can be used in combination with
404
K. Zhang et al.
other factors such as boundary length modifiers which encourage spatially compact solutions, as well as any other cost metric such as monetary cost of land parcels and species weighted by their importance. Although a distance cost has been previously described (Nalle et al. 2002), it was based on the centroid of the existing reserve system, potentially biasing results where the existing system is irregularly shaped. Here we have provided a method that successfully overcomes this drawback. It is effective in selecting parcels near to the existing reserve system and can be combined with other variables to improve spatial compactness while meeting biodiversity targets. It provides an alternative solution for use by reserve planners when extending reserve systems.
Downloaded by [UNSW Library] at 20:36 30 June 2011
Acknowledgements This work was supported by the National Natural Science Foundation of China (id: 40730526) L¸ State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing (08I01), and Australian Research Council Linkage Project LP0774833 ‘Managing Ecosystem Change in the Greater Blue Mountains World Heritage Area’.
References Ball, I.R., Possingham, H.P., and Watts, M., 2009. Marxan and relatives: Software for spatial conservation prioritisation. In: Spatial conservation prioritisation: Quantitative methods and computational tools. A. Moilanen, K.A. Wilson and H.P. Possingham Eds. Oxford: Oxford University Press, 185–195. Cook, R.R. and Auster, P.J., 2005. Use of simulated annealing for identifying essential fish habitat in a multispecies context. Conservation Biology, 19, 876–886. Department of the Environment and Heritage, 2005. Greater Blue Mountains World Heritage Area draft strategic plan. Available from: http://www.environment.nsw.gov.au/resources/parks/ bluemountainsWHA_strategydraft.pdf (accessed 20 September 2010). Fischer, D.T. and Church, R.L., 2003. Clustering and compactness in reserve site selection: an extension of the Biodiversity Management Area Selection model. Forest Science, 49, 555–565. Foster, D., Swanson, F., Aber, J., Burke, I., Brokaw, N., Tilman, D., and Knapp, A., 2003. The importance of land-use legacies to ecology and conservation. Bioscience, 53, 77–88. Game, E.T. and Grantham, H.S., 2008. Marxan User Manual: For Marxan version 1.8.10. Vancouver, British Columbia, Canada: University of Queensland, St. Lucia, Queensland, Australia and Pacific Marine Analysis and Research Association. Jime´nez-Valverde, A. and Lobo, J.M., 2007. Threshold criteria for conversion of probability of species presence to either-or presence-absence. Acta Oecologica, 31, 361–369. McDonnell, M.D., et al., 2002. Mathematical methods for spatially cohesive reserve design. Environmental Modeling & Assessment, 7, 107–114. Nalle, D.J., Arthur, J.L., and Sessions, J., 2002. Designing compact and contiguous reserve networks with a hybrid heuristic algorithm. Forest Science, 48, 59–68. Possingham, H.P., Ball, I.R., and Andelman, S., 2000. Mathematical methods for identifying representative reserve networks. In: S. Ferson and M. Burgman, eds. Quantitative methods for conservation biology. New York: Springer-Verlag, 291–305. Prendergast, J.R., Quinn, R.M., and Lawton, J.H., 1999. The gaps between theory and practice in selecting nature reserves. Conservation Biology, 13, 484–492. Pressey, R.L., 1994. Ad hoc reservations – forward or backward steps in developing representative reserve systems. Conservation Biology, 8, 662–668. R Development Core Team, 2007. R: a language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Stewart, R.R. and Possingham, H.P., 2005, Efficiency, costs and trade-offs in marine reserve system design. Environmental Modeling & Assessment, 10, 203–213. Williams, J.C., ReVelle, C.S., and Levin, S.A., 2005. Spatial attributes and reserve design models: a review. Environmental Modeling & Assessment, 10, 163–181. Wilson, K.A., et al., 2005. Sensitivity of conservation planning to different approaches to using predicted species distribution data. Biological Conservation, 122, 99–112.
