Integrating conservation and development: effective ... - Springer Link

Biodiversity and Conservation 5, 431-446 (1996)

Integrating conservation and development: effective trade-offs between biodiversity and cost in the selection of protected areas D.P. F A I T H * and P.A. W A L K E R Division of Wildlife and Ecology, CSIRO, PO Box 84, Lyneham, ACT 2602, Australia Received 7 September 1994; Revised and accepted 25 March 1995

Strategies are needed for reconciling competing demands at the regional level when areas are to be selected for protection and there are associated costs, possibly equivalent to forgone development opportunties. As an alternative to the fixed scaling (or weighting) of costs and benefits required by cost-benefit analysis, multi-criteria analyses allow the exploration of alternative weightings and a summary trade-off curve to determine preferred solutions. For alternative sets of areas, total cost could be plotted against total represented biodiversity, but a more consistent approach should look at trade-off space at the level of individual areas. For a given weighting, an area is assigned protection if and only if its contribution to total biodiversity, CB, exceeds its equivalent cost, EC (in biodiversity units). Because CB for a given area depends on which other areas are also protected, it can be more or less than EC. Here we develop an iterative strategy for selecting areas, such that, for a given weighting, an area is in the final protected set if and only if its final CB value is greater than its EC value. Sensitivity analysis is used to identify those areas that: (1) are assigned protection even when low weight is given to biodiversity, or (2) are not assigned protection even when high weight is given to biodiversity. This approach is applicable in principle to any surrogate measure for biodiversity; here examples are presented in which environmental data are summarized as an environmental space.

Keywords: multi-criteria; environmental diversity; trade-off: reserve selection; sensitivity analysis

Introduction Limited resources for the protection of biodiversity call for m e t h o d s for facilitating trade-offs and compromise. The context of interest in this p a p e r is a regional one, where a set of protected areas is to be selected (or perhaps one or m o r e areas added to, or subtracted from, an existing protected set), and there are costs associated with the allocation of protection to different areas. T h e costs, for example, m a y be m o n e t a r y or reflect c o m p e t i n g land use suitabilities. These benefits and costs both must be integrated into the allocation process. A simple f o r m of integration is one in which there is some b u d g e t constraint, so that the m a x i m u m a m o u n t o f biodiversity is to be achieved within this budget. A n o t h e r conceptually simple case is one in which there is a countable set of attributes of biodiversity (e.g. w h e n an 'indicator' g r o u p o f species is used as surrogate information) and each *To whom correspondence should be addressed. 0960-3115 © 1996 Chapman & Hall

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attribute minimally must be represented at least once, but as cheaply as possible (e.g. Margules et al., 1994), These scenarios are relatively simple in that there is no requirement that biodiversity and costs be placed on the same scale. If we have some costs (or measures of potential forgone development opportunity) associated with each area, and the surrogate for biodiversity consists of countable attributes (types, species, classes or other units), then methods already exist (see Pressey et al., 1993: Margules et al., 1994) for searching for a set of areas representing each attribute at least once and having minimum cost, or for maximizing the number of represented attributes under the budget constraint. Similarly, these algorithms can be applied to find the cheapest set of areas under the constraint that each attribute appears n times. The focus of this paper will be on other allocation problems that by their nature require some nomination of a relative weighting of biodiversity and costs. These problems arise when there is no clear budget constraint, or when there is no complete, countable, set of attributes to be sampled as cheaply as possible. The absence of attributes arises from a consideration of the best-possible use of surrogate data for biodiversity (Faith and Walker, submitted). We describe below an alternative strategy that uses a continuous pattern rather than discrete attributes, and then examine its implications for trade-offs. In the simple scenarios described above, there is a degree of arbitrariness inherent in the nomination of a number of attributes (particularly when these are derived using numerical methods) and also in the nomination of the number of times each attribute should bc represented. Elsewhere (Faith and Walker, 1993; 1996) we have described one solution to the problem of arbitrariness of attributes, based on the use of continuous pattern among areas (for example pattern summarizing environmental variation among areas): either a hierarchical pattern or a continuum (ordination) pattern may be used. The amount of this 'pattern diversity' that is represented by a set of areas is a surrogate for the amount o1 biodiversity at the species level (Faith, 1994). The use of pattern, because it is "open-ended' (every new area has something to contribute), would seem to make the possibility of defining trade-offs with costs even more remote. One could nominate some arbitrary target level of total biodiversity as indicated by the pattern-surrogate, and find a set of areas that achieves this at minimum cost. But it seems unlikely in practice that the goals will be defined in terms of some level ol represented biodiversity to be achieved, or even in terms of some maximum budget. Similarly, even when one area is to be chosen, and some trade-off between costs and biodiversity-gain is called for, there is no one clear answer to what the trade-off should be. These open-ended problems suggest that the selection among alternative options must somehow respond to a prescribed relative weighting of costs and benefits (here biodiversity gained). One approach to estimating such trade-offs views the problem as ~m example of cost-benefit analysis: 'assessing the appropriate trade-off between biodiversity conservation and other values, requires some assessment of the price individuals, conservation groups and commercial concerns would be willing to pay for various levels of conservation." (Chisholm and Moran. 1993; p. 153). Applied to protected-areas selection, this would mean that alternative sets of areas would have both biodiversity and associated costs expressed in dollar-equivalents, so that the best set of areas for protection is clearly the one implying the greatest difference between monetary gain and loss.

