One- and two-objective approaches to an area-constrained habitat reserve site selection problem

We compare several ways to model a habitat reserve site selection problem in which an upper bound on the total area of the selected sites is included. The models are cast as optimization coverage models drawn from the location science literature. Classic covering problems typically include a constraint on the number of sites that can be selected. If potential reserve sites vary in terms of area, acquisition cost or land value, then sites need to be differentiated by these characteristics in the selection process. To address this within the optimization model, the constraint on the number of selected sites can either be replaced by one limiting the total area of the selected sites or area minimization can be incorporated as a second objective. We show that for our dataset and choice of optimization solver average solution time improves considerably when an area-constrained reserve site selection problem is modeled as a two objective rather than a single objective problem with a constraint limiting the total area of the selected sites. Computational experience is reported using a large dataset from Australia.     

Two paths to a suboptimal solution - once more about optimality in reserve selection

Several studies have compared the performances of exact algorithms (integer programming) and heuristic methods in the solution of conservation resource allocation problems, with the conclusion that exact methods are always preferable. Here, I summarize a potentially major deficiency in how the relationship between exact and heuristic methods has been presented: the above comparisons have all been done using relatively simple (linear) maximum coverage or minimum set models that are by definition solvable using integer programming. In contrast, heuristic or meta-heuristic algorithms can be applied to less simplified nonlinear and/or stochastic problems. The focus of this study is two kinds of suboptimality, first-stage suboptimality caused by model simplification and second-stage suboptimality caused by inexact solution. Evidence from comparisons between integer programming and heuristic solution methods suggests a suboptimality level of around 3%-10% for well-chosen heuristics, much depending on the problem and data. There is also largely anecdotal evidence from a few studies that have evaluated results from simplified conservation resource allocation problems using more complicated (nonlinear) models. These studies have found that dropping components such as habitat loss rates or connectivity effects from the model can lead to suboptimality from 5% to 50%. Consequently, I suggest that more attention should be given to two topics, first, how the performance of a conservation plan should be evaluated, and second, what are the consequences of simplifying the ideal conservation resource allocation model? Factors that may lead to relatively complicated problem formulations include connectivity and evaluation of long-term persistence, stochastic habitat loss and availability, species interactions, and distributions that shift due to climate change.     

Optimal reserve selection in a dynamic world

In this paper we present a novel expansion of the problem of optimal reserve site selection over time. We explore a case where areas with valuable biodiversity cannot all be protected immediately due to budget restrictions and there is a probability of species extinction on reserved as well as non-reserved sites. Add to this the risk of land-use conversion facing all non-reserved areas. We furthermore introduce a new type of control by making the planning authorities have the option to sell reserved land on which biodiversity value has decreased. We formulate and solve this problem through stochastic dynamic integer-programming. The current study shows that, due to the dynamic and stochastic nature of biodiversity evolution, the inclusion of a swapping option may increase overall efficiency. Finally, we test a number of decision criteria (heuristics) to investigate alternatives to the cumbersome task of determining the true optimum.     

Incorporating ontogenetic dispersal, ecological processes and conservation zoning into reserve design

Computational methods for marine reserve design are frequently used as decision-support tools for the identification of conservation areas. Most reserve-selection algorithms minimise the cost of the reserve system whilst aiming to meet specified biodiversity objectives. Here, we extend a widely-used selection algorithm, Marxan, to incorporate several important considerations related to biodiversity processes and management. First we relax the scorched earth assumption to allow conservation features in non-reserve zones to contribute explicitly to conservation objectives. To achieve this, we generate conservation targets at landscape scales rather than focusing purely on the representation of features within reserves. Second, we develop the notion of spatial dependencies further to incorporate spatial heterogeneity in the value of individual conservation features such as habitat types. We use the example of ontogenetic migrations of fish from mangroves to coral reefs because it nicely demonstrates how spatial ecological processes generate predictable heterogeneity in habitat value that should be considered in the reserve design process. Lastly, we show how habitat value can be disaggregated into ecosystem processes and services. Using a case study for the Belize Barrier Reef we compare reserve networks generated using our new approach with the results of traditional analyses. Consideration of the contribution of different protection zones, connectivity among habitats and more complex management goals resulted in up to a 52% increase in the mean biomass of commercially and ecologically-important fish species represented in the landscape. Our approach strengthens the ecological basis of reserve-design algorithms and might facilitate the uptake of ecosystem-based management into reserve design.     

