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Place prioritization for biodiversity reserve network design: a comparison of the SITES and ResNet software packages for coverage and efficiency

Place prioritization for biodiversity reserve network design: a comparison of the SITES and... Introduction One of the major tasks of conservation biology is that of selecting reserve networks that are fully representative of the biodiversity of an area. In real‐world scenarios, however, full representation is often impossible, because not all places of biological interest can be conserved. Consequently, the practical problem must be reduced to that of the representation of biodiversity surrogates up to a specified target as efficiently as possible, with efficiency being measured by criteria such as the minimum total area or cost. Places must therefore be prioritized before a final set is selected for reservation or other conservation action. Place prioritization algorithms are becoming a critical tool in the practice of biodiversity conservation. The purpose of this note is to compare the respective performances of two software packages implementing radically different place prioritization algorithms, SITES and ResNet, on four datasets to determine which is preferable for use in systematic conservation planning, or how they may be used together profitably. Both of these packages can be downloaded freely from the web (see Ball, 2000 for the design of SITES; Andelman ., 1999 for downloading SITES; and Aggarwal ., 2000 and Sarkar ., 2002 for downloading ResNet). The algorithms incorporated in these packages, although not the specific packages themselves, have been compared previously by Csuti ., 1997 ; see also Pressey (1997 ). The algorithms implemented in SITES and ResNet are radically different. SITES implements the widely used simulated annealing algorithm ( Kirkpatrick ., 1983 ; Otten ., 1989 ). Using a cost equation which computes the sum of a set of weighted components, the procedure iteratively selects new places, compares resulting changes to the cost equation, and attempts to minimize the total cost. A unique feature of SITES is the large number of optional parameters which can be incorporated into the calculation of the cost, and which require user‐defined weights for the search process. These parameters include a boundary length modifier (which allows the user greater control over the level of adjacency or ‘clumping’ of cells), conservation categories and a penalty factor for under‐representing the target. SITES has been utilized in several conservation projects in the United States, including regions in southern California and the Columbia Plateau ( Andelman & Fagan, 2000 ). ResNet implements a hierarchically controlled, rarity–complementarity‐based selection algorithm ( Margules ., 1988 ; Aggarwal ., 2000 ). The place prioritization procedure is initialized by the selection of a first cell on the basis of rarity, richness or from a user‐defined set of cells. (The last option is relevant if a reserve network is to be built by extension of an existing set of reserves.) ResNet then employs an iterative procedure that selects places on the basis of rarity; then, to break ties between cells with equally rare surrogates, it uses complementarity (that is, it selects the cell that contains the most surrogates not already represented up to the specified target among the cells that have already been chosen). Should ties still remain, ResNet optionally uses adjacency (when a cell adjacent to already selected cells is preferred to one that is not); and finally selects by lexical order (that is, randomly). The user also has the option of incorporating a redundancy check, as well as area and cost constraints. ResNet has been applied to datasets from Québec, Namibia and Islas Malvinas/Falkland Islands ( Sarakinos ., 2001 ; Sarkar ., 2001 ), and has been used in conjunction with the GAP Analysis Project in Texas ( Sarkar ., 2001 ). Although the two algorithms can be compared using a variety of different criteria, the radically disparate strategies used by the two algorithms narrow the ambit of quantitative evaluation. Only completeness in surrogate coverage (meeting the specified target levels), efficiency (doing so while selecting the minimum possible area) and computational time are parameters common to the performance of both algorithms. These were used as the most important indices of comparison in this analysis. Efficiency is particularly important because both SITES and ResNet use heuristic algorithms. While both attempt to produce a solution that meets a specified target, neither guarantees that a better (that is to say, more efficient) solution is not possible. [In other words, both algorithms guarantee that a local optimum solution is obtained; neither guarantees that the global optimum is found. For a discussion of algorithms that find the global optimum, but require much more computational time, and for a discussion of the relative merits of algorithms that are minor variants of the one implemented in ResNet, see Csuti . (1997 ).] Methods Both packages were run on an IBM‐compatible personal computer. The first dataset consists of 1250 data cells (each 0.25 × 0.25 degrees of longitude and latitude) in Namibia containing records of the presence of 33 termite genera (cf. Sarkar ., 2002 for a full description of the dataset). The second dataset consists of 254 cells (each 10 km × 10 km) in the Falkland Islands/Islas Malvinas, containing records of the presence of 65 breeding bird species (cf. Sarkar ., 2002 for a full description of the dataset). The third dataset consists of 1183 cells (each a hexagon of about 649 km 2 produced by the GAP Analysis Project) in Texas containing records of the presence of 655 vertebrate species (cf. Sarkar ., 2001 for a full description of the dataset). The fourth dataset consists of 16 500 data cells (each 0.2 × 0.2 degrees of longitude and latitude) in Québec, containing records of the presence of 387 species of flora and fauna at risk distributed over 709 of the data cells (cf. Sarakinos ., 2001 for a full description of the dataset). Each algorithm was run with the target of representation of surrogates specified at 1, 5, 10, 15 and 20. Only the target of 1 is guaranteed to be met by all surrogates because each surrogate must occur at least once in the dataset. When faced with a surrogate for which the assigned target cannot be met because it does not occur that many times in the dataset, ResNet automatically revises that surrogate's target level to its total presence. We will refer to these target levels of representation as the ‘initial target’ and the ‘revised target’. The first two datasets are computationally simple; they are also far too sparse to be of much use in any realistic policy formulation situation; the last two are much more complex and can potentially be used in practice for reserve network design. (The Québec dataset has already been used by Sarakinos ., 2001 to make policy recommendations.) For each target of representation, SITES produces up to six output files: (i) projectName _best.txt ( ‘best file’), a prioritized list of places containing all cells selected in the single most cost‐effective of the runs; (ii) projectName _ssoln.txt ( ‘summed solution file’); which contains the complete list of cells selected in every run where these cells are grouped into frequency categories depending on the number of runs in which they were selected (thus for our purposes there were 50 frequency categories because there were up to 50 runs — see below); (iii) projectName _mvbest.txt file, which contains information on the extent to which the surrogates selected in the best run meet the targets of representation; (iv) projectName _sum.txt file, which records summary statistics for all runs for a given target; (v) projectName _sen.dat file, which provides a general performance report and information on the algorithm employed; and (vi) finally, a file in which one