Biodiversity, costs and protected areas

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Such monetary values on conservation options will not be easy to estimate (e.g. see Jansenn, 1991), though some progress is being made in developing approaches appropriate to biodiversity values (Brown et al., 1993). A different approach that nevertheless addresses the question of a relative weighting of costs and benefits, and already has been applied to biodiversity allocation problems, is multi-criteria analysis (e.g. see Jansenn, 1991; Munasinghe, 1993). While multi-criteria analysis has been applied to biodiversity-versus-cost trade-off problems, there have been no formulations of this approach for the case where the options being compared consist of alternative sets of areas (to be protected for representation of biodiversity). This is a case requiring special consideration, because the conservation/ biodiversity value of any area is context dependent - it depends on which other areas also are taken to be part of the protected set (the principle of complementarity; see e.g. Margules et al., 1994). We will show below how this affects our strategy for exploring trade-offs. The approach will be illustrated for both continuous-pattern surrogates and for attributes.

An approach using trade-off space Figure la shows a simple plot in which the horizontal axis is the total cost of a set of protected areas and the vertical axis is a measure of total forgone biodiversity. Suppose that the total cost and total amount of biodiversity left unprotected can be evaluated for any combination of allocations of individual areas to protection. Any set of protected areas (any 'solution') then can be represented by a point in this space (Fig. la). A desirable solution then is one whose position along both axes is close to the origin. If all possible solutions are plotted, it is of interest to note those particular solutions which are 'dominated' (e.g. see Nijkamp 1979; Munasinghe, 1993) by one or more other solutions. A solution is dominated by another in the present context if the first solution has both higher forgone biodiversity and higher cost. Such a scenario implies that, no matter how cost and forgone-biodiversity are weighted relative to one another, the first solution must imply smaller total net benefit. These dominated solutions, at least in the absence of other constraints, can be excluded from the set of feasible solutions. The set of all non-dominated solutions, in the present context, can be expected generally to approximate a curve as shown in Fig. lb. At the upper end of the curve, there is little biodiversity already protected, so that any area on average will contribute a lot to biodiversity; a shift to another solution-combination, by adding an area, can be accomplished with a large gain in biodiversity relative to the increase in cost. At the lower end of the curve, new areas will tend to contribute smaller amounts to overall biodiversity, while average costs of areas will not change; thus, the biodiversity forgone decreases little for the given average cost of the additional area. A weighting assigned to each of the two axes will mean that an amount of cost is equated with an amount of biodiversity. This means that total net benefit is increased (for example when an additional area is protected) if the biodiversity contribution of the area exceeds its cost, expressed (based on the weighting) in equivalent biodiversity units. If a particular weighting (or scaling) for the two axes is assumed, this weighting will imply a series of equal-net-benefit lines (in the case of a simple linear weighting) in the space (Fig. lc). For any one of these lines, all solutions falling along it have equal total net benefit (or its opposite, total net forgone benefit, equal to a linear combination of forgone biodiversity