Methods for reserve selection: Interior point search

Spatial reserve design concerns the planning of biological reserves for conservation. Typical reserve selection formulations operate on a large set of landscape elements, which could be grid cells or irregular sites, and selection algorithms aim to select the set of sites that achieves biodiversity target levels with minimum cost. This study presents a completely different optimization approach to reserve design. The reserve selection problem can be considerably simplified given the reasonable assumptions that: (i) maximum reserve cost is known; (ii) the approximate number of new reserves to be established is known; (iii) individual reserves need to be spatially contiguous. Further assuming the ability to construct a set of reserves in an efficient and close to optimal manner around designated reserve locations, the reserve selection problem can be turned into a search for a single interior point and area for each reserve. The utility of the proposed method is demonstrated for a data set of seven indicator species living in an conservation priority area in Southern Australia consisting of ca 73,000 selection units, with up to 10,000 cells chosen for inclusion in a reserve network. Requirements (ii) and (iii) above make interior point search computationally very efficient, allowing use with landscapes in the order of millions of elements. The method could also be used with non-linear species distribution models.     

Population viability, ecological processes and biodiversity: Valuing sites for reserve selection

No-take reserves constitute one tool to improve conservation of marine ecosystems, yet criteria for their placement, size, and arrangement remain uncertain. Representation of biodiversity is necessary in reserve planning, but will ultimately fail for conservation unless factors affecting species’ persistence are also incorporated. This study presents an empirical example of the divergent relationships among multiple metrics used to quantify a site’s conservation value, including those that address representation (habitat type, species richness, species diversity), and others that address ecological processes and viability (density and reproductive capacity of a keystone species, in this case, the black chiton, Katharina tunicata). We characterized 10 rocky intertidal sites across two habitats in Barkley Sound, British Columbia, Canada, according to these site metrics. High-richness and high-production sites for K. tunicata were present in both habitat types, but high richness and high-production sites did not overlap. Across sites, species richness ranged from 29 to 46, and adult K. tunicata varied from 6 to 22 individuals m⁻². Adult density was negatively correlated with species richness, a pattern that likely occurs due to post-recruitment growth and survival because no correlation was evident with non-reproductive juveniles. Sites with high adult density also contributed disproportionately greater potential reproductive output (PRO), defined by total gonad mass. PRO varied by a factor of five across sites and was also negatively correlated with species richness. Compromise or relative weighting would be necessary to select valuable sites for conservation because of inherent contradictions among some reserve selection criteria. We suspect that this inconsistency among site metrics will occur more generally in other ecosystems and emphasize the importance of population viability of strongly interacting species.     

Species specific connectivity in reserve-network design using graphs

Systematic conservation planning applications based solely on the presence/absence of a large number of species are not sufficient to guarantee their persistence in highly fragmented landscapes. Recent developments have thus incorporated much desired spatial design considerations, and reserve-network connectivity has received increased attention. Nonetheless, connectivity is often determined without regard to species-specific responses to habitat fragmentation. But species differ in their dispersal ability and habitat requirements, making proximate priority areas necessary for some species, while undesirable for others. We present a novel approach that incorporates species-specific connectivity needs in reserve-network design. Importantly, our method differs from previous approaches in that connectivity is not part of the objective function, but part of the constraints, thus avoiding typical undesirable trade-off that may result in high connectivity for some species but null connectivity for others. We use graphs to describe the dispersal pattern of each species and our goal is to identify minimum sets of reserves with connected sites for each of the species. This is not a trivial problem and we present three algorithms, one heuristic and two integer cutting algorithms that guarantee optimality, based on different 0-1 linear programming formulations. Applications to simulated data show that one of the algorithms that guarantee optimality is superior to the other, although both have limited application due to the number of sites and species they can manage. Remarkably, the heuristic can obtain very satisfactory solutions in short computational times, surpassing the limitations of the exact algorithms.     

Locating and protecting critical reserve sites to minimize expected and worst-case losses

There has been much recent interest in the development of systematic reserve selection methods that are capable of incorporating uncertainty associated with site destruction. This paper makes a contribution to this line of research by presenting two different optimization models for minimizing species losses within a planning region. Given limited acquisition budgets, the first minimizes expected species losses over all possible site loss patterns outside the reserve network while the second minimizes maximum species losses following the worst-case loss of a restricted subset of nonreserve sites. By incorporating the uncertainty of site destruction directly into the decision planning process, these models allow a conservation planner to take a less defensive and more strategic view of reserve selection that seeks to minimize species losses through the targeted acquisition of high-value/high-risk sites. We compare both of these methods to a more standard approach, which simply maximizes within reserve representation without regard for the varied level of threat faced by different sites and species. Results on a realistic dataset show that significant reductions in species losses can be achieved using either of these more intelligent modeling frameworks.     

