A Scenario Optimization Model for Dynamic Reserve Site Selection

Conservation planners are called upon to make choices and trade-offs about the preservation of natural areas for the protection of species in the face of development pressures. We addressed the problem of selecting sites for protection over time with the objective of maximizing species representation, with uncertainty about future site development, and with periodic constraints on the number of sites that can be selected. We developed a 0–1, linear optimization model with 2 periods to select the sites that maximize expected species coverage subject to budget constraints. The model is based on the idea that development uncertainty can be characterized by a set of scenarios, each of which is a possible second-period development outcome for the set of sites. We also suggest that our 2-period model can be used in a sequential fashion that is consistent with adaptive planning. Results are presented for the Fox River watershed in Chicago.     

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.     

A Robust Optimization Model for an Invasive Species Management Problem

Invasive species pose a significant threat to global biodiversity. Managing invasive species often involves modeling the species’ spread pattern, estimating control costs and damage costs due to the invasion, designing control efforts, and accounting for uncertainties in model parameters. Dealing with uncertainty is arguably the most important part of the process, since biological, environmental, and economic factors can cause parameter values to vary greatly. Managers need decision tools that are robust to such limited or variable information. Here, we present a robust spatial optimization model to select treatment sites in a way that maximally reduces the size of an invasive population, given a constraint on financial resources. We develop an integer programming model that includes population dynamics and management costs over space and time. The model incorporates uncertainty in the available budget and the invasive spread rate as sets of discrete scenarios to determine a robust, cost-effective management plan in a novel way.     

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.     

How to Take into Account Uncertainty in Species Extinction Probabilities for Phylogenetic Conservation Prioritization

In this article, we are concerned with the general problem of choosing from a set of taxa T a subset S to protect in order to try to contribute to halting biodiversity loss as efficiently as possible given limited resources. The protection of a taxon decreases its extinction probability, and the impact of protecting the taxa of S is measured by the resulting expected phylogenetic diversity (ePD) of the set T. The primary challenge posed by this approach lies in determining the extinction probability of a taxon (protected or unprotected). To deal with this difficulty, the uncertainty about the extinction probabilities can be described through a set of possible scenarios, each corresponding to different extinction probability values for each taxon. We show how to determine an “optimal robust set” of taxa to protect, defined as the set of taxa that minimizes the maximum “regret,” i.e., the maximum relative gap, over all the scenarios, between (1) the ePD of T obtained by protecting the taxa of this set and (2) the ePD of T which would be produced by protecting the subset of taxa optimal for the considered scenario. In our experimental conditions covering 100 cases, this gap is almost always less than 1%. Consequently, the ePD of T obtained by protecting the taxa of the optimal robust set is not far from the maximum ePD of T that could have been obtained if we had known the true scenario. In other words, a way of escaping (in large part, at least) from the uncertainty related to the extinction probabilities of the taxa consists of choosing to protect those belonging to the optimal robust set. We also compare the optimal robust set to other relevant subsets of T.     

The Impact of Uncertainty in Climate Targets and CO2 Storage Availability on Long-Term Emissions Abatement

A major characteristic of our global interactive climate-energy system is the large uncertainty that exists with respect to both future environmental requirements and the means available for fulfilling these. Potentially, a key technology for leading the transition from the current fossil fuel-dominated energy system to a more sustainable one is carbon dioxide capture and storage. Uncertainties exist, however, concerning the large-scale implementability of this technology, such as related to the regional availability of storage sites for the captured CO₂. We analyze these uncertainties from an integrated assessment perspective by using the bottom-up model TIAM-ECN and by studying a set of scenarios that cover a range of different climate targets and technology futures. Our study consists of two main approaches: (1) a sensitivity analysis through the investigation of a number of scenarios under perfect foresight decision making and (2) a stochastic programming exercise that allows for simultaneously considering a set of potential future states-of-the-world. We find that, if a stringent climate (forcing) target is a possibility, it dominates the solution: if deep CO₂ emission reductions are not started as soon as possible, the target may become unreachable. Attaining a stringent climate target comes in any case at a disproportionally high price, which indicates that adaptation measures or climate damages might be preferable to the high mitigation costs such a target implies.     