--

• 000 • • 00 000

0000 o 000 O0 O 0

I oooo


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Figure 1. (a) A trade-off space in which the horizontal axis is total cost and the vertical axis is total biodiversity forgone. Each point represents a solution, defined as a combination of areas allocated to protection. (b) A trade-off space in which the horizontal axis is total cost and the vertical axis is total biodiversity forgone. The curve shows the approximate pattern of the non-dominated solutions from a). For further information see text. (c) A trade-off space in which the horizontal axis is total cost and the vertical axis is total biodiversity forgone. Each line represents a set of points in the space having equal value for total net benefit, as defined by a given weighting. Lines closer to the origin (lower left) represent larger values of total net benefit. The solution along the non-dominated curve that intersects a line with largest total net benefit would be preferred over all solutions, for the given weighting. (d) A trade-off space in which the horizontal axis is total cost and the vertical axis is total biodiversity forgone. In practice, solutions falling along the curve in b) can be found by nominating a maximum-total-cost and then searching for the set of allocated areas that is maximally diverse (minimizing forgone biodiversity) with cost less than the maximum-total-cost. However, this solution also must be checked against other possible solutions that are equally diverse with still lower cost (and therefore dominate). Here, the dot on the right is a solution with maximum biodiversity for the maximum-total-cost, represented by its projection onto the horizontal axis. The dot on the left is another solution with equal biodiversity and less cost. (e) A different view of trade-off space, applicable to individual areas. The horizontal axis is the cost of the area and the vertical axis is the contribution of the area to total biodiversity, given some other partial set of protected areas. The line represents the same weighting of biodiversity and cost as in (a)-(d), but the vertical axis here shows increasing biodiversity going up the axis. For the given weighting, an area can be selected for protection only if it falls in the region of the space above the line, implying that its CB (contribution to total biodiversity) is greater than its EC (equivalent cost in biodiversity units). For further information, see text. (f) A trade-off space in which the horizontal axis is total cost and the vertical axis is total biodiversity forgone. The lines represent a given weighting and the point shown is a partial set of areas, subject to additions and deletions to satisfy the CB > EC constraint. (g) The trade-off space as in (f). An area will be added to this set if its CB exceeds its EC; this will correspond to a new solution at the end of the arrow, having greater total net benefit. (h) The trade-off space as in (f). An area will be deleted from this set if its CB is less than its EC (possibly because addition of other areas has reduced its complementarity-based contribution to biodiversity); this will correspond to a new solution at the end of the arrow, also having greater total net benefit. (i) The trade-off space as in (f). In theory, total net benefit would be increased by adding or deleting an area such that total cost and total biodiversity forgone both decreased, resulting in a solution at the end of the arrow. However, such a change is not possible unless there are negative costs associated with some areas, or biodiversity increases in the absence of protection for some areas. (j) A trade-off space as in (f), showing a sequence of additions and deletions of areas, such that total net benefit is maximized and all areas in the final set satisfy the constraint that CB > EC. and cost). Further, solutions falling on lines closer to the lower left h a n d c o r n e r (having b o t h lower f o r g o n e biodiversity and lower cost) naturally are those with greater total net benefit. Thus, any particular weighting points to a best-possible solution, for example, a m o n g all those plotted in Fig. lb; this solution, equivalent to a set of areas allocated to protection, c o r r e s p o n d s to the point falling along the line closest to the origin (Fig. lc). The set of solutions falling along the curve shown in Fig. l b can be f o u n d by repeatedly n o m i n a t i n g a total cost, and then searching for the set of allocated areas that is maximally diverse (minimizing f o r g o n e biodiversity), with cost less than the threshold. Such a