Accounting for habitat loss rates in sequential reserve selection: Simple methods for large problems

We develop reserve selection methods for maximizing either species retention in the landscape or species representation in reserve areas. These methods are developed in the context of sequential reserve selection, where site acquisition is done over a number of years, yearly budgets are limited and habitat loss may cause some sites to become unavailable during the planning period. The main methodological development of this study is what we call a site-ordering algorithm, which maximizes representation within selected sites at the end of the planning period, while accounting for habitat loss rates in optimization. Like stochastic dynamic programming, which is an approach that guarantees a globally optimal solution, the ordering algorithm generates a sequence in which sites are ideally acquired. As a distinction from stochastic dynamic programming, the ordering is generated via a relatively fast approximate process, which involves hierarchic application of the principle of maximization of marginal gain. In our comparisons, the ordering algorithm emerges a clear winner, it does well in terms of retention and is superior to simple heuristics in terms of representation within reserves. Unlike stochastic dynamic programming, the ordering algorithm is applicable to relatively large problem sizes, with reasonable computation times expected for problems involving thousands of sites.     

Incorporating uncertainty about species’ potential distributions under climate change into the selection of conservation areas with a case study from the Arctic Coastal Plain of Alaska

This analysis presents a conservation planning framework for decisions under uncertainty and applies it to the Arctic Coastal Plain of Alaska. Uncertainty arises from variable distributional shifts of species’ ranges due to climate change. The planning framework consists of a two-stage optimization model that selects a nominal conservation area network in the first stage and evaluates its performance under the climate scenarios in the second stage. The model is applied to eleven at-risk species in Alaska including the threatened Spectacled Eider and Steller’s Eider sea ducks and the polar bear. The 109th United States Congress and 2008 federal budget proposed opening for oil and gas development the “1002 Area” of the Arctic National Wildlife Refuge, which intersects the Plain. This analysis finds that, if Arctic Alaska experiences 1.5 °C of warming by 2040 (as predicted by the Intergovernmental Panel on Climate Change’s A2 scenario), then potential habitat will decrease significantly for eight of these at-risk species, including the polar bear. This analysis also shows that there is synergism between oil and gas development and climate change. For instance, climate change accompanied by no development of the 1002 Area results in an increase of potential habitat for Steller’s Eider. However, if development accompanies climate change, then there is a 20% decrease in that area. Further, this analysis quantifies the tradeoff between development and maintenance of suitable habitat for at-risk species.     

Optimisation in reserve selection procedures—why not?

Linear programming techniques provide an appropriate tool for solving reserve selection problems. Although this has long been known, most published analyses persist in the use of intuitive heuristics, which cannot guarantee the optimality of the solutions found. Here, we dispute two of the most common justifications for the use of intuitive heuristics, namely that optimisation techniques are too slow and cannot solve the most realistic selection problems. By presenting an overview of processing times obtained when solving a diversity of reserve selection problems, we demonstrate that most of those published could almost certainly be solved very quickly by standard optimisation software using current widely available computing technology. Even for those problems that take longer to solve, solutions with low levels of sub-optimality can be obtained quite quickly, presenting a better alternative to intuitive heuristics.     

Designing spatially-explicit reserve networks in the presence of mandatory sites

In the selection of reserve networks there are special sites whose ecologic, strategic or morphologic values dictate their inclusion. The existence of regional rare or confined-distribution species is one among other reasons that often determines the existence of such mandatory sites. Moreover, quite often these mandatory sites are located far apart. Although several methods have been proposed to accommodate structural connectivity in reserve selection, they were not devised to deal specifically with such mandatory sites. Those that encourage aggregation of sites by means of criteria incorporated in the objective function do not seem suitable to acquire consistent connectivity levels in the presence of mandatory sites. Methods that enforce “full connectivity” tend to produce long and narrow solutions, which results in efficiency deficits and biological unsuitability, as they force the selection of more sites of less quality to ensure connectivity. Hence specific methods to select ecological reserves when mandatory sites exist are needed. Here we discuss and propose a 0-1 linear programming model to deal with this issue. The model was applied in two data sets of forest breeding birds and butterflies. Its solutions and computational performances are discussed.     

Soil C and N changes on conservation reserve program lands in the Central Great Plains

The Conservation Reserve Program (CRP) was initiated to reduce water and wind erosion on marginal, highly erodible croplands by removing them from production and planting permanent, soil-conserving vegetation such as grass. We conducted a field study at two sites in Wyoming, USA, in order to quantify changes in soil C and N of marginal croplands seeded to grass, and of native rangeland plowed and cropped to wheat–fallow. Field plots were established on a sandy loam site and a clay loam site on wheat–fallow cropland that had been in production for 60+ years and on adjacent native rangeland. In 1993, 6 years after the study was initiated, the surface soil was sampled in 2.5 cm depth increments, while the subsurface soil was composited as one depth increment. All soil samples were analyzed for total organic C and N, and potential net mineralized C and N. After 60+ years of cultivation, surface soils at both study sites were 18–26% lower (by mass) in total organic C and N than in the A horizons of adjacent native range. Six years after plowing and converting native rangeland to cropland (three wheat–fallow cycles), both total and potential net mineralized C and N in the surface soil had decreased and NO₃–N at all depths had increased to levels found after 60+ years of cultivation. We estimate that mixing of the surface and subsurface soil with tillage accounted for 40–60% of the decrease in surface soil C and N in long-term cultivated fields; in the short-term cultivated fields, mixing with tillage may have accounted for 60–75% of the decrease in C, and 30–60% of the decrease in N. These results emphasize the need to evaluate C and N in the entire soil solum, rather than in just the surface soil, if actual losses of C and N due to cultivation are to be distinguished from vertical redistribution. Five years after reestablishing grass on the sandy loam soil, both total and potential net mineralized C and N in the surface soil had increased to levels equal to or greater than those observed in the A horizon of the native range. On the clay loam soil, however, significant increases in total organic C were observed only in the surface 2.5 cm of N-fertilized grass plots, while total organic N had not significantly increased from levels observed in the long-term cultivated fields.     

Wood-inhabiting macrofungi in Danish beech-forests - conflicting diversity patterns and their implications in a conservation perspective

Macrofungal diversity was investigated on 281 decaying beech trees distributed across 14 forests in Denmark, based on sporocarp inventories. Two aspects of diversity were considered, i.e., species richness per fallen tree and the incidence of red-listed species occurrence per tree. For both diversity measures the effects of both tree and site variables were tested. In total, 319 fungal species were identified, including 28 red-listed. Decay stage and wood volume were identified as key variables influencing species richness as well as red-listed species incidence. Red-listed species, however, showed a preference for more decayed trees than non red-listed species. Further, red-listed species incidence was found to be significantly higher on broken trees, compared to fallen trees with a distinct root-plate, indicating tree death cause to be important for some red-listed species. The relations between diversity measures and site variables were conflicting. Species richness per tree decreased with increasing maximum tree age and dead wood continuity, possibly a consequence of competitive exclusion of unspecialised opportunistic species in old-grown stands. For red-listed species the opposite trend was evident, and it is concluded that forest history may have fundamental effects on the community structure of wood-inhabiting fungi. Accordingly, simple species richness may be a misleading conservation measure if the aim is to conserve the most threatened aspects of forest biodiversity.     

Conservation management for Orthoptera in the Dadia reserve, Greece

The diversity patterns, the ecological structure and the typical species of the orthopteran assemblage in the Dadia reserve are investigated. The reserve was designed to protect the black vulture (Aegypius monachus) and other raptors. A total of 39 orthopteran species were found, including Paranocarodes chopardi, a pamphagid species with very restricted distribution. All species can be represented in a network of six complementary habitats, including open oak woodlands, agricultural fields separated with hedges, humid grasslands, as well as serpentine grasslands. The buffer zone of the reserve is far more important for Orthoptera conservation than the core areas, which host most of the black vulture nests. Management focusing on raptors is in general compatible with conservation of Orthoptera. We suggest the maintenance of forest openings in the buffer zone, the maintenance of forest heterogeneity, the enhancement of periodical livestock grazing, and the use of nine indicator species and Paranocarodes chopardi in the reserve monitoring program.     

High human density in the irreplaceable sites for African vertebrates conservation

The identification of priority sites that ensure the achievement of conservation goals is key to direct conservation efforts. An estimation of the level of vulnerability of each priority area allows the identification of sites that need urgent conservation action. We present a systematic reserve selection for 1654 African mammals and amphibians that uses habitat suitability models as estimates of the area occupied by each species. These are based on the geographic range and habitat preferences for each species, which we collected in the framework of the World Conservation Union (IUCN) Global Amphibian Assessment and IUCN Global Mammal Assessment. Our results showed that in addition to existing protected areas, approximately 2.8 million km² of land is irreplaceable to achieve the protection of 10% of the area occupied by all amphibians and mammals. This figure is higher than previous estimates from other studies. Most irreplaceable sites are located in the sub-Saharan region. More than half (55%) of the irreplaceable sites have high human population density; for only 17% the human population density is low. African amphibians and mammals have therefore to be conserved in densely populated areas where innovative management policies will be required to accommodate conservation successfully.     

Habitat selection and conservation of an endemic spanish lizard Algyroides marchi (reptilia, lacertidae)

We study the habitat selection of Algyroides marchi, a small lizard endemic to the southeastern mountains of the Iberian Peninsula whose populations are concentrated in a few small localities. Three spatial scales of study were used to analyse the different factors affecting the species distribution patterns: regional scale, local scale and within-habitat use of different substrates. The results obtained at these different spatial scales showed a high consistency, suggesting that the same ecological pressures probably acted at different scales. Localities occupied by A. marchi were characterized by high altitude, high geomorphological complexity, northern aspect, high cover of large rocks, and presence of water. Density of A. marchi in a favourable locality was 213 adult-subadult lizards/ha. Abundance and use of space of A. marchi (at local and individual levels) were directly associated with extent of water (streams and small pools) and the presence of large rocks, and inversely with hours of direct solar radiation and cover of small stones and vegetation. Considering the habitat selection of A. marchi and the management practices within its geographical range, potential risks for the conservation of the species are identified.     

Within-site habitat configuration in reserve design: A case study with a peatland bird

This study assesses the effects of considering within-site habitat configuration when designing reserve networks. This attribute takes all its importance in situations where the long-term integrity of (within-site) habitat patches cannot be preserved without protecting their surrounding environment. We addressed this issue through the concrete problem of selecting a reserve network of natural peatlands in southern Québec, Canada. We used a reserve-selection algorithm that minimized the total number of peatlands to include within networks. The algorithm was constrained to include peatlands containing habitat patches that met specific size thresholds. Five habitat-clustering thresholds were used to set the eligibility of each site to the selection process. The resulting reserve networks were evaluated according to their representation efficiency and to the expected consequences for the Palm Warbler (Dendroica palmarum), an area and isolation-sensitive bird restricted to peatlands in southern Québec.Constraining the algorithm to include peatlands showing increasingly larger patches of habitats led to larger networks, both in terms of area and number of sites, and to networks composed of smaller sites. These effects increased with the representation target (i.e., the % of each habitat preserved). With respect to the Palm Warbler, selecting peatlands with larger patches of habitats had only an indirect effect on its site-occupancy pattern. Indeed, despite the fact that the probability of occurrence of the warbler was negatively correlated with the size of habitat patches, the habitat-clustering threshold influenced the incidence of the warbler mainly via its effect on the physical attributes of the selected networks - including the area, isolation level, and the number of selected sites. Because increasing the habitat-clustering threshold led indirectly to a greater regional availability of prime breeding habitats for the Palm Warbler, it mitigated the severe negative impact of an hypothetical alteration or destruction of non-selected peatlands. Our study thus emphasizes the importance of determining how the different factors describing within-site configuration are correlated with other intrinsic characteristics of the sites available to the selection process before opting for a site-selection strategy.     

Effect of different sampling schemes on the spatial placement of conservation reserves in Utah, USA

We evaluated the effect of three different sampling schemes used to organize spatially explicit biological information had on the spatial placement of conservation reserves in Utah, USA. The three sampling schemes consisted of a hexagon representation developed by the EPA/EMAP program (statistical basis), watershed boundaries (ecological), and the current county boundaries of Utah (socio-political). Four decision criteria were used to estimate effects, including amount of area, length of edge, lowest number of contiguous reserves, and greatest number of terrestrial vertebrate species covered. A fifth evaluation criterion was the effect each sampling scheme had on the ability of the modeled conservation reserves to cover the six major ecoregions found in Utah. Of the three sampling schemes, county boundaries covered the greatest number of species, but also created the longest length of edge and greatest number of reserves. Watersheds maximized species coverage using the least amount of area. Hexagons and watersheds provide the least amount of edge and fewest number of reserves. Although there were differences in area, edge and number of reserves among the sampling schemes, all three schemes covered all the major ecoregions in Utah and their inclusive biodiversity.