Taking an environmental ethics perspective to understand what we should expect from EIA in terms of biodiversity protection

As a globally mandated decision-support tool, Environmental Impact Assessment (EIA) has the potential to contribute to the protection of biodiversity, which is increasingly under threat because of human activities. Concern over its ability to do this, however, has led to the addition of trade-off rules, Ecosystem Services Assessment (ESA), and biodiversity offsets. But given that EIA is set in a political decision-making context, what is reasonable to expect of EIA? In this paper we seek to explore what level of biodiversity protection we can expect EIA to support (and therefore whether these additions are worthwhile). Our point of departure is that EIA supports its political context and associated societal goals, and those goals typically (explicitly or implicitly) reflect some form of sustainable development. Given that the appropriate level of biodiversity protection is a moral consideration, we take an environmental ethics perspective to explain how different levels of protection are associated with different ethical positions on a spectrum from anthropocentrism (where only humans have intrinsic rights) through to ecocentrism (where all individuals of all species have intrinsic rights). We then investigate how different sustainable development discourses, one economic (on a spectrum from weak to strong sustainability) and one ecological (on a spectrum from shallow to deep ecology) map against the environmental ethics spectrum. We find that the economic discourse on sustainable development, which tends to prevail in political decision-making, is heavily anthropocentric, whereas an ecological discourse has some potential to deliver ecocentrism, but only where a deep ecology interpretation is adopted. We then show that the practise of EIA (with or without the addition of other approaches) maps against, and is bounded by, an economic discourse on sustainable development. The reality is, therefore, that EIA can do no more than contribute to delaying incremental biodiversity loss. If EIA were legislated to protect biodiversity using a deep ecology discourse, then only brownfield development would be possible.     

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.     

Development and Parameterization of a Rain- and Fire-driven Model for Exploring Elephant Effects in African Savannas

We describe the development and parameterization of a grid-based model of African savanna vegetation processes. The model was developed with the objective of exploring elephant effects on the diversity of savanna species and structure, and in this formulation concentrates on the relative cover of grass and woody plants, the vertical structure of the woody plant community, and the distribution of these over space. Grid cells are linked by seed dispersal and fire, and environmental variability is included in the form of stochastic rainfall and fire events. The model was parameterized from an extensive review of the African savanna literature; when available, parameter values varied widely. The most plausible set of parameters produced long-term coexistence between woody plants and grass, with the tree–grass balance being more sensitive to changes in parameters influencing demographic processes and drought incidence and response, while less sensitive to fire regime. There was considerable diversity in the woody structure of savanna systems within the range of uncertainty in tree growth rate parameters. Thus, given the paucity of height growth data regarding woody plant species in southern African savannas, managers of natural areas should be cognizant of different tree species growth and damage response attributes when considering whether to act on perceived elephant threats to vegetation.     

Assessing the wildlife habitat value of New England salt marshes: II. Model testing and validation

We tested a previously described model to assess the wildlife habitat value of New England salt marshes by comparing modeled habitat values and scores with bird abundance and species richness at sixteen salt marshes in Narragansett Bay, Rhode Island USA. As a group, wildlife habitat value assessment scores for the marshes ranged from 307-509, or 31-67% of the maximum attainable score. We recorded 6 species of wading birds (Ardeidae; herons, egrets, and bitterns) at the sites during biweekly survey. Species richness (r (2)=0.24, F=4.53, p=0.05) and abundance (r (2)=0.26, F=5.00, p=0.04) of wading birds significantly increased with increasing assessment score. We optimized our assessment model for wading birds by using Akaike information criteria (AIC) to compare a series of models comprised of specific components and categories of our model that best reflect their habitat use. The model incorporating pre-classification, wading bird habitat categories, and natural land surrounding the sites was substantially supported by AIC analysis as the best model. The abundance of wading birds significantly increased with increasing assessment scores generated with the optimized model (r (2)=0.48, F=12.5, p=0.003), demonstrating that optimizing models can be helpful in improving the accuracy of the assessment for a given species or species assemblage. In addition to validating the assessment model, our results show that in spite of their urban setting our study marshes provide substantial wildlife habitat value. This suggests that even small wetlands in highly urbanized coastal settings can provide important wildlife habitat value if key habitat attributes (e.g., natural buffers, habitat heterogeneity) are present.     