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solution also must be checked against other possible solutions that are equally diverse with lower cost (and therefore dominate the initial solution; Fig. ld). A nominated weighting then will determine a best-possible solution from this set. These evaluations can be carried out using the DIVERSITY package (Walker and Faith, 1994), described below. A slightly different approach is developed in this paper, that will overcome an inconsistency in using weights as described above. Fig. l e helps to clarify this problem, in showing the implications of a given weighting for individual areas. The horizontal axis is the cost of protection of any particular area, and the vertical axis is the amount of biodiversity contributed by the area in the context of a given set of already-protected areas: this is the ~complementarity' value of the area. The line extending from the origin represents the same weighting shown in Fig. lb. This weighting implies that, if total net benefit is to be maximized, then a particular area should be protected if and only if its complementarity-based contribution to biodiversity, CB, exceeds the associated cost by falling in the region above the line. One way to interpret this is that the line equates a given cost, C, with an 'equivalent cost in biodiversity units'. EC. EC can be thought of as cost re-expressed in units of equivalent amounts of biodiversity. Protecting a given area implies a cost that equals an effective amount of biodiversity lost, as indicated by the value along the vertical axis for the point where a vertical line through the cost intersects the weighting-line (Fig. le). We will refer to the constraint that the contribution to biodiversitv exceed equivalent cost, as ~CB > EC'. It should be noted that solutions chosen by considering only total costs, as in Fig. lb, for a given weighting may not be fully consistent with the area-based constraint. The reason is that, for the given weighting, not all areas whose values fall above the corresponding weighting-line (as in Fig. le) are necessarily protected in those solutions based only on total biodiversity and costs. For example, a solution may be found with minimum forgone biodiversity for some maximum cost, but for the nominated weighting an unprotected area may remain whose complementarity contribution exceeds its weighted cost. To aw)id this limitation, individual areas must be evaluated relative to the CB > EC constraint. Operationally, a weight can be nominated and an iterative procedure used to ensure that all areas having a CB that exceeds the corresponding gain from non-protection (EC) are indeed assigned to protection. Of course, since the biodiversity-contribution for any area depends on the set of other areas currently nominated for protection, the algorithm (as implemented in DIVERSITY: see below) must add and subtract areas to find a combination of allocations that not only satisfies the constraint "CB > EC', but also maximises total net benefit (the solution falls along a line as close as possible to the origin in a plot of overall costs as in Fig. l c). While examples of such weighting lines in allocation trade-off spaces are found, for example in Jansenn (1991), there has been no previous application to the case where values along a biodiversity axis incorporate the principle of complementarity (see above). The second half of Fig. l(f-j) shows an example of the overall trade-off space and illustrates how the iterative algorithm in DIVERSITY (Walker and Faith, 1994; see examples below) searches for such a solution. The point shown in Fig. I f represents the solution at the end of an iteration. At this stage, a number of areas are assigned to protection with some corresponding reduction in the total forgone biodiversity, and with some associated total cost. An area is added to the protected set if it corresponds t~ ~ change as shown in Fig. lg: forgone biodiversity is reduced at a small enough additional cost such that the new solution falls on a line closer to the origin. Alternatively, an area is

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deleted from the protected list if the result corresponds to that shown in Fig. lh: there is a reduction in cost with a small enough increase in forgone biodiversity so that the new solution falls on a line closer to the origin. Such a deleted area may have initially (at an earlier stage in adding and deleting areas to build up a set) yielded a large gain in total net benefit, but addition of other areas might have reduced its biodiversity contribution, through complementarity. While Fig. lg and h show possible changes as a result of addition or deletion of areas, a change as shown in Fig. li in which addition of an area decreases both forgone biodiversity and costs is not possible, unless the cost of the area is negative (a scenario not considered here; Faith, Walker, and Ive, unpublished data). The end result of a series of additions and deletions is that the final solution, for the nominated weighting, is a non-dominated point (Fig. lj) which also satisfies the constraint that an area is protected if and only if its contribution exceeds its weighted cost. This strategy provides one algorithm, under the CB > EC constraint, for estimating a land use allocation that maximizes 'total net benefit', under the assumptions implicit in the weighting or scaling of biodiversity versus costs. That is, an allocation is found that minimizes the weighted sum of forgone biodiversity and cost (or forgone suitability for another land-use). This property makes clear the relationship of this strategy to other applications of multi-criteria analyses to biodiversity/cost trade-offs that address net benefits (e.g. Munasinghe, 1993; Lutz and Munasinghe, 1994). The iterative process as described above used only one nominated weighting among many possible. The above search strategy then can be repeated for other nominated weightings, producing a trade-off curve tracing alternative solutions. We show below how sensitivity analysis can be used to interpret these results.

