Applying mathematical programming to reserve selection

During the last 10–15 years heuristic methods have been developed for problems in optimal reserve selection. Unfortunately, there is no guarantee that heuristics will find optimal solutions. In recognizing this limitation, analysts have formulated reserve selection problems as set covering problems, for which matrix reduction and integer (0/1) programming can be used to find optimal solutions. In this paper we restate the set covering formulation and review solution techniques. A new 0/1 programming model, which is a generalization of the set covering model, is then presented and applied to a hypothetical reserve selection problem. Objectives of minimizing the number of sites selected and maximizing the number of species represented are addressed. Solutions which characterize the tradeoffs between these objectives provide a rich set of information for planners and decision makers. Applications of mathematical programming to related problems in land use planning and forestry are also discussed.     

Analysis of the Threshold and Expected Coverage Approaches to the Probabilistic Reserve Site Selection Problem

Two approaches to formulating the reserve site selection problem when species occurrence data is probabilistic were solved for terrestrial vertebrates in a small set of potential reserve sites in Oregon. The expected coverage approach, which maximizes the sum of the occurrence probabilities, yielded solutions that covered more species on average in Monte Carlo simulations than the threshold approach, which maximizes the number of species for which the occurrence probability exceeds some threshold.     

Efficiency,costs and trade-offs in marine reserve system design

With marine biodiversity conservation the primary goal for reserve planning initiatives, a site's conservation potential is typically evaluated on the basis of the biological and physical features it contains. By comparison, socio-economic information is seldom a formal consideration of the reserve system design problem and generally limited to an assessment of threats, vulnerability or compatibility with surrounding uses. This is perhaps surprising given broad recognition that the success of reserve establishment is highly dependent on widespread stakeholder and community support. Using information on the spatial distribution and intensity of commercial rock lobster catch in South Australia, we demonstrate the capacity of mathematical reserve selection procedures to integrate socio-economic and biophysical information for marine reserve system design. Analyses of trade-offs highlight the opportunities to design representative, efficient and practical marine reserve systems that minimise potential loss to commercial users. We found that the objective of minimising the areal extent of the reserve system was barely compromised by incorporating economic design constraints. With a small increase in area (<3%) and boundary length (<10%), the economic impact of marine reserves on the commercial rock lobster fishery was reduced by more than a third. We considered also how a reserve planner might prioritise conservation areas using information on a planning units selection frequency. We found that selection frequencies alone were not a reliable guide for the selection of marine reserve systems, but could be used with approaches such as summed irreplaceability to direct conservation effort for efficient marine reserve design.     

Novel operations research methods for efficiently determining irreplaceable sites for conservation

We examine the irreplaceability of sites in the context of the species set covering problem and the maximal covering species problem. We show that a succession of 0-1 programming problems can be solved to quickly determine the set of irreplaceable sites. For the widely available Oregon data set, we find a general lack of trend in the number of irreplaceable sites with the number of sites available for selection used. Moreover, we observe that irreplaceability at one level of resource may not be a predictor of irreplaceability at a higher or a lower level of resource. Finally, we investigate the economic value of irreplaceable sites by trial removals of those sites. This paper is dedicated to the memory of Dr. Charles S. ReVelle.     

Counterpart Models in Facility Location Science and Reserve Selection Science

Five classes of zero–one programming models for discrete facility location problems are compared to counterpart models for the selection of conservation reserves. The basic problem of siting facilities to cover demand for services is analogous to the problem of selecting reserves to support species diversity. The classes of models include the set covering and maximal covering models, as well as models for backup and redundant coverage. Issues of reliability and uncertainty are addressed by chance constrained covering models and maximal expected covering models. Exact and heuristic solution approaches are discussed. Multi-objective and economic issues are considered.     

Representational success: A new paradigm for achieving species protection by reserve site selection

Models for designing habitat reserve networks have focused on minimizing the number of sites necessary to cover each species one or more times. A solution to this problem is usually one from among a large number of alternative optimal configurations of sites. This paper develops an iterative method for building reserve networks that produces an optimal solution to the species set covering problem (SSCP) and also maximizes the number of species covered two or more times, three or more times, and so on, conditional on the solution to the previous iteration. We refer to this as representational success. Thus, a pareto optimal species set covering is achieved that is preferable to an arbitrary optimal solution to the SSCP.     