also has the option of recording the different solutions obtained for each of the runs. The last option was not used for this analysis. The summed solution file is a unique feature of the SITES software package, intended to support the analysis of the robustness of the corresponding ‘best file’. Its potential use in this context will be discussed below. (cf. Andelman ., 1999 for a more detailed explanation of the various data reporting options offered in the SITES software package.) ResNet produces up to five output files. Four of these output files consist of lists of prioritized places. These five files are: (i) for every application of ResNet, the first output file (‘basic output file’) records the solution arrived at without the use of adjacency or a check for redundancy; (ii) if the ‘adjacency’ option is selected, a second output file records the corresponding solution when adjacent cells are given preference as explained above; (iii) if the ‘redundancy’ option is selected, a third output file records the corresponding solution when redundant cells are removed; (iv) if the procedure described in (iii) is modified with a ‘secondary adjacency’ checking option, which results in the retention of redundant cells which are adjacent to a selected nonredundant cell, a fourth output file records the corresponding solution; and (v) finally, for every application of ResNet, a log file is produced that records, for each cell contained in the prioritized list, the rule under which it was selected, and the percentage of surrogates which have cumulatively met the revised target of representation. The ‘adjacency’ and ‘secondary adjacency’ modifications were not used in this analysis. SITES was tested according to the recommended minimum standards (50 runs, 10 6 iterations per run) ( Andelman ., 1999 ). To ensure testing integrity, SITES was also subjected to a longer ‘control run’ using 100 runs and 2 × 10 6 iterations at a target level of 10 to see if increasing the size of the computation improved performance. The result was negligibly different (and, in fact, slightly worse). For all targets of representation, ResNet was initialized by rarity which is known to produce the most efficient results ( Sarkar ., 2002 ), and run with and without the removal of redundant cells. The distance between two solutions was defined as the ratio of the number of unshared selected cells to the total number of selected cells (in both solutions). Thus, if all cells are shared, the distance is 0; if no cells are shared, the distance is 1. In the first comparison, reported in Table 1 , the relative efficiency of the two place prioritization algorithms was compared by setting an initial target of representation for each surrogate and comparing the total number of cells selected by each algorithm in attaining the revised target. ResNet automatically guarantees complete surrogate coverage by the end of a run of the program. In general, SITES does not guarantee such coverage; since it tries to optimize over other parameters besides the presence of surrogates, the program may terminate before complete coverage is attained because other parameters have been optimized sufficiently. For this analysis, complete surrogate coverage was achieved through a trial‐and‐error process of sufficiently weighting the surrogate absence penalty factor of the cost equation to prevent target incompleteness. 1a Data from Namibia. Results of the direct comparison of SITES and ResNet. SITES was forced to achieve complete surrogate coverage by assigning a severe penalty for incomplete coverage. For more details, see text 1 2 3 4 5 6 7 8 1 33/33 6 6 0.333 3 < 0 : 00 : 01 0 : 07 : 05 5 26/33 29 29 0.349 2 < 0 : 00 : 01 0 : 07 : 26 10 23/33 54 54 0.241 6 < 0 : 00 : 01 0 : 07 : 15 15 21/33 73 73 0.068 12 0 : 00 : 01 0 : 07 : 10 20 19/33 85 85 0.141 1 0 : 00 : 02 0 : 07 : 16 Explanation of the columns: 1. The initial target of representation for each surrogate. 2. The number of surrogates for which the initial target can be met/the total number of surrogates. 3. The number of cells selected for revised target levels by ResNet's basic output file. 4. The number of cells selected for revised target levels by the SITES best file. (Parameters: surrogate absence penalty factor sufficiently weighted to ensure target completeness; all optional modifiers off; annealing schedule set at 10 6 iterations per run; 50 runs per target level. See text for more details.) 5. The distance between the solutions. 6. The ordinal number of the SITES run (of the 50 runs in the annealing schedule) that was selected by SITES as the best file. 7. The run time of ResNet. 8. The run time of SITES over the full annealing schedule. In the second comparison, SITES was run with site costs uniformly set equal to each other, and the penalty factor costs for surrogate absence were given equal weights to the cost of a site. In this method of comparison efficiency can no longer be measured simply by comparing the number of cells selected by the algorithms for a given target level. The comparison of efficiency of the two algorithms must be indirect. Three different methods were used. ResNet was asked to terminate after selecting exactly the same number of cells as contained in the SITES ‘best file’ and the number of surrogates for which targets were met by each algorithm were compared. In an effort to establish more wide‐ranging comparisons between the two algorithms, similar tests were conducted with two subsets of the SITES ‘summed solution file’: (i) the group of cells selected in every run for a given target (and thus falling within the highest frequency category, which will be referred to as the ‘common set’); and (ii) the group of cells with the highest frequency measured across all runs for a given target, up to the number of cells selected by ResNet for that target (which will be referred to as the ‘top set’). (In other words, if ResNet selects n cells for a given target, then the ‘top set’ consists of SITES’ n most frequently selected cells.) Results The numerical results are reported in Tables 1a,b −4a,b . In all Tables, initial targets of representation for each run are listed in Column 1. Column 2 lists the number of surrogates that met or exceeded the initial target level. 1b Data from Namibia. Results of the indirect comparison of SITES and ResNet. For more details, see text 1 2 3 4 5 6 7 8 9 1 33/33 6 6 31/33 31/33 2 22/22 32 5 26/33 29 27 27/33 27/31 9 15/11 31 10 23/33 54 44 26/33 26/30 19 16/17 29 15 21/33 73 52 24/33 24/29 18 8/12 29 20 19/33 85 71 26/33 26/31 34 9/20 31 10 11 12 13 14 15 16 17 18 7 4 0.333 2 5 55 56′ < 0 : 00 : 01 0 : 06 : 19 30 18 0.357 9 23 90 90 < 0 : 00 : 01 0 : 06 : 47 61 37 0.245 19 46 133 135′ < 0 : 00 : 01 0 : 06 : 53 81 44 0.296 18 61 135 137′ 0 : 00 : 01 0 : 06 : 56 91 58 0.256 34 73 178 178 0 : 00 : 02 0 : 06 : 57 The SITES selections (column 15) were insufficient for complete target representation. The additional cells were selected using ResNet. Explanation of the columns: 1. The initial target of representation for each surrogate. 2. The number of surrogates for which the initial target can be met/the total number of surrogates. 3. The number of cells selected for revised target levels by ResNet's basic output file. 4. The number of cells selected for the revised target levels by the SITES best file. (Parameters: surrogate absence penalty factor and site cost factor weighted equally; all optional modifiers off; annealing schedule set at 10 6 iterations per run; 50 runs per target level. See text for more details.) 5. The number of surrogates selected in the SITES best file/the total number of surrogates in the dataset. 6. The number of surrogates for which revised targets were met in the SITES best file/the number of surrogates for which the revised target levels were met when ResNet selected only the same number of cells as in the SITES best file (column 4). 7. The number of cells selected in the SITES ‘common set’ (that is, those grouped into the highest frequency category of 50). 