Examples Environmental diversity

We referred above to the use of pattern as surrogate information for biodiversity assessment. When environmental data are summarized as a continuous environmental space or ordination pattern, a measure of'environmental diversity' (ED) indicates relative amounts of expected biodiversity at the species level for sets of areas (Faith and Walker, 1993; Faith, 1994; Faith and Walker, 1996). Figure 2 shows a simple environmental space for 17 areas, used in the examples below. The ED value of a set of protected areas, chosen from among these 17, is given by the sum ('SUM' in the examples below) of distances from each point in the space to its nearest selected (protected) area. This SUM estimates the relative number of species that are left unprotected by the nominated set of protected areas (Faith and Walker, 1996). The examples in this section use the DIVERSITY package (Walker and Faith, 1994), which allows environmental diversity to be calculated iteratively; one option (#11) implements the CB > EC constraint. In practice, a given run in DIVERSITY is defined by nominating a scaling (weighting) of costs, C, into equivalent cost, 'EC', expressed in units of biodiversity: EC = a + b C

(1)

The examples below illustrate the effect of the CB > EC contraint on the final set of areas selected for protection; on some occasions, alternative sets of areas, with about the same

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o 10 o 12

o 17

09 08

o7

o 15

o6 o 11

o 13 o 14

o16 o3 o2

o4 05

ol Figure 2, A hypothetical two-dimensional environmental space for 17 areas. If only three areas can be chosen to represent overall biodiversity, then the ED criterion would choose areas 12, 15, and 2. For further information see text. total biodiversity as when costs are ignored, can be found that largely avoid including areas with high cost. For the 17 areas (Fig. 2) suppose that there are estimated suitabilities for an alternative land-use to protection (e.g. forestry production; Table I a). These values provide the costs in formula 1. In the first example, a is assigned 1.0 and b is assigned 4.0 in formula (1). Table lb shows the subsequent iterative selection of areas using D I V E R S I T Y under option 11. Some areas with medium to high suitabilities for forestry are initially selected, but as more areas are added, these areas are gradually replaced by "near-substitutes' found in about the same part of the space, but having lower EC values (Table lb). At the end of the run, all 8 selected areas have CB greater than EC, and only area 16, among those with moderate-to-high suitability for forestry (EC 29.4), remains as part of the set; it uniquely occupies one portion of the space (Fig. 2), and so contributes a large amount to represented biodiversity. A reanalysis of the same example is shown in Table 2, but with a much higher EC value for a given C (b 10: i.e. forestry is valued more, in that a given C value is equated with a larger amount of biodiversity). Now, all areas having non-zero C values are effectively excluded. Even area 16 is excluded from the final set; in fact, its EC is so high (73.5) that it is replaced early in the iterations. However, the consequence of this higher weighting of forestry over biodiversity is that the amount of forgone biodiversity increases from 331 to 398 as reflected in the final value of SUM. Clusters or attributes and trade-offs E D also can be used for assessment of total net benefit when an environmental space is not available, and environmental attributes/clusters must be used - e.g. community types


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Table 1. ED analysis for areas in Fig. 2. (a) Suitabilities for forestry development. 1

0

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

7 6.900 4.500 0 7.200 7.800 7.400 5.300 0 0 5.200 4.600 0 0 7.100 0

(b) In formula (1) we assign a = 1.0, b = 4.0. Area 16, among those with high forestry suitability~ remains in the final list of selected areas. Dots indicate that part of the iterative ED output is not shown. Member area number

Increase in SUM if removed

EC value

14 557.7469 16 168.5571 Current SUM for selected areas is 693.22; Best to add 3

1.000t3 29.4000

14 152.1510 16 168.5571 3 128.5999 Current SUM for selected areas is 564.62; Best to add 12

1.0000 29.4000 28.6000

14 90.4048 16 168.5571 3 104.1819 12 76.6031 Current SUM for selected areas is 488.02; Best to add 17

1.0000 29.4000 28.6000 21.8000

Best to add 10 14 16 3 12 17 4 1 15 10

26.0620 54.1872 29.9660 19.2026 31.4604 51.0388 21.4951 18.9801 16.6403

1.0000 29.4000 28.6000 21.8000 1.0000 19.010 1.0000 1.0000 1.000

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Faith and Walker Table 1 (Continued) M e m b e r area n u m b e r