The SITES reserve selection system: A critical review

Numerous models have been put forth to help with the growing demand for the establishment of biodiversity reserves. One site selection model that has been used in several recent studies is SITES [S.J. Andelman, I. Ball, F.W. Davis and D.M. Stoms, SITES V 1.0: an analytical toolbox for designing ecoregional conservation portfolios, Unpublished manual prepared for the nature conservancy, 1999, 1–43. (available at )]. SITES includes two heuristic solvers: based on Greedy and Simulated Annealing. We discuss the formulation of the SITES model, present a new formulation for that problem, and solve a number of test problems optimally using off-the-shelf software. We compared our optimal results with the SITES Simulated Annealing heuristic and found that SITES frequently returns significantly suboptimal solutions. Our results add further support to the argument, started by Underhill [L.G. Underhill, Optimal and suboptimal reserve selection algorithms, Biol. Conserv. 70 (1994) 85–87], continuing through Rodrigues and Gaston [A.S.L. Rodrigues and K.J. Gaston, Optimization in reserve selection procedures – why not?, Biol. Conserv. 107 (2002) 123–129], for greater integration of optimal methods in the reserve design/selection literature.     

Marine Reserve Design with Ocean Currents and Multiple Objectives

There is a growing tendency to consider marine reserves as a management and conservation tool. We investigate a spatial bio-economic model to determine fishery profits under conservation efforts. Rather than imposing a marine reserve on our model, we ask, “When and where should a marine reserve be implemented ?” For one-dimensional habitat, we determine conditions under which marine reserves emerge as a part of the optimal policy. Depending upon the size of the habitat, the optimal strategy is either to avoid fishing or to fish at maximum rate. The effect of ocean currents is analyzed through numerical simulations. We find that in the presence of strong currents, a marine reserve may become ineffective. If the currents are at low rate, a marine reserve could emerge as a variable management tool.     

Integrating Land Market Feedbacks into Conservation Planning—A Mathematical Programming Approach

Nature reserves are often designated ad hoc. Despite increasing conservation efforts, loss of biodiversity is still accelerating. Considering land scarcity and demand for alternative uses, efficiency in conservation strongly correlates with efficiency in land allocation. Systematic conservation planning can effectively prioritize conservation activities. Previous studies minimize opportunity costs for given conservation targets. However, these studies assume constant marginal costs of habitat protection. We extend this cost minimization approach by also considering a dynamic representation of marginal costs. The more land is allocated to nature reserves, the higher are opportunity costs, i.e., costs of forgone agricultural production. This increase in costs results from changes in the prices of agricultural commodities. We employ a deterministic, spatially explicit mathematical optimization model to allocate species habitats by minimizing opportunity costs for setting aside land for conservation purposes. The model is designed as a mixed integer programming problem and solved with GAMS/CPLEX. Our results show the need for integrating land market feedbacks into conservation planning. We find that ignoring land rent adjustments can lead to highly cost-ineffective solutions in reserve selection.     

Limitations of habitats as biodiversity surrogates for conservation planning in estuaries

Increasing pressures on global biodiversity and lack of data on the number and abundance of species have motivated conservation planners and researchers to use more readily available information as proxies or surrogates for biodiversity. “Habitat” is one of the most frequently used surrogates but its assumed value in marine conservation planning is not often tested. The present study developed and tested three alternative habitat classification schemes of increasing complexity for a large estuary in south-east Australia and tested their effectiveness in predicting spatial variation in macroinvertebrate biodiversity and selecting estuarine protected areas to represent species. The three habitat classification schemes were: (1) broad-scale habitats (e.g., mangroves and seagrass), (2) subdivision of each broad-scale habitat by a suite of environmental variables that varied significantly throughout the estuary, and (3) subdivision of each broad-scale habitat by the subset of environmental variables that best explained spatial variation in macroinvertebrate biodiversity. Macroinvertebrate assemblages differed significantly among the habitats in each classification scheme. For each classification scheme, habitat richness was significantly correlated with species richness, total density of macroinvertebrates, assemblage dissimilarity, and summed irreplaceability. However, in a reserve selection process designed to represent examples of each habitat, no habitat classification scheme represented species significantly better than a random selection of sites. Habitat classification schemes may represent variation in estuarine biodiversity; however, the results of this study suggest they are inefficient in designing representative networks of estuarine protected areas.     