8. The number of surrogates which meet revised targets in the SITES ‘common set’/the number of surrogates for which the revised target levels were met when ResNet selected the same number of cells as in the SITES ‘common set’. 9. The number of surrogates in the SITES ‘top set’ (the cells most frequently selected by SITES when it selects as many cells as are required by ResNet to meet the targets) that meet revised target. 10. The number of cells in a solution when: (i) from the SITES summed solution file, the same number of cells is selected as is required by ResNet to meet the target (that is, column 3); and (ii) then ResNet is used to extend the selected set until all targets are met. 11. The number of cells shared by the SITES best files (column 4) and the corresponding ResNet solutions (column 3). 12. The distance between the two solutions mentioned in column 11. 13. The number of cells shared by the SITES ‘common sets’ (column 7) and the corresponding ResNet solution (column 3). 14. The number of cells shared by the SITES ‘top sets’ (column 8) and the corresponding ResNet solution (column 3). 15. The total number of cells contained in the SITES summed solution file (that is, those selected at least once over all 50 runs). 16. The number of cells within the summed solution file required to attain completeness of surrogate coverage (as evaluated by running ResNet with the summed solution file as an input sets). 17. The run time of ResNet. 18. The run time of SITES over the full annealing schedule. 2a Data from Falkland Islands/Islas Malvinas. Results of the direct comparison of SITES and ResNet. SITES was forced to achieve complete surrogate coverage by assigning a severe penalty for incomplete coverage. For more details, see text 1 2 3 4 5 6 7 8 1 61/65 7 7 0.143 1 < 0 : 00 : 01 0 : 12 : 53 5 53/65 26 24 0.200 4 0 : 00 : 01 0 : 13 : 11 10 49/65 53 53 0.132 1 0 : 00 : 01 0 : 13 : 37 15 45/65 78 78 0.064 1 0 : 00 : 01 0 : 13 : 47 20 40/65 100 100 0.050 1 0 : 00 : 02 0 : 13 : 27 2b Data from Falkland Islands/Islas Malvinas. Results of the indirect comparison of SITES and ResNet. For more details, see text 1 2 3 4 5 6 7 8 9 1 61/65 7 7 65/65 65/65 3 57/52 64 5 53/65 26 24 65/65 65/64 14 46/47 65 10 49/65 53 46 61/65 61/58 30 49/49 63 15 45/65 78 67 57/65 57/59 49 50/53 62 20 40/65 100 85 53/65 53/59 61 48/51 59 10 11 12 13 14 15 16 17 18 8 5 0.286 3 5 12 12 < 0 : 00 : 01 0 : 12 : 05 26 20 0.200 12 21 40 40 0 : 00 : 01 0 : 13 : 03 56 41 0.167 30 45 72 74′ 0 : 00 : 01 0 : 13 : 36 81 62 0.145 49 73 92 94′ 0 : 00 : 01 0 : 13 : 53 109 83 0.103 61 91 105 111′ 0 : 00 : 02 0 : 13 : 50 The SITES selections (column 15) were insufficient for complete target representation. The additional cells were selected using ResNet. 3a Data from Texas. Results of the direct comparison of SITES and ResNet. SITES was forced to achieve complete surrogate coverage by assigning a severe penalty for incomplete coverage. For more details, see text 1 2 3 4 5 6 7 8 1 655/655 21 22 0.721 2 0 : 00 : 06 4 : 06 : 53 5 646/655 107 * 109 0.435 12 0 : 00 : 24 4 : 14 : 09 10 641/655 200 ** 199 0.328 19 0 : 00 : 44 4 : 15 : 59 15 632/655 291 292 0.238 38 0 : 01 : 03 4 : 14 : 54 20 619/655 372 372 0.220 22 0 : 01 : 43 4 : 14 : 25 Redundancy checks removed * one cell; ** removed three cells. 3b Data from Texas. Results of the indirect comparison of SITES and ResNet. For more details, see text 1 2 3 4 5 6 7 8 9 1 655/655 21 21 652/655 652/655 1 325/331 638 5 646/655 107 * 98 646/655 646/653 10 322/331 641 10 641/655 200 ** 177 646/655 646/650 47 475/484 642 15 632/655 291 266 635/655 635/652 85 495/531 644 20 619/655 372 359 649/655 649/653 170 566/582 641 10 11 12 13 14 15 16 17 18 29 6 0.714 1 9 222 222 0 : 00 : 06 3 : 37 : 00 126 61 0.404 10 73 445 446 0 : 00 : 24 4 : 03 : 15 227 119 0.369 46 149 549 550′ 0 : 00 : 44 4 : 13 : 46 314 204 0.268 85 247 573 574 0 : 01 : 03 4 : 17 : 09 401 296 0.190 170 319 699 659 0 : 01 : 43 4 : 18 : 51 Redundancy check removed * one cell; ** removed three cells. The SITES selections (column 15) were insufficient for complete target representation. The additional cells were selected using ResNet. 4a Data from Quebec. Results of the direct comparison of SITES and ResNet. SITES was forced to achieve complete surrogate coverage by assigning a severe penalty for incomplete coverage. For more details, see text 1 2 3 4 5 6 7 8 1 387/387 73 75 0.230 5 0 : 00 : 15 1 : 36 : 02 5 240/387 257 * 258 0.076 29 0 : 01 : 11 1 : 39 : 14 10 151/387 376 376 0.027 22 0 : 01 : 40 1 : 44 : 49 15 95/387 458 458 0.031 25 0 : 02 : 06 1 : 40 : 33 20 56/387 523 523 0.027 1 0 : 02 : 17 1 : 42 : 52 * Redundancy checks removed one cell. 4b Data from Quebec. Results of the indirect comparison of SITES and ResNet. For more details, see text 1 2 3 4 5 6 7 8 9 1 387/387 73 62 376/387 376/372 19 254/257 382 5 240/387 257 * 212 352/387 352/354 117 262/265 380 10 151/387 376 295 329/387 329/338 205 283/268 384 15 95/387 458 375 328/387 328/347 273 279/272 382 20 56/387 523 434 330/387 330/359 316 286/293 380 10 11 12 13 14 15 16 17 18 78 57 0.156 19 65 200 111 0 : 00 : 15 1 : 34 : 58 265 200 0.147 117 243 346 281 0 : 01 : 11 1 : 38 : 52 380 287 0.145 205 369 451 393 0 : 01 : 40 1 : 43 : 01 468 362 0.131 273 445 525 484 0 : 02 : 06 1 : 40 : 55 533 418 0.126 316 487 576 554 0 : 02 : 17 1 : 42 : 21 * The redundancy check removed one cell from this set. In the first (direct) comparison for efficiency ( Tables 1a–4a ), the number of cells selected by ResNet (column 3) was occasionally slightly lower than that selected by SITES (column 4) for revised targets of one and five representations, whereas for revised targets of 10, 15 and 20 representations the algorithms were almost equally efficient. Owing to the high penalty for surrogate absence imposed on the SITES algorithm (see above), ResNet and SITES both achieved completeness in surrogate coverage. For all targets, ResNet completed computation in approximately 1% of the time required by SITES (see columns 7, 8) for the datasets from Namibia, the Falklands/Malvinas and Québec. In the case of Texas, SITES took more time to make its selection over ResNet by a factor of at least 250 ( Table 3a , columns 7, 8). Thus, both complex datasets presented severe problems for SITES with respect to the time required to produce a solution. Column 6 records the ordinal number of the run during the annealing procedure in which SITES found an optimal solution. These vary widely (from 1 to 38); that not more than 38 runs were needed in any case may suggest that a smaller number of runs than recommended (50) can be used. However, this increases the risk of not finding a solution during one annealing schedule. Since the number of runs does not seem to make a significant difference in the computation time (column 8), such a reduction of the annealing procedure is not recommended. The distance between the solutions ( Table 1 , column 5) is large when the target is 1 for the two larger datasets (Texas and Québec), but becomes small with bigger targets indicating that similar sets of cells were being selected by both programs. For the smaller datasets (Namibia and Falklands/Malvinas), the distance is consistently small. In the second (indirect) comparison of the two software packages ( Tables 1b−4b ), ResNet consistently selected more cells per target level than the SITES ‘best files’ (columns 3, 4) but satisfied the (revised) targets of representation. However, SITES never achieved complete surrogate coverage except in two cases ( Table 2b , column 5 with targets of 1 and 5); the performance became worse with higher targets (column 5). When ResNet was constrained to select the same number of cells as contained in the SITES ‘best files’ solution, the SITES best file achieved a higher target completeness than the ResNet solution for a target of 1; for all higher target levels, the SITES achieved less completeness (column 6) except in three cases ( Table 2b , column 6 with targets of 1, 5 and 