Increase in S U M if r e m o v e d

EC value

C u r r e n t S U M for selected areas is 303.78: for 12, CB Area 12 deleted from select list Best to add 5 14 23.7664 16 54.1872 17 31.4604 4 16.3433 I 52.20115 15 18.9801 I {) 42.1448 11 33.1251 5 8.6813 C u r r e n t S U M for selected areas is 314.92: for 4, CB Area 4 deleted from select list

19.2/)26 < EC -- 21.800()

1.0000 29.4001/ 1.0000 19.0000 1.0000 1.0001) 1.0000 1.0000 1.00(X1 16.3433 < E C -~ 19.00()

14 24.4236 1.0000 16 66.3677 29.4000 17 31,46114 1.0000 I 52.2005 1.011O0 15 18.9801 1.0000 10 42.1448 1.0000 1I 33.1252 1.0000 5 43.3768 1.0000 Current S U M for selected areas is 33t.27: No reduction in SUM is possible - stop Table 2. E D analysis for high forestry weight. In formula (1) wc assign a = 1.0, b = 10.0. Now, only areas with low forest suitability values are on tinal list of protected areas. Dots indicate that part of the iterative E D output is not shown. M e m b e r area n u m b e r

Increase in SUM if r e m o v e d

EC value

14 17 4 15 I II IO C u r r e n t S U M for selected areas is

23.7664 31.4604 79.2442 25.1276 64.8438 33.1251 42.1448 377.79; Best to add 5

1.0000 1.0000 46.0000 .0000 .0000 .0000 .0000

14 17 4 15 I I1 Ill 5 Current S U M for selected areas is Area 4 deleted from select list

23.7664 31.4604 28.5238 25.1276 52.211O5 33.1251 42.1448 8.6813 369.1 I: for 4, CB

14 17 15 l 1I IO 5 C u r r e n t S U M for selected areas is

1.0000 24.4236 31.4604 1.0OOO 1.0()0() 35.3624 1.0000 52.2005 33.1252 1.0000 42.1448 1.0000 1.0000 59.4017 397.63: No reduction in S U M is possible - stop

.00(~) .(X)(II) 46.(X)00 1.0000 1.0000 1.0000 1.0000 1.0000 28.5238- EC : 46.00110


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or environmental domains (Richards et al., 1990). The 'attributes' alternatively might correspond to indicator-species. For these analyses, the attributes are first described by 'dummy' variables that replace the usual environment space variables. The ED procedure then proceeds in the usual way. In the example shown in Table 3(a-d), a set of three areas is found that represents all of the attributes at least once, and, analogously with the earlier examples, avoids conflict with competing suitabilities. Note that area 6 is chosen initially, as it has three of the five attributes, but the procedure subsequently replaces this area with others having smaller costs/suitabilities.

Sensitivity analysis for environmental - diversity (SAFE-D) Costanza (1993) has called for better methods to incorporate uncertainty into policy making and management. He distinguishes uncertainty from risk; a risk analysis differs from uncertainty analysis in having some assessment of the relative probabilities of different events. The assessment approach in this paper, when combined with environmental diversity (ED), uses a model that provides relative probabilities for species richness of different sets of areas, so that alternative options (alternative sets of protected areas) are assessed relative to their different amounts of expected biodiversity. In this sense the approach is close to a form of risk analysis - based on the assumed probabilities, actions can be taken that maximize expected biodiversity. However, the overall approach may be best characterized as dealing with uncertainty; the exact values for costs and for species-richness are poorly known in general. The approach advocated here deals with uncertainty in two (related) ways. First, a robust surrogate for biodiversity is used that avoids unwarranted assumptions and is flexible enough to allow other information to be added in. Second, the fact that this information about both biodiversity and cost is not exact means that it is evaluated as part of a sensitivity analysis. The environmental diversity approach is an attempt to use environmental data as a surrogate for biodiversity at the species level, while avoiding unwarranted assumptions about the relationship of species to environment. ED is consequently open to the criticism that it is too simplistic, particularly in assuming that all points in space are equally species rich (but see Faith and Walker, 1993). However, ED provides a flexible framework that allows additional information, when available, to be incorporated in a way consistent with the basic underlying model relating species to environmental pattern. The set of areas assumed already-protected, the boundaries of the realized environmental space, the variation in species richness among areas, the biodiversity contribution of production/ management areas, the suitability of areas for other land uses, and other factors can be built into the analysis in a consistent way (Faith and Walker, 1993; 1996). A practical difficulty is that, while these factors may properly influence the priorities for conservation to varying degrees, the exact values for these parameters are generally missing. This adds to the high uncertainty already inherent in biodiversity assessments. However, exact values for these quantities are not necessarily required in order to gain useful information for distinguishing among land-use options. Sensitivity analysis is well-established in decision-support procedures for land allocation (e.g. see Jansenn, 1991; Kuusipalo and Kangas, 1994), but has not been used for the problem of choosing areas to form a set of representative protected areas. ED can be combined with a form of sensitivity

