### Introduction

- Top of page
- Summary
- Introduction
- Materials and methods
- Results
- Discussion
- Acknowledgements
- Reference

Reserve selection approaches in common use seek to identify minimum sets of areas (minimum total area or minimum number of sites) that represent, say, at least one population of each target species (or a percentage of its original extent) in the region of interest (Csuti *et al*. 1997; Pressey *et al*. 1993; Margules, Nicholls & Usher 1994; Pressey, Possingham & Margules 1996). Alternative approaches seek to identify reserve networks that increase representation of biodiversity for a given cost or area (Church, Stoms & Davis 1996). All these approaches often use a single snapshot of presence–absence data and imply that species would persist within reserves if represented. Nonetheless, some studies have attempted to refine the assumptions of the most simplistic reserve selection approaches by incorporating criteria for persistence within reserve selection procedures. For instance, some studies have used thresholds to define the minimum size of selection units, or used abundance data instead of presence–absence data (reviewed by Cabeza & Moilanen 2001). More recent approaches have used the local probability of occurrence of target species as a surrogate for species local persistence (Araújo & Williams 2000; Williams & Araújo 2000; Araújo, Williams & Fuller 2002) while others have considered the spatial locations of the reserves, implicitly acknowledging the role of spatial population dynamics on species persistence (Nicholls & Margules 1993; Possingham *et al*. 1993; Possingham, Ball & Andelman 2000).

#### probability of occurrence

Reserve selection methods have been adapted to deal with estimates of probability of occurrence (Williams & Araújo 2000; Williams & Araújo 2002 and references therein for an introduction to the use of probability of occurrence in reserve selection). Estimates of probability of persistence are obtained by modelling current species probability of occurrence from habitat quality (ability to survive) and dispersal (ability to colonize) factors. Probability of occurrence is generally expected to correlate to probability of persistence, at least for relatively short time periods, as shown for breeding birds in Great Britain (Araújo, Williams & Fuller 2002). However, the correspondence between probability of occurrence and probability of persistence within reserves depends on several additional factors. For example, the reported tendency of areas of high biodiversity to coincide with areas of high human pressure (Araújo 2003) may cause selected conservation areas to face greater challenges than expected (Araújo, Williams & Turner 2002). Furthermore, the factors used to calculate probability of occurrence are assumed to remain stable once the reserve system is established. However, in areas where competition for land is high, the pressure on non-selected sites will be greater than in designated conservation areas. Habitat fragmentation may follow and several studies have reported its negative consequences, from reduced migration success to several kinds of edge effects (Yahner 1988; Saunders, Hobbs & Margules 1991; Andrén 1994; Andrén 1997). Consequently, developments outside the reserves might have implications for the future probability of occurrence of the species in the reserve (Woodroffe & Ginsberg 1998). Hence, ideally, probability of occurrence should be estimated dynamically, in relation to the selected sites and to the consequent threats to biodiversity in and around the reserves.

#### spatial reserve design

Another way to address persistence within reserve selection procedures is to select reserves that are close together (Nicholls & Margules 1993; Possingham *et al*. 1993; Possingham, Ball & Andelman 2000; Leslie *et al*. 2003). Most minimum set approaches do not account explicitly for the spatial relationships among the sites selected and, therefore, the resulting reserve system is likely to be overdispersed. Reserves with high edge-to-area ratios will suffer from edge effects, including vulnerability to invasions, increased predation pressure and negative effects from abiotic factors like humidity and wind, etc. (Andrén & Angelstam 1988; Yahner 1988; Saunders, Hobbs & Margules 1991). From a metapopulation perspective, having a set of sites close together will enhance the regional persistence of a species by facilitating dispersal and allowing recolonization of unoccupied but suitable sites (Adler & Nürnberger 1994; Hanski 1999). From an economic perspective, boundaries need to be maintained, and longer boundaries often mean more neighbours and more cost. Nicholls & Margules (1993) and Possingham, Ball & Andelman (2000) introduced optimization methods that promote the clustering of reserves (i) by including a rule that chooses sites close together when breaking ties in iterative algorithms (Nicholls & Margules 1993) and (ii) by minimizing a linear combination of reserve network area and boundary length (Possingham, Ball & Andelman 2000). The level of aggregation of reserves achieved by the former method is low because compact spatial structure is not a primary aim of the algorithm.

#### integrating spatial constraints with high probabilities of occurrence

In this study we used models for the probability of occurrence coupled with spatial reserve design in order to select a compact network of reserves that represents all target species with a chosen target probability. By adding spatial constraints we can obtain more compact reserves. Consequently the potential negative effects of losing non-selected sites on the probabilities of occurrence are minimized.

Including additional constraints on the reserve selection process usually increases the cost of the solution in terms of the number of sites or the total area. For instance, Possingham, Ball & Andelman (2000) have shown how clustered reserve networks tend to need a larger number of reserves. When the largest weight for clustering was used, a completely clustered network of reserves was achieved but five times more sites were needed. The best balance between total area and clustering can be found by comparing the increase of area vs. decrease in boundary length when using different weights for the clustering. An intermediate value for the weighting can be chosen so that, even though the area is increasing, the boundary length is decreasing at a greater rate (Possingham, Ball & Andelman 2000).

We applied the new reserve selection approach to a data set of 26 species of butterflies from the 35-km^{2} Creuddyn Peninsula in north Wales. The distribution of these species has been mapped accurately on a 500-m grid throughout the landscape, and their densities have been measured on transect counts in 16 major habitat types within the peninsula. Therefore, we have detailed and accurate information on patterns of abundance, habitat association and distribution for each of the species, as well as some knowledge of the dispersal capacities of each species (Cowley *et al*. 2000, 2001a,b). Furthermore, logistic regression models applied to the distributions of these species have correctly classified between 58% and 98% (mean 83%) of presences and absences, based on the distribution of 16 habitat types (Cowley *et al*. 2000). The Creuddyn Peninsula is also an area of high conservation value, containing two endemic butterfly races restricted to the peninsula, as well as numerous other species that are more widespread or abundant in the study area than elsewhere in north Wales.

### Results

- Top of page
- Summary
- Introduction
- Materials and methods
- Results
- Discussion
- Acknowledgements
- Reference

Both algorithms selected clustered reserves when the boundary length penalty (*b*) was larger than zero, i.e. when the cost of the boundary length was considered. In general, the boundary length of the solutions decreases when increasing *b* until it converges to the minimum value found by the particular algorithm at the particular probability target (Fig. 2). As expected, the sizes of the reserve systems, in terms of number of sites and boundary length, were larger for larger probability targets. By increasing the probability target we can observe how the solutions might shift from needing only one cluster, to two clusters and again to one cluster (Fig. 3)

The smallest solutions are generally found by the backwards algorithm but it varies for different scenarios. The backwards algorithm seems to be more efficient and consistent at intermediate *b* values (Figs 2–4) and there is a difference in the number of clusters in the final solution.

For this particular data set, clustering can be achieved at very little cost (in terms of number of sites). Across all solutions, the average increase in the number of sites was 8% while the average decrease of boundary length was 53% (Fig. 5). The backwards algorithm appears to achieve major reductions in boundary length with smaller increases in the number of sites (average increase in number of sites was 0·5%, average decrease in boundary length was 55%). This is in agreement with the fact that the backwards algorithm is not forced to select only one large cluster.

These results are expected to be highly dependent on the data. Other data sets might require larger number of sites to achieve clustered solutions (Possingham, Ball & Andelman 2000). Nevertheless, comparing the rates of increase in the number of sites with the rates of decrease in boundary length, an intermediate point (corresponding to an intermediate value of *b*) can be chosen that satisfies both the cost and the clustering for the particular conservation problem. The choice of the level of cost (area) and clustering is likely to be a heuristic choice involving political and economical criteria.

For this particular case study the solutions for mid values of *b* seem to be the most pragmatic. The advantage of the algorithm is the ability to include both habitat quality (i.e. probability of occurrence) and spatial configuration. Intermediate *b* values do not give too much weight to either of the components. High values of *b* produce good solutions in terms of species persistence; however, many of the selected sites that link the clusters were already of low quality, and their inclusion in the final selection might not increase the probability of species persistence, especially for high probability targets.

Using filtered data reduces the flexibility in the choice of cells to be selected (sites that had low probabilities in the non-filtered data set do not contribute at all for particular species in the filtered data set). The final solutions, although clustered, have larger boundary lengths than the solutions for the unfiltered data set.

Also, it will be possible to achieve better levels of protection for critical or rare species at lower expenditure (i.e. relatively few cells) if information about the conservation priorities of species (Fig. 6) is available. For instance, a large probability target (0·9999 and 0·999) and a clustered solution can be achieved for particular species (endemic and regionally significant) without increasing the area needed to represent all species at a smaller probability target (0·95) (Fig. 4, *T*= 0·95; Fig. 6b).

### Discussion

- Top of page
- Summary
- Introduction
- Materials and methods
- Results
- Discussion
- Acknowledgements
- Reference

In this study we bring together two different reserve selection approaches that implicitly deal with improving the chances of species persistence in reserve networks. (i) Using probabilities of occurrence, predicted from habitat models, to choose a set of areas that together represent each species with a targeted probability (probability of having at least one occurrence of species *j* in any site) (Araújo & Williams 2000; Williams & Araújo 2001; Williams & Araújo 2002). (ii) Clustering of the reserves by minimizing the boundary length of the reserve system in the optimization process (Possingham *et al*. 1993; Possingham, Ball & Andelman 2000).

Araújo, Williams & Fuller (2002) have shown how the probability of extinction for a set of species can be reduced if reserve areas are selected to maximize the probability of occurrence of those species at the present time. Using data on passerine birds for two time periods, 20 years apart, they showed that the networks selected with the probability method improved the persistence of the species in the reserve system (i.e. 100% of the species were still represented in the second time period) compared with the performance of areas selected with classical single representation algorithms. Unlike the present study, the estimates of occurrence in Araújo, Williams & Fuller (2002) were based on a contagion measure, i.e. for a species in a site the probability of occurrence is higher the larger the number of occupied neighbours. This means that, if the selected reserves include areas of high probability but do not include the neighbours, there is no guarantee that the probabilities of persistence in the reserves are still high following habitat loss in the non-selected neighbouring cells.

Cabeza & Moilanen (2003) simulated species’ spatial population dynamics and showed that when reserves are selected far apart and manage to represent each species only one or a few times, species’ extinctions may be expected. The chances of species extinction in such a reserve system are even greater if the habitat surrounding the reserve is lost. When the group of reserves was selected as a cluster, the number of extinctions in the presence of habitat loss was much smaller (Cabeza & Moilanen 2003).

By incorporating spatial constraints in the selection process, the chances that the probabilities of occurrence remain more or less stable are larger, as effects of habitat fragmentation are reduced. Interestingly, as shown in this study, clustering of reserves may be achieved at a low cost (in terms of total area or number of sites). Therefore, we suggest that spatial constraints should be taken into account in reserve network design. The costs (in terms of increased total area or number of sites) of minimizing the boundary length of the reserve system should be evaluated and, whenever affordable, clustering of reserves should be favoured.

Nonetheless, there might also be reasons to avoid clustering. In situations where catastrophes can impact large areas and cause local extinctions, it may be less risky to choose reserves in at least two or three separate places, rather than having them all clustered together (Hess 1996; Lei & Hanski 1997). However, if reserves are widely separated from each other, they should be large enough to allow species to persist as independent populations.

The question of whether to use exact algorithms or heuristic algorithms in the field of reserve design has been a topic of major discussion (Cocks & Baird 1989; Church, Stoms & Davis 1996; Pressey, Possingham & Margules 1996; Pressey, Possingham & Day 1997; Cabeza & Moilanen 2001; Rodrigues & Gaston 2002). Exact algorithms may be theoretically preferred because they can be guaranteed to find an exact optimal solution (Cabeza & Moilanen 2001; Underhill 1994; Camm *et al*. 1996), but in practical applications heuristics are preferred for their clarity and speed, allowing interactive reserve selection actions. Also, exact algorithms cannot be easily adapted to solve all reserve selection problems. The problem addressed here is one of these examples: it is a highly non-linear problem because of the way combined probabilities are calculated and because the cost of adding a site to the reserve system depends on which other sites are already protected, and on the spatial relationships between candidate sites and those already selected.

We have introduced in this paper a new iterative heuristic algorithm that works backwards in respect to commonly used algorithms in reserve selection approaches. Common iterative algorithms select a set of sites, adding, at each iteration, the best site to the solution. The backwards algorithm, instead, starts by including all sites in the solution, and then removes one site at each iteration, until achieving the solution given the constraints. The forwards algorithm tends to select a single large cluster, whereas the backwards algorithm usually selects different clusters. This is because starting a new cluster is much more costly for the forwards algorithm than adding sites to the current selected cluster. Instead, the backwards algorithm starts by throwing away ‘bad’ patches, creating different clusters from the beginning of the iterative process, and then keeps on reducing the size of these clusters as long as the target is fulfilled for all species.

For the problem and data set used in this study, the backwards algorithm appears to be more consistent and yields, in general, better results than the forwards algorithm. However, the backwards algorithm does not guarantee to find the exact optimal solution. When the efficiency of the results is an important feature, numerical stochastic global search methods can be used (e.g. simulated annealing; Possingham, Ball & Andelman 2000; Leslie *et al*. 2003). In any case, when an exact algorithm cannot be used because of the characteristics of the problem, we recommend the use of more than one heuristic to increase confidence in the results.

A more complete consideration of the effects of spatial configuration on species persistence would require a more explicit consideration of spatial population dynamics. This can only be done if a habitat model (or a metapopulation model) with an explicit spatial component (e.g. species-specific dispersal ability) can be parameterized (Moilanen & Cabeza 2002; Cabeza 2003). In cases where such information is not available the reserve selection approach presented in this paper, which selects high-quality sites in an aggregated manner, increases the potential for long-term persistence of species in the reserve network.

Other issues that could be further considered in the context of the present approach to reserve selection include improved landscape modelling, irreplaceability of sites, uncertainty analysis and scheduling of conservation action.