Spatial attributes and reserve design models: A review

A variety of decision models have been formulated for the optimal selection of nature reserve sites to represent a diversity of species or other conservation features. Unfortunately, many of these models tend to select scattered sites and do not take into account important spatial attributes such as reserve shape and connectivity. These attributes are likely to affect not only the persistence of species but also the general ecological functioning of reserves and the ability to effectively manage them. In response, researchers have begun formulating reserve design models that improve spatial coherence by controlling spatial attributes. We review the spatial attributes that are thought to be important in reserve design and also review reserve design models that incorporate one or more of these attributes. Spatial modeling issues, computational issues, and the trade-offs among competing optimization objectives are discussed. Directions for future research are identified. Ultimately, an argument is made for the development of models that capture the dynamic interdependencies among sites and species populations and thus incorporate the reasons why spatial attributes are important.     

Economic and Spatial Impacts of an Existing Reserve Network on Future Augmentation

An optimization model for land reservation was developed that explicitly selects parcels in the most compact or contiguous manner possible while meeting habitat requirements and a budget limitation. The model was used to compare the effects of an existing reserve network on future parcel spatial locations and total cost. Using habitat and land value data from Josephine County, Oregon, it was found that a system of existing reserves created by various policies and overseen by different agencies can decrease future reserve compactness and contiguity, and increase total cost. This work suggests that coordinated planning can result in more efficient conservation efforts for less cost.     

Theoretical and practical criteria for the selection of ecosystem monitoring plots in Swiss forests

A great deal of attention has been paid to the selection of nature reserves. These are important from a conservation viewpoint but, for long-term evaluations, it is important to monitor ecosystems. The need for long-term monitoring plots has been recognized for some time in forest ecology. Of the natural ecosystems, forests are some of the most difficult to monitor because of the time-scales involved in the life-spans of the dominant organisms (100 1000 years). The selection of long-term forest ecosystem monitoring plots is a critical process involving decisions that need to remain valid for many years. Traditional sampling theory suggests that some form of systematic or random sampling may be appropriate, but this is usually inappropriate for the selection of ecosystem monitoring plots. Instead, the selection of plots more closely resembles some of the procedures that are used in the selection of nature reserves. In Switzerland, a monitoring programme has been established which uses a number of criteria for the selection of sites. These include site homogeneity, the abundance and sensitivity of the plant communities to change and the presence of pre-existing data series or monitoring equipment. In addition, the human factor is incorporated by selecting sites from throughout the country, with the willingness of the local forest managers to help with the project being an important factor influencing the final choice of plots. In contrast to most inventories, statistical representativeness is not a requirement for the programme, as the plots are treated as a series of case studies.     

Designing Connected and Compact Nature Reserves

It is generally accepted that for many species, the ability to get around a reserve promotes their long-term persistence. Here, we measure the ease with which species can move by two spatial criteria: (i) the connectivity of the reserve, that is to say, the possibility to go through the whole reserve without leaving it, and (ii) the compactness of the reserve, that is to say, the remoteness of the sites in relation to each other, the distance between two sites being measured by the shortest distance to travel to get from one site to another without leaving the reserve. To protect the reserve of external disturbances, we also impose a connectivity constraint for the area outside the reserve. This article presents a method based on integer linear programming to define connected and compact reserves. Computational experiments carried out on artificial instances with 400 sites and 100 species are presented to illustrate the effectiveness of the approach.     

Coupling GIS and mulitvariate approaches to reference site selection for wadeable stream monitoring

Geographic Information System (GIS) was used to identify potential reference sites for wadeable stream monitoring, and multivariate analyses were applied to test whether invertebrate communities reflected a priori spatial and stream type classifications. We identified potential reference sites in segments with unmodified vegetation cover adjacent to the stream and in >85% of the upstream catchment. We then used various landcover, amenity and environmental impact databases to eliminate sites that had potential anthropogenic influences upstream and that fell into a range of access classes. Each site identified by this process was coded by four dominant stream classes and seven zones, and 119 candidate sites were randomly selected for follow-up assessment. This process yielded 16 sites conforming to reference site criteria using a conditional-probabilistic design, and these were augmented by an additional 14 existing or special interest reference sites. Non-metric multidimensional scaling (NMS) analysis of percent abundance invertebrate data indicated significant differences in community composition among some of the zones and stream classes identified a priori providing qualified support for this framework in reference site selection. NMS analysis of a range standardised condition and diversity metrics derived from the invertebrate data indicated a core set of 26 closely related sites, and four outliers that were considered atypical of reference site conditions and subsequently dropped from the network. Use of GIS linked to stream typology, available spatial databases and aerial photography greatly enhanced the objectivity and efficiency of reference site selection. The multi-metric ordination approach reduced variability among stream types and bias associated with non-random site selection, and provided an effective way to identify representative reference sites.     

A Hierarchical Approach to Designing Compact Ecological Reserve Systems

A number of mathematical models and solution techniques have been developed to design systems of reserve sites to protect species and their natural habitats. This paper presents two optimization models for obtaining ecological reserve systems that are spatially compact. Compact reserve systems will increase species persistence relative to more fragmented systems and can reduce the costs associated with reserve boundaries. These optimization models employ a hierarchical approach that incorporates both the boundary length of all clusters and the sum of within-cluster distances. Unlike previous approaches, we argue that measuring the distance between sites within clusters (and not between clusters) is more appropriate. Numerical experiments are conducted on synthetic grid systems and on a real-world hexagonal data set. These experiments confirm that the models produce reasonably compact clusters of reserve sites that respect species availability and budget constraints. Simplifications to the models are developed that significantly reduce the computational effort, while still identifying reasonable sets of reserve clusters. Sensitivity of the results to changes in model parameters (number of allowable sites, number of possible clusters, and rarity of species covered) is also explored.     

Rebuilding Migratory Flyways Using Directed Conditional Covering

There has been much recent research on site selection for species preservation, although most of this research has focused on terrestrial plant and animal species. There is increasing evidence that lack of suitable habitat for migratory birds is contributing to their diminishing numbers. We extend the literature of site selection with a specific application to migratory birds. We develop reserve planning models, based on the novel idea of Directed Conditional Covering, to identify superior configurations of locations to be included in migratory flyways.     

Models for preserving species diversity with backup coverage

The problem of selecting land for preservation of species has been a rich and active area of research over the past two decades. Typically, reserve selection models have tried to maximize species diversity by preserving areas that contain the greatest number of species. However, several studies have shown that seldom do these species-rich areas contain the rarest species most in need of protection. Most reserve selection models seek to maximize diversity by choosing parcels so that all species are covered by or represented in at least one parcel. This approach would usually be expected to result in coverage by a single parcel for the rarest species, especially for those that do not coincide with more abundant species. It is precisely these rare species, however, that would be lost or whose survivability would be most challenged, if the single parcels in which they are represented became unavailable due to some unforeseen event. In this paper, we introduce to reserve selection models the concept of secondary, or backup, coverage of species. Briefly stated, a species is said to have backup representation in the system of reserves if it is covered by, or represented in, two or more parcels. Having backup coverage guarantees that every species is still covered in the event that a natural or man-made catastrophe makes a given parcel uninhabitable. The results show that backup coverage can be obtained at little additional cost (as expressed by the number of parcels selected). Bi-objective formulations that trade-off primary with backup coverage show that backup coverage can be guaranteed for larger numbers of species with little reduction in primary coverage.     

丹江湿地国家级自然保护区及其内外区域2000—2015年土地覆被变化分析

为研究2000—2015年丹江湿地国家级自然保护区及其内外生态状况变化和保护成效,基于高分1号数据生产的2m高分辨率遥感影像数据对丹江湿地国家级自然保护区2015年人类活动状况进行分析,基于30 m分辨率的4期TM遥感影像生产的土地覆被数据和基于Modis遥感影像生产的植被覆盖度数据,对淅川县、丹江湿地国家级自然保护区及其核心区的土地覆被状况、土地覆被转类指数及其土地覆被转类途径的主导程度和3个相关区域范围内的生态系统质量以及不同区域土地覆被变化的主要变化原因进行分析。结果表明,保护区核心区的格局和质量在该区域处于最优,且土地覆被变化状况也以核心区转类指数最高;丹江湿地国家级自然保护区内的主要人类活动影响为耕地,其次包括居民点、采石场、养殖场; 15年间,保护区内外土地覆被均呈现转好趋势,但是保护区内变化优于保护区外,保护区核心区优于整个保护区,且转好的主导因素均是耕地变为湿地; 15年间植被覆盖度变化较小。