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Faith and Walker Table 3 (a) A n example in which t h e r e are 5 attributes; here, a special form of the n o r m a l set of e n v i r o n m e n t a l variables is t h e n created. 1 2 3 4 5

0 0 1 0 0

0 1 0 0 0

0 0 0 l 0

l 0 (J 0 0

(J (J () 0 l

(b) T h e r e are 9 areas, each c o n t a i n i n g one or m o r e of the attributes, as s h o w n (for example, area 1 has 2 attributes, n u m b e r s 4 a n d 5). 1 4 5 2 4 3 1 5 4 1 3 5 1 6 1 2 5 7 2 4 8 2 9 5

2

1 2

2

1 3

2

1 1

(c) T h e 9 areas have suitabilities for a "'competing" land use as shown. 1 2 3 4 5 6 7 8 9

0.2 0.6 0.3 0.3 0.8 0.8 0.1 0.3 0.7


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Table 3 (Continued) (d) ED iterations for the 9 areas. Dots indicate that part of the iterative ED output is not shown. Member area number

Increase in SUM if removed

EC value

6 2.8284 4.0000 7 1.4142 0.5000 Current SUM for selected areas is 1.41; for 6, CB = 2.8284 < EC = 4.0000 Area 6 deleted from select list 7 4.2426 Current SUM for selected areas is 4.24; Best to add 4 7 2.8284 4 2.8284 Current SUM for selected areas is 1.41; Best to add 1

0.5000 1.5000

7 1.4142 0.5000 4 2.8284 1.5000 1 1.4142 1.0000 Current SUM for selected areas is 0.00; No reduction in SUM is possible - stop analysis (sensitivity analysis for environmental-diversity: SAFE-D), in which the land-use implications implied by a range of different parameter values are explored. The section below describes an example of SAFE-D, in which the implications of the assignment of different weights for competing land-use suitabilities are explored.

An example of sensitivity analysis This example uses the simple environmental space of Fig. 2, and the corresponding suitabilities from Table la. The sensitivity analysis in this case is based on exploring variation in the relative importance given to forestry development, as expressed by the size of the 'b' value assigned under option 11 (constraints option). 'b' was assigned values from 0.5 to 5.0 in successive ED runs. Two questions were asked: (1) which of the 17 areas (among those not already committed to protection) would be assigned to protection based on total net benefit, even if the weight given to forestry suitability was quite high? (2) which of the 17 areas (among those not already committed to protection) would not be assigned to protection based on total net benefit, even if the weight given to forestry was quite low? Based on successive ED analysis with different weights ('b' values), the answer to (1) is that areas 16 and, to a lesser extent, 7 (or 6) and 4 would be justified for protection based on total net benefit (while all other available areas would be assigned to forestry), even when forestry was given relatively high weight (b = 3). The answer to (2) is that areas 9, 13, and 7 (or 6) would not be justified for protection based on total net benefit (while all other available areas would be protected), even when forestry was given low weight (b < < 1). Note that areas 7 and 6, as near-substitutes for each other (Fig. 2), figure in both parts of the analysis; having one of the two will be attractive for biodiversity even when forestry is

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highly weighted, while having both will not be attractive for biodiversity protection, even when forestry suitability of areas is given low weight. The results of this sensitivity analysis might be used, for example, to argue for high priority for the protection of area 16. Discussion

The approach to trading-off biodiversity and cost advocated in this paper has several properties that highlight differences from traditional cost-benefit analyses. These include the definition of value, the application of safe-minimum-standard (SMS), and the use of multi-criteria analysis. Our definition in this paper of biodiversity/conservation value is compatible with the guidelines of SMS. SMS promotes a view, contrary to cost-benefit analysis, that all the objects in question should be taken to be equal in value: a given object then is to be protected unless costs are 'intolerable' (e.g. Bishop, 1993; Myers, 1993). This perspective has the appeal that it is arguably a reasonable response to our inability to estimate actual differential values of objects in the future. For regional allocation of protection to areas, the "objects" of SMS might be equated with the different areas, implying that all areas are to be considered as having equal biodiversity value. However, we view SMS in the context of assessment of the biodiversity of sets of areas as properly applied at the level of the more fundamental objects of interest - namely, species. Adopting the SMS consequently will not imply that all areas must be viewed as equal, but rather that all species are equal (at least at this level of decision-making; see also Faith, 1994). Thus, the SMS view of all-objects-equal in fact provides a justification for differential conservation values to be placed on areas: areas are of differential value because they differ in the number of (equally-weighted) species that they can contribute to a set. The importance of SMS in this context is that it provides a basic rationale for identifying differential values of areas, without introducing hard-to-quantify economic valuations. SMS also clarifies the role of costs in allocation of protection to different areas in that il defines the burden of proof of protection. Applying SMS means that a given species is to be protected unless the costs are 'intolerable'. The fact that areas have differential conservation value and costs immediately suggests one way in which intolerable costs might be identified. If a particular area can be substituted-for by other areas of lower cost. without any penalty in overall biodiversity represented, then protection of this area (and its species) arguably would represent a case of intolerable costs. Sensitivity analysis may play an important role in such assessments. In the presence of uncertainty, intolerable cost also may be associated with small likelihoods of relatively high conservation value. An area whose CB value would be greater than its EC value only if other parameters take quite extreme values (e.g. the costs associated with other areas are so high that they are not protected) is arguably an area whose protection involves an intolerable cost. Conclusion

This paper demonstrates that the problem of identifying a candidate set of protected areas that is maximally biodiverse and avoids high costs can be approached using trade-off space. when the implications of relative weightings are properly explored at the level of individual


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areas. We also illustrate the contribution of sensitivity analysis to dealing with the uncertainty inherent in biodiversity allocations, relating to both the diodiversity contributions of areas and their associated costs. Elsewhere (Faith and Walker, in preparation) we describe the application of sensitivity analysis also to vulnerability values of areas, as part of the allocation procedures. Future work will focus on algorithmic aspects of the problem of trading off biodiversity and costs. We note that there may be multiple solutions, even for a given weighting, that satisfy the constraint introduced here that an included area's CB be greater than its EC. A linear programming approach will be explored elsewhere for searching among all constrained solutions for the one that has maximum total net benefit. Such an approach will be useful when context-dependency is considered also for the costs (e.g. when the forestry opportunity for a given area is greater if fewer areas are committed to forestry over the region). Version 3.0 of DIVERSITY will incorporate the same 'CB > EC' option into a method based on hierarchical pattern ('PD'; Walker and Faith, 1993; Faith, 1994), so that the number of features, species, community-types, or environmental classes contained in a reserve-set can be maximized under this same constraint. The strategy developed here then will be applicable to any surrogate measure of biodiversity. Elsewhere (Faith et al., 1994; 1996) we describe an application of this approach to land-use allocation problems in the south-east forests of Australia, integrating the DIVERSITY package with suitabilities for various land uses produced by a land-use planning information system ('LUPIS'; Ive and Cocks, 1988).

Acknowledgements A preliminary report on the trade-off strategy developed here was prepared for the User's Guide to DIVERSITY. We thank John Bowers for his helpful comments on an earlier draft of this paper and thank S. Smith for artwork. We thank two anonymous referees from the Northern Territory for constructive and timely comments on this and its companion papers.

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