Investments in Power Generation Under Uncertainty—a MIP Specification and Large-Scale Application for EU

Investments in power generation constitute a typical budget allocation problem in the context of multiple objectives, while all factors influencing investor’s decisions for power plants are subject to considerable uncertainties. The paper introduces a multi-objective stochastic model designed to optimize budget allocation decisions for power generation in the context of risk aversion taking into account several sources of uncertainty, especially with regard to volatility of fossil fuel and electricity prices, technological costs, and climate policy variability. Probability distributions for uncertain factors influencing investment decisions are directly derived from the stochastic global energy model PROMETHEUS and thus they take into account complex interactions between variables in the systemic context. In order to fully incorporate stochastic characteristics of the problem, the model is specified as an optimization problem in which the probability that an objective exceeds a given threshold is maximized (risk aversion) subject to a set of deterministic and probabilistic constraints. The model is formulated as a mixed integer program providing complete flexibility on the joint distributions of rates of return of technologies competing for investments, as it can handle non-symmetric distributions and take automatically into account complex covariance patterns as emerging from comprehensive PROMETHEUS stochastic results. The analysis shows that risk is a crucial factor for power generation investments with investors not opting for technologies subject to uncertainty related to climate policies and fossil fuel prices. On the other hand, combination of options with negative covariance tends to benefit in the context of risk-hedging behavior.     

Assessing possible visitor-use impacts on water quality in Yosemite National Park, California

There is concern that visitor-use associated activities, such as bathing, dish washing, wastewater production, and stock animal use near lakes and streams, could cause degradation of water quality in Yosemite National Park. A study was conducted during 2004-2007 to assess patterns in nutrient and Escherichia coli (E. coli) concentrations in the Merced and Tuolumne Rivers and characterize natural background concentrations of nutrients in the park. Results indicated that nutrient and E. coli concentrations were low, even compared to other undeveloped sites in the United States. A multiple linear regression approach was used to model natural background concentrations of nutrients, with basin characteristics as explanatory variables. Modeled nitrogen concentrations increased with elevation, and modeled phosphorus concentrations increased with basin size. Observed concentrations (±uncertainty) were compared to modeled concentrations (±uncertainty) to identify sites that might be impacted by point sources of nutrients, as indicated by large model residuals. Statistically significant differences in observed and modeled concentrations were observed at only a few locations, indicating that most sites were representative of natural background conditions. The empirical modeling approach used in this study can be used to estimate natural background conditions at any point along a study reach in areas minimally impacted by development, and may be useful for setting water-quality standards in many national parks.     

Accounting for Uncertainty in Value Judgements when Applying Multi-Attribute Value Theory

In environmental decisions, analysts commonly face substantial uncertainties around stakeholders’ values judgments. Multi-Attribute Value Theory (MAVT), a family of multi-criteria decision analysis techniques, is applied in participative settings to articulate stakeholders’ values in decision-making. In MAVT, value judgments represent the intensity of individuals’ preferences in a set of objectives, which are operationalized as scaling factors or weights. Different sets of weights may express variation in people’s preferences or value judgments. Unfortunately, there are still important methodological gaps regarding how to incorporate uncertainty and the substantial variation commonly encountered in stakeholders’ preferences. This article presents a model of uncertainty that encompasses the dispersion of value judgments in MAVT. To achieve this goal, we draw on info-gap theory, which provides a mathematically grounded method for exploring sensitivity to preference weights when there are relatively high levels of uncertainties. We experimentally tested the uncertainty model in an environmental decision problem. We found that MAVT can use info-gap analysis to deal with multiple value judgments, avoiding exclusive reliance on nominal expected values to inform decisions. We explored a mechanism to explicitly consider the trade-offs between the performance of alternatives and the level of uncertainty that in any specified context a decision maker is willing to accept. Findings emphasize the potential of MAVT to support environmental management decisions, particularly in situations where multiