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.     

Systematic reserve design as a dynamic process: F-TRAC and the Florida Forever program

Systematic conservation planning has become an important tool for increasing the efficiency of conservation decisions, but many planning efforts result in static plans that may lose relevance over time. We developed a process whereby planning is integrated into the decision-making process and updated every six months in response to conservation actions. The Florida Forever program is a 10-year, $3 billion land acquisition program expected to acquire approximately 1.25 million acres (607,000 ha) for conservation in Florida through the year 2010. With limited funding and duration, the program needs to be able to efficiently protect the most natural resources for a fixed cost, a situation well suited to a systematic reserve design approach. To inform this program, we conducted an assessment of natural resource conservation needs and developed the Florida Forever Tool for Efficient Resource Acquisition and Conservation (F-TRAC), a systematic reserve design analysis based on a simulated annealing site selection algorithm using Marxan software. The analysis considered conservation needs for a variety of natural resources including species, natural communities, high quality watersheds, wetlands, and sustainable forestry. Each 6-month analysis identifies an efficient portfolio of sites for resource protection, given the amount of land area likely remaining to be acquired by the Florida Forever program. The Spring 2004 model portfolio had a cost threshold of 206,308 ha, met conservation targets for 18 of 32 resource conservation features, and identified approximately 116,000 ha outside of current land acquisition projects. This study also demonstrates the use of reserve design results to evaluate existing and proposed land acquisition projects and inform decision makers; and the evaluation of acquisition trends and program success based on potential achievements as indicated by reserve design analyses.     

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.     

First-best, second-best, and heuristic solutions in conservation reserve site selection

Previous studies which dealt with the conservation reserve site selection problem used either optimization methods, specifically linear integer programming (IP), or heuristic algorithms. The trade-off between computational efficiency versus optimality has been discussed in some articles and conflicting messages were signaled. Although the problem of suboptimality was acknowledged, some authors argued that heuristics may be preferable to exact optimization because IP models are computationally complex and may not be solvable when too many reserve sites are involved. On the other hand, some studies reported that fairly large problems could be solved easily. This paper shows that although the computational complexity argument can be valid for large reserve selection problems, by properly guiding the solver and exploiting the problem structure, formal optimization can deliver second-best (near-optimal) solutions that dominate the greedy heuristic solutions.     

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.     

The importance of in situ site loss in nature reserve selection: Balancing notions of complementarity and robustness

Because the threat of habitat destruction can never be entirely eliminated, there is a legitimate concern that some reserve networks, especially highly complementary ones with minimal species overlap, may be predisposed to severe losses in species representation if one or more core reserve sites are destroyed. In order to address this problem in a systematic way, we propose the use of two different optimization models for designing complementary reserve networks that are also highly robust to possible site losses. Given limited budgets, the first maximizes expected species representation over all possible site loss patterns while the second maximizes a combination of representation given all sites and remaining representation following the worst-case loss of a restricted subset of reserve sites. By incorporating reserve loss in fundamentally different ways, these two models provide a range of options in terms of information requirements, assumptions about risk aversion, and structural complexity. We compare both of these methods to a more standard approach, which completely ignores the inherent risk posed by reserve site loss. Results confirm that significantly more robust solutions can be obtained for a marginal decrease in initial species representation within the reserve system.     

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.     

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.     

Reserve selection with minimum contiguous area restrictions: An application to open space protection planning in suburban Chicago

Conservation efforts often require site or parcel selection strategies that lead to spatially cohesive reserves. Although habitat contiguity is thought to be conducive to the persistence of many sensitive species, availability of funding and suitable land may restrict the extent to which this spatial attribute can be pursued in land management or conservation. Using optimization modeling, we explore the economic and spatial tradeoffs of retaining or restoring grassland habitat in contiguous patches of various sizes near the Chicago metropolitan area. The underlying mathematical construct is the first exact, generalized formulation that directly models spatial contiguity in optimal reserve selection. The construct allows conservation planners to analyze and weigh different minimum contiguous habitat size requirements that are to be used in specific land acquisition or retention projects.