10). Nevertheless, the number of shared cells in the corresponding solutions (column 11) and the distance between the two solution sets ( Table 2 , column 12) indicate that the cell sets selected by both algorithms are highly similar. This is increasingly so for greater target levels, although the increase does not appear to be significant. The cells in the SITES ‘common set’, which were common to all 50 runs ( Tables 1b−4b , column 7) did not yield effective surrogate coverage. This is not surprising because these sets contained so few cells; as is to be expected, these cells were also selected by ResNet (which is why there is a great deal of agreement between columns 7 and 13). When ResNet was constrained to select the same number of cells as in the SITES ‘common set’ there were mixed results on completeness of surrogate coverage. The ResNet solutions also greatly under‐represented the revised targets of representation (column 8). While the SITES ‘top sets’ attained a higher level of surrogate coverage than the SITES ‘common sets’ for each target (compare Tables 1b –4b , columns 9 and 8), these sets were still less effective than ResNet solutions which obtain complete coverage. However, the difference does not appear to be significant (see column 2, column 9). The number of cells shared between the ‘top sets’ and those selected by ResNet are shown in Table 2 , column 14. As a final test, the entirety of the ‘summed solutions’ file was evaluated with respect to completeness of surrogate coverage for each target level. The number of cells contained in the ‘summed solution file’ is shown in Tables 1b−4b , column 15, whereas the number of those actually needed to obtain full surrogate coverage is listed in column 16. When cells were selected from these, using ResNet, to meet targets, the solutions were only slightly larger than those produced by ResNet (column 10). This comparison is important because the SITES ‘summed solutions’ file provides one way to use SITES and ResNet together. Finally, columns 17 and 18 once again underscore how computationally expensive SITES is when compared to ResNet. Discussion The main advantages of rarity‐complementarity based algorithms such as the one implemented in ResNet are computational speed and a guarantee of complete surrogate target coverage. SITES took over an hour to process the Québec dataset and more than four hours to process the Texas dataset (with one exception). Moreover, as will be detailed further below, the speed permits the exploration of a variety of solutions using different initializations or randomizations of the dataset. This is important for three reasons. Starting with a large number of solutions which all satisfy the target set for the biodiversity surrogates: (i) biological considerations that did not enter into the prioritization process, such as the prognosis for the biodiversity contents of a place (their ‘viability’) can be used to refine the solution set; (ii) other considerations such as social and economic cost can be used to find ‘non‐dominated’ solutions (which are not worse than some other on every relevant criterion). These non‐dominated solution sets can then be presented as alternatives to be perused by policy makers (see below). As has been recognized in the literature on reserve design ( Faith, 1995 ; Sarkar ., 2001 ), most conservation projects require the production of several such alternative lists of prioritized places in order to represent the feasibility of trade‐offs between multiple, and often conflicting, constraints on their implementation on the ground; and (iii) it is likely to produce solutions that are, purely by accident, close to the global optimum (see Csuti ., 1987 who show that an exact algorithm does marginally better than a rarity–complementarity‐based algorithm even with a single initialization). Compared to SITES, ResNet is so much faster because its algorithm iteratively adds cells singly, unlike the more global approach in the SITES algorithm which computes the cost equation for an entire set of cells at each step. In many planning scenarios, new plans, for instance, starting with a new initial set of selected areas may have to be devised very rapidly, perhaps during a planning meeting. In such situations, the several hours required by a reasonable annealing schedule in programs such as SITES compromises the utility of these programs. Another advantage of ResNet is that the cell selection is transparent, because the rule used for every selection is explicitly documented. Thus, decision‐makers can know exactly what a new cell is adding to a plan. However, an apparent disadvantage of using ResNet is that the differences in cost or area between cells are not incorporated explicitly into the iterative selection procedure. ResNet can be run using the option of terminating the selection procedure if some maximum permissible cost or area is exceeded. ResNet was written with the view that considerations other than biodiversity should not be reduced to a single parameter along with biodiversity. Multiple criteria, although important, are often incompatible and must be analysed separately. Sarkar (in preparation) generated 32 distinct solutions from the Texas dataset, all satisfying the criterion of meeting biodiversity targets, using ResNet. These ‘feasible’ solutions were then analysed further to find those two solutions which were ‘non‐dominated’ with respect to social and economic costs. Potentially these can now be forwarded to planners for the last stage of selecting a reserve network. Such an extensive analysis was possible only because of the speed with which ResNet produces results; the program was run 100 times to find these solutions in less than 2 hours. The main advantage of the SITES software package is the availability of the large number of optional parameters which allows a user to tailor its cost equation in many ways. Moreover, the assignment of user‐defined weights to selection criteria, insofar as they allow cost considerations to play a role in the iterative procedure, may give SITES the ability to produce solutions that take many more relevant criteria for reserve design than ResNet. However, the problem is that many of these weights can only be assigned arbitrarily. This results in two potential problems: (i) the weights may be misleading; and (ii) it assumes that all the criteria that go into reserve design (biodiversity, social cost, economic cost, etc.) are commensurable on a single scale. (As noted earlier, this approach is rejected intentionally in ResNet.) At the technical level, another disadvantage to using SITES is that its approach to place prioritization requires back‐propagation of error detection to correct weights in the algorithm, and this is a resource‐intensive and imprecise procedure. The set of cells in the ‘summed solution file’ provides one potential way in which ResNet and SITES can be used together. The initial set of cells can be screened once to remove those that are apparently undesirable under all the criteria of interest using SITES in a computationally intensive phase. Then ResNet can be used to achieve completeness of surrogate coverage and efficiency with different initializations in a computationally fast way. This may well be the most effective use of SITES and ResNet together. Since most conservation projects require the production of several alternative lists of prioritized places, we suggest that the two programs could be applied fruitfully together to yield a diversity of conservation scenarios for a given region. These scenarios could then be the basis for the selection of individual plans on socio‐political grounds which can probably never be incorporated into precise algorithms. Acknowledgments We thank Hugh Possingham and an anonymous referee for comments on an earlier draft. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Diversity and Distributions Wiley

Place prioritization for biodiversity reserve network design: a comparison of the SITES and ResNet software packages for coverage and efficiency

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Publisher
Wiley
Copyright
Copyright © 2002 Wiley Subscription Services, Inc., A Wiley Company
ISSN
1366-9516
eISSN
1472-4642
DOI
10.1046/j.1472-4642.2002.00155.x
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See Article on Publisher Site

Abstract

Introduction One of the major tasks of conservation biology is that of selecting reserve networks that are fully representative of the biodiversity of an area. In real‐world scenarios, however, full representation is often impossible, because not all places of biological interest can be conserved. Consequently, the practical problem must be reduced to that of the representation of biodiversity surrogates up to a specified target as efficiently as possible, with efficiency being measured by criteria such as the minimum total area or cost. Places must therefore be prioritized before a final set is selected for reservation or other conservation action. Place prioritization algorithms are becoming a critical tool in the practice of biodiversity conservation. The purpose of this note is to compare the respective performances of two software packages implementing radically different place prioritization algorithms, SITES and ResNet, on four datasets to determine which is preferable for use in systematic conservation planning, or how they may be used together profitably. Both of these packages can be downloaded freely from the web (see Ball, 2000 for the design of SITES; Andelman ., 1999 for downloading SITES; and Aggarwal ., 2000 and Sarkar ., 2002 for downloading ResNet). The algorithms incorporated in these packages, although not the specific packages themselves, have been compared previously by Csuti ., 1997 ; see also Pressey (1997 ). The algorithms implemented in SITES and ResNet are radically different. SITES implements the widely used simulated annealing algorithm ( Kirkpatrick ., 1983 ; Otten ., 1989 ). Using a cost equation which computes the sum of a set of weighted components, the procedure iteratively selects new places, compares resulting changes to the cost equation, and attempts to minimize the total cost. A unique feature of SITES is the large number of optional parameters which can be incorporated into the calculation of the cost, and which require user‐defined weights for the search process. These parameters include a boundary length modifier (which allows the user greater control over the level of adjacency or ‘clumping’ of cells), conservation categories and a penalty factor for under‐representing the target. SITES has been utilized in several conservation projects in the United States, including regions in southern California and the Columbia Plateau ( Andelman & Fagan, 2000 ). ResNet implements a hierarchically controlled, rarity–complementarity‐based selection algorithm ( Margules ., 1988 ; Aggarwal ., 2000 ). The place prioritization procedure is initialized by the selection of a first cell on the basis of rarity, richness or from a user‐defined set of cells. (The last option is relevant if a reserve network is to be built by extension of an existing set of reserves.) ResNet then employs an iterative procedure that selects places on the basis of rarity; then, to break ties between cells with equally rare surrogates, it uses complementarity (that is, it selects the cell that contains the most surrogates not already represented up to the specified target among the cells that have already been chosen). Should ties still remain, ResNet optionally uses adjacency (when a cell adjacent to already selected cells is preferred to one that is not); and finally selects by lexical order (that is, randomly). The user also has the option of incorporating a redundancy check, as well as area and cost constraints. ResNet has been applied to datasets from Québec, Namibia and Islas Malvinas/Falkland Islands ( Sarakinos ., 2001 ; Sarkar ., 2001 ), and has been used in conjunction with the GAP Analysis Project in Texas ( Sarkar ., 2001 ). Although the two algorithms can be compared using a variety of different criteria, the radically disparate strategies used by the two algorithms narrow the ambit of quantitative evaluation. Only completeness in surrogate coverage (meeting the specified target levels), efficiency (doing so while selecting the minimum possible area) and computational time are parameters common to the performance of both algorithms. These were used as the most important indices of comparison in this analysis. Efficiency is particularly important because both SITES and ResNet use heuristic algorithms. While both attempt to produce a solution that meets a specified target, neither guarantees that a better (that is to say, more efficient) solution is not possible. [In other words, both algorithms guarantee that a local optimum solution is obtained; neither guarantees that the global optimum is found. For a discussion of algorithms that find the global optimum, but require much more computational time, and for a discussion of the relative merits of algorithms that are minor variants of the one implemented in ResNet, see Csuti . (1997 ).] Methods Both packages were run on an IBM‐compatible personal computer. The first dataset consists of 1250 data cells (each 0.25 × 0.25 degrees of longitude and latitude) in Namibia containing records of the presence of 33 termite genera (cf. Sarkar ., 2002 for a full description of the dataset). The second dataset consists of 254 cells (each 10 km × 10 km) in the Falkland Islands/Islas Malvinas, containing records of the presence of 65 breeding bird species (cf. Sarkar ., 2002 for a full description of the dataset). The third dataset consists of 1183 cells (each a hexagon of about 649 km 2 produced by the GAP Analysis Project) in Texas containing records of the presence of 655 vertebrate species (cf. Sarkar ., 2001 for a full description of the dataset). The fourth dataset consists of 16 500 data cells (each 0.2 × 0.2 degrees of longitude and latitude) in Québec, containing records of the presence of 387 species of flora and fauna at risk distributed over 709 of the data cells (cf. Sarakinos ., 2001 for a full description of the dataset). Each algorithm was run with the target of representation of surrogates specified at 1, 5, 10, 15 and 20. Only the target of 1 is guaranteed to be met by all surrogates because each surrogate must occur at least once in the dataset. When faced with a surrogate for which the assigned target cannot be met because it does not occur that many times in the dataset, ResNet automatically revises that surrogate's target level to its total presence. We will refer to these target levels of representation as the ‘initial target’ and the ‘revised target’. The first two datasets are computationally simple; they are also far too sparse to be of much use in any realistic policy formulation situation; the last two are much more complex and can potentially be used in practice for reserve network design. (The Québec dataset has already been used by Sarakinos ., 2001 to make policy recommendations.) For each target of representation, SITES produces up to six output files: (i) projectName _best.txt ( ‘best file’), a prioritized list of places containing all cells selected in the single most cost‐effective of the runs; (ii) projectName _ssoln.txt ( ‘summed solution file’); which contains the complete list of cells selected in every run where these cells are grouped into frequency categories depending on the number of runs in which they were selected (thus for our purposes there were 50 frequency categories because there were up to 50 runs — see below); (iii) projectName _mvbest.txt file, which contains information on the extent to which the surrogates selected in the best run meet the targets of representation; (iv) projectName _sum.txt file, which records summary statistics for all runs for a given target; (v) projectName _sen.dat file, which provides a general performance report and information on the algorithm employed; and (vi) finally, a file in which one also has the option of recording the different solutions obtained for each of the runs. The last option was not used for this analysis. The summed solution file is a unique feature of the SITES software package, intended to support the analysis of the robustness of the corresponding ‘best file’. Its potential use in this context will be discussed below. (cf. Andelman ., 1999 for a more detailed explanation of the various data reporting options offered in the SITES software package.) ResNet produces up to five output files. Four of these output files consist of lists of prioritized places. These five files are: (i) for every application of ResNet, the first output file (‘basic output file’) records the solution arrived at without the use of adjacency or a check for redundancy; (ii) if the ‘adjacency’ option is selected, a second output file records the corresponding solution when adjacent cells are given preference as explained above; (iii) if the ‘redundancy’ option is selected, a third output file records the corresponding solution when redundant cells are removed; (iv) if the procedure described in (iii) is modified with a ‘secondary adjacency’ checking option, which results in the retention of redundant cells which are adjacent to a selected nonredundant cell, a fourth output file records the corresponding solution; and (v) finally, for every application of ResNet, a log file is produced that records, for each cell contained in the prioritized list, the rule under which it was selected, and the percentage of surrogates which have cumulatively met the revised target of representation. The ‘adjacency’ and ‘secondary adjacency’ modifications were not used in this analysis. SITES was tested according to the recommended minimum standards (50 runs, 10 6 iterations per run) ( Andelman ., 1999 ). To ensure testing integrity, SITES was also subjected to a longer ‘control run’ using 100 runs and 2 × 10 6 iterations at a target level of 10 to see if increasing the size of the computation improved performance. The result was negligibly different (and, in fact, slightly worse). For all targets of representation, ResNet was initialized by rarity which is known to produce the most efficient results ( Sarkar ., 2002 ), and run with and without the removal of redundant cells. The distance between two solutions was defined as the ratio of the number of unshared selected cells to the total number of selected cells (in both solutions). Thus, if all cells are shared, the distance is 0; if no cells are shared, the distance is 1. In the first comparison, reported in Table 1 , the relative efficiency of the two place prioritization algorithms was compared by setting an initial target of representation for each surrogate and comparing the total number of cells selected by each algorithm in attaining the revised target. ResNet automatically guarantees complete surrogate coverage by the end of a run of the program. In general, SITES does not guarantee such coverage; since it tries to optimize over other parameters besides the presence of surrogates, the program may terminate before complete coverage is attained because other parameters have been optimized sufficiently. For this analysis, complete surrogate coverage was achieved through a trial‐and‐error process of sufficiently weighting the surrogate absence penalty factor of the cost equation to prevent target incompleteness. 1a Data from Namibia. Results of the direct comparison of SITES and ResNet. SITES was forced to achieve complete surrogate coverage by assigning a severe penalty for incomplete coverage. For more details, see text 1 2 3 4 5 6 7 8 1 33/33 6 6 0.333 3 < 0 : 00 : 01 0 : 07 : 05 5 26/33 29 29 0.349 2 < 0 : 00 : 01 0 : 07 : 26 10 23/33 54 54 0.241 6 < 0 : 00 : 01 0 : 07 : 15 15 21/33 73 73 0.068 12 0 : 00 : 01 0 : 07 : 10 20 19/33 85 85 0.141 1 0 : 00 : 02 0 : 07 : 16 Explanation of the columns: 1. The initial target of representation for each surrogate. 2. The number of surrogates for which the initial target can be met/the total number of surrogates. 3. The number of cells selected for revised target levels by ResNet's basic output file. 4. The number of cells selected for revised target levels by the SITES best file. (Parameters: surrogate absence penalty factor sufficiently weighted to ensure target completeness; all optional modifiers off; annealing schedule set at 10 6 iterations per run; 50 runs per target level. See text for more details.) 5. The distance between the solutions. 6. The ordinal number of the SITES run (of the 50 runs in the annealing schedule) that was selected by SITES as the best file. 7. The run time of ResNet. 8. The run time of SITES over the full annealing schedule. In the second comparison, SITES was run with site costs uniformly set equal to each other, and the penalty factor costs for surrogate absence were given equal weights to the cost of a site. In this method of comparison efficiency can no longer be measured simply by comparing the number of cells selected by the algorithms for a given target level. The comparison of efficiency of the two algorithms must be indirect. Three different methods were used. ResNet was asked to terminate after selecting exactly the same number of cells as contained in the SITES ‘best file’ and the number of surrogates for which targets were met by each algorithm were compared. In an effort to establish more wide‐ranging comparisons between the two algorithms, similar tests were conducted with two subsets of the SITES ‘summed solution file’: (i) the group of cells selected in every run for a given target (and thus falling within the highest frequency category, which will be referred to as the ‘common set’); and (ii) the group of cells with the highest frequency measured across all runs for a given target, up to the number of cells selected by ResNet for that target (which will be referred to as the ‘top set’). (In other words, if ResNet selects n cells for a given target, then the ‘top set’ consists of SITES’ n most frequently selected cells.) Results The numerical results are reported in Tables 1a,b −4a,b . In all Tables, initial targets of representation for each run are listed in Column 1. Column 2 lists the number of surrogates that met or exceeded the initial target level. 1b Data from Namibia. Results of the indirect comparison of SITES and ResNet. For more details, see text 1 2 3 4 5 6 7 8 9 1 33/33 6 6 31/33 31/33 2 22/22 32 5 26/33 29 27 27/33 27/31 9 15/11 31 10 23/33 54 44 26/33 26/30 19 16/17 29 15 21/33 73 52 24/33 24/29 18 8/12 29 20 19/33 85 71 26/33 26/31 34 9/20 31 10 11 12 13 14 15 16 17 18 7 4 0.333 2 5 55 56′ < 0 : 00 : 01 0 : 06 : 19 30 18 0.357 9 23 90 90 < 0 : 00 : 01 0 : 06 : 47 61 37 0.245 19 46 133 135′ < 0 : 00 : 01 0 : 06 : 53 81 44 0.296 18 61 135 137′ 0 : 00 : 01 0 : 06 : 56 91 58 0.256 34 73 178 178 0 : 00 : 02 0 : 06 : 57 The SITES selections (column 15) were insufficient for complete target representation. The additional cells were selected using ResNet. Explanation of the columns: 1. The initial target of representation for each surrogate. 2. The number of surrogates for which the initial target can be met/the total number of surrogates. 3. The number of cells selected for revised target levels by ResNet's basic output file. 4. The number of cells selected for the revised target levels by the SITES best file. (Parameters: surrogate absence penalty factor and site cost factor weighted equally; all optional modifiers off; annealing schedule set at 10 6 iterations per run; 50 runs per target level. See text for more details.) 5. The number of surrogates selected in the SITES best file/the total number of surrogates in the dataset. 6. The number of surrogates for which revised targets were met in the SITES best file/the number of surrogates for which the revised target levels were met when ResNet selected only the same number of cells as in the SITES best file (column 4). 7. The number of cells selected in the SITES ‘common set’ (that is, those grouped into the highest frequency category of 50). 8. The number of surrogates which meet revised targets in the SITES ‘common set’/the number of surrogates for which the revised target levels were met when ResNet selected the same number of cells as in the SITES ‘common set’. 9. The number of surrogates in the SITES ‘top set’ (the cells most frequently selected by SITES when it selects as many cells as are required by ResNet to meet the targets) that meet revised target. 10. The number of cells in a solution when: (i) from the SITES summed solution file, the same number of cells is selected as is required by ResNet to meet the target (that is, column 3); and (ii) then ResNet is used to extend the selected set until all targets are met. 11. The number of cells shared by the SITES best files (column 4) and the corresponding ResNet solutions (column 3). 12. The distance between the two solutions mentioned in column 11. 13. The number of cells shared by the SITES ‘common sets’ (column 7) and the corresponding ResNet solution (column 3). 14. The number of cells shared by the SITES ‘top sets’ (column 8) and the corresponding ResNet solution (column 3). 15. The total number of cells contained in the SITES summed solution file (that is, those selected at least once over all 50 runs). 16. The number of cells within the summed solution file required to attain completeness of surrogate coverage (as evaluated by running ResNet with the summed solution file as an input sets). 17. The run time of ResNet. 18. The run time of SITES over the full annealing schedule. 2a Data from Falkland Islands/Islas Malvinas. Results of the direct comparison of SITES and ResNet. SITES was forced to achieve complete surrogate coverage by assigning a severe penalty for incomplete coverage. For more details, see text 1 2 3 4 5 6 7 8 1 61/65 7 7 0.143 1 < 0 : 00 : 01 0 : 12 : 53 5 53/65 26 24 0.200 4 0 : 00 : 01 0 : 13 : 11 10 49/65 53 53 0.132 1 0 : 00 : 01 0 : 13 : 37 15 45/65 78 78 0.064 1 0 : 00 : 01 0 : 13 : 47 20 40/65 100 100 0.050 1 0 : 00 : 02 0 : 13 : 27 2b Data from Falkland Islands/Islas Malvinas. Results of the indirect comparison of SITES and ResNet. For more details, see text 1 2 3 4 5 6 7 8 9 1 61/65 7 7 65/65 65/65 3 57/52 64 5 53/65 26 24 65/65 65/64 14 46/47 65 10 49/65 53 46 61/65 61/58 30 49/49 63 15 45/65 78 67 57/65 57/59 49 50/53 62 20 40/65 100 85 53/65 53/59 61 48/51 59 10 11 12 13 14 15 16 17 18 8 5 0.286 3 5 12 12 < 0 : 00 : 01 0 : 12 : 05 26 20 0.200 12 21 40 40 0 : 00 : 01 0 : 13 : 03 56 41 0.167 30 45 72 74′ 0 : 00 : 01 0 : 13 : 36 81 62 0.145 49 73 92 94′ 0 : 00 : 01 0 : 13 : 53 109 83 0.103 61 91 105 111′ 0 : 00 : 02 0 : 13 : 50 The SITES selections (column 15) were insufficient for complete target representation. The additional cells were selected using ResNet. 3a Data from Texas. Results of the direct comparison of SITES and ResNet. SITES was forced to achieve complete surrogate coverage by assigning a severe penalty for incomplete coverage. For more details, see text 1 2 3 4 5 6 7 8 1 655/655 21 22 0.721 2 0 : 00 : 06 4 : 06 : 53 5 646/655 107 * 109 0.435 12 0 : 00 : 24 4 : 14 : 09 10 641/655 200 ** 199 0.328 19 0 : 00 : 44 4 : 15 : 59 15 632/655 291 292 0.238 38 0 : 01 : 03 4 : 14 : 54 20 619/655 372 372 0.220 22 0 : 01 : 43 4 : 14 : 25 Redundancy checks removed * one cell; ** removed three cells. 3b Data from Texas. Results of the indirect comparison of SITES and ResNet. For more details, see text 1 2 3 4 5 6 7 8 9 1 655/655 21 21 652/655 652/655 1 325/331 638 5 646/655 107 * 98 646/655 646/653 10 322/331 641 10 641/655 200 ** 177 646/655 646/650 47 475/484 642 15 632/655 291 266 635/655 635/652 85 495/531 644 20 619/655 372 359 649/655 649/653 170 566/582 641 10 11 12 13 14 15 16 17 18 29 6 0.714 1 9 222 222 0 : 00 : 06 3 : 37 : 00 126 61 0.404 10 73 445 446 0 : 00 : 24 4 : 03 : 15 227 119 0.369 46 149 549 550′ 0 : 00 : 44 4 : 13 : 46 314 204 0.268 85 247 573 574 0 : 01 : 03 4 : 17 : 09 401 296 0.190 170 319 699 659 0 : 01 : 43 4 : 18 : 51 Redundancy check removed * one cell; ** removed three cells. The SITES selections (column 15) were insufficient for complete target representation. The additional cells were selected using ResNet. 4a Data from Quebec. Results of the direct comparison of SITES and ResNet. SITES was forced to achieve complete surrogate coverage by assigning a severe penalty for incomplete coverage. For more details, see text 1 2 3 4 5 6 7 8 1 387/387 73 75 0.230 5 0 : 00 : 15 1 : 36 : 02 5 240/387 257 * 258 0.076 29 0 : 01 : 11 1 : 39 : 14 10 151/387 376 376 0.027 22 0 : 01 : 40 1 : 44 : 49 15 95/387 458 458 0.031 25 0 : 02 : 06 1 : 40 : 33 20 56/387 523 523 0.027 1 0 : 02 : 17 1 : 42 : 52 * Redundancy checks removed one cell. 4b Data from Quebec. Results of the indirect comparison of SITES and ResNet. For more details, see text 1 2 3 4 5 6 7 8 9 1 387/387 73 62 376/387 376/372 19 254/257 382 5 240/387 257 * 212 352/387 352/354 117 262/265 380 10 151/387 376 295 329/387 329/338 205 283/268 384 15 95/387 458 375 328/387 328/347 273 279/272 382 20 56/387 523 434 330/387 330/359 316 286/293 380 10 11 12 13 14 15 16 17 18 78 57 0.156 19 65 200 111 0 : 00 : 15 1 : 34 : 58 265 200 0.147 117 243 346 281 0 : 01 : 11 1 : 38 : 52 380 287 0.145 205 369 451 393 0 : 01 : 40 1 : 43 : 01 468 362 0.131 273 445 525 484 0 : 02 : 06 1 : 40 : 55 533 418 0.126 316 487 576 554 0 : 02 : 17 1 : 42 : 21 * The redundancy check removed one cell from this set. In the first (direct) comparison for efficiency ( Tables 1a–4a ), the number of cells selected by ResNet (column 3) was occasionally slightly lower than that selected by SITES (column 4) for revised targets of one and five representations, whereas for revised targets of 10, 15 and 20 representations the algorithms were almost equally efficient. Owing to the high penalty for surrogate absence imposed on the SITES algorithm (see above), ResNet and SITES both achieved completeness in surrogate coverage. For all targets, ResNet completed computation in approximately 1% of the time required by SITES (see columns 7, 8) for the datasets from Namibia, the Falklands/Malvinas and Québec. In the case of Texas, SITES took more time to make its selection over ResNet by a factor of at least 250 ( Table 3a , columns 7, 8). Thus, both complex datasets presented severe problems for SITES with respect to the time required to produce a solution. Column 6 records the ordinal number of the run during the annealing procedure in which SITES found an optimal solution. These vary widely (from 1 to 38); that not more than 38 runs were needed in any case may suggest that a smaller number of runs than recommended (50) can be used. However, this increases the risk of not finding a solution during one annealing schedule. Since the number of runs does not seem to make a significant difference in the computation time (column 8), such a reduction of the annealing procedure is not recommended. The distance between the solutions ( Table 1 , column 5) is large when the target is 1 for the two larger datasets (Texas and Québec), but becomes small with bigger targets indicating that similar sets of cells were being selected by both programs. For the smaller datasets (Namibia and Falklands/Malvinas), the distance is consistently small. In the second (indirect) comparison of the two software packages ( Tables 1b−4b ), ResNet consistently selected more cells per target level than the SITES ‘best files’ (columns 3, 4) but satisfied the (revised) targets of representation. However, SITES never achieved complete surrogate coverage except in two cases ( Table 2b , column 5 with targets of 1 and 5); the performance became worse with higher targets (column 5). When ResNet was constrained to select the same number of cells as contained in the SITES ‘best files’ solution, the SITES best file achieved a higher target completeness than the ResNet solution for a target of 1; for all higher target levels, the SITES achieved less completeness (column 6) except in three cases ( Table 2b , column 6 with targets of 1, 5 and 10). Nevertheless, the number of shared cells in the corresponding solutions (column 11) and the distance between the two solution sets ( Table 2 , column 12) indicate that the cell sets selected by both algorithms are highly similar. This is increasingly so for greater target levels, although the increase does not appear to be significant. The cells in the SITES ‘common set’, which were common to all 50 runs ( Tables 1b−4b , column 7) did not yield effective surrogate coverage. This is not surprising because these sets contained so few cells; as is to be expected, these cells were also selected by ResNet (which is why there is a great deal of agreement between columns 7 and 13). When ResNet was constrained to select the same number of cells as in the SITES ‘common set’ there were mixed results on completeness of surrogate coverage. The ResNet solutions also greatly under‐represented the revised targets of representation (column 8). While the SITES ‘top sets’ attained a higher level of surrogate coverage than the SITES ‘common sets’ for each target (compare Tables 1b –4b , columns 9 and 8), these sets were still less effective than ResNet solutions which obtain complete coverage. However, the difference does not appear to be significant (see column 2, column 9). The number of cells shared between the ‘top sets’ and those selected by ResNet are shown in Table 2 , column 14. As a final test, the entirety of the ‘summed solutions’ file was evaluated with respect to completeness of surrogate coverage for each target level. The number of cells contained in the ‘summed solution file’ is shown in Tables 1b−4b , column 15, whereas the number of those actually needed to obtain full surrogate coverage is listed in column 16. When cells were selected from these, using ResNet, to meet targets, the solutions were only slightly larger than those produced by ResNet (column 10). This comparison is important because the SITES ‘summed solutions’ file provides one way to use SITES and ResNet together. Finally, columns 17 and 18 once again underscore how computationally expensive SITES is when compared to ResNet. Discussion The main advantages of rarity‐complementarity based algorithms such as the one implemented in ResNet are computational speed and a guarantee of complete surrogate target coverage. SITES took over an hour to process the Québec dataset and more than four hours to process the Texas dataset (with one exception). Moreover, as will be detailed further below, the speed permits the exploration of a variety of solutions using different initializations or randomizations of the dataset. This is important for three reasons. Starting with a large number of solutions which all satisfy the target set for the biodiversity surrogates: (i) biological considerations that did not enter into the prioritization process, such as the prognosis for the biodiversity contents of a place (their ‘viability’) can be used to refine the solution set; (ii) other considerations such as social and economic cost can be used to find ‘non‐dominated’ solutions (which are not worse than some other on every relevant criterion). These non‐dominated solution sets can then be presented as alternatives to be perused by policy makers (see below). As has been recognized in the literature on reserve design ( Faith, 1995 ; Sarkar ., 2001 ), most conservation projects require the production of several such alternative lists of prioritized places in order to represent the feasibility of trade‐offs between multiple, and often conflicting, constraints on their implementation on the ground; and (iii) it is likely to produce solutions that are, purely by accident, close to the global optimum (see Csuti ., 1987 who show that an exact algorithm does marginally better than a rarity–complementarity‐based algorithm even with a single initialization). Compared to SITES, ResNet is so much faster because its algorithm iteratively adds cells singly, unlike the more global approach in the SITES algorithm which computes the cost equation for an entire set of cells at each step. In many planning scenarios, new plans, for instance, starting with a new initial set of selected areas may have to be devised very rapidly, perhaps during a planning meeting. In such situations, the several hours required by a reasonable annealing schedule in programs such as SITES compromises the utility of these programs. Another advantage of ResNet is that the cell selection is transparent, because the rule used for every selection is explicitly documented. Thus, decision‐makers can know exactly what a new cell is adding to a plan. However, an apparent disadvantage of using ResNet is that the differences in cost or area between cells are not incorporated explicitly into the iterative selection procedure. ResNet can be run using the option of terminating the selection procedure if some maximum permissible cost or area is exceeded. ResNet was written with the view that considerations other than biodiversity should not be reduced to a single parameter along with biodiversity. Multiple criteria, although important, are often incompatible and must be analysed separately. Sarkar (in preparation) generated 32 distinct solutions from the Texas dataset, all satisfying the criterion of meeting biodiversity targets, using ResNet. These ‘feasible’ solutions were then analysed further to find those two solutions which were ‘non‐dominated’ with respect to social and economic costs. Potentially these can now be forwarded to planners for the last stage of selecting a reserve network. Such an extensive analysis was possible only because of the speed with which ResNet produces results; the program was run 100 times to find these solutions in less than 2 hours. The main advantage of the SITES software package is the availability of the large number of optional parameters which allows a user to tailor its cost equation in many ways. Moreover, the assignment of user‐defined weights to selection criteria, insofar as they allow cost considerations to play a role in the iterative procedure, may give SITES the ability to produce solutions that take many more relevant criteria for reserve design than ResNet. However, the problem is that many of these weights can only be assigned arbitrarily. This results in two potential problems: (i) the weights may be misleading; and (ii) it assumes that all the criteria that go into reserve design (biodiversity, social cost, economic cost, etc.) are commensurable on a single scale. (As noted earlier, this approach is rejected intentionally in ResNet.) At the technical level, another disadvantage to using SITES is that its approach to place prioritization requires back‐propagation of error detection to correct weights in the algorithm, and this is a resource‐intensive and imprecise procedure. The set of cells in the ‘summed solution file’ provides one potential way in which ResNet and SITES can be used together. The initial set of cells can be screened once to remove those that are apparently undesirable under all the criteria of interest using SITES in a computationally intensive phase. Then ResNet can be used to achieve completeness of surrogate coverage and efficiency with different initializations in a computationally fast way. This may well be the most effective use of SITES and ResNet together. Since most conservation projects require the production of several alternative lists of prioritized places, we suggest that the two programs could be applied fruitfully together to yield a diversity of conservation scenarios for a given region. These scenarios could then be the basis for the selection of individual plans on socio‐political grounds which can probably never be incorporated into precise algorithms. Acknowledgments We thank Hugh Possingham and an anonymous referee for comments on an earlier draft.

Journal

Diversity and DistributionsWiley

Published: Sep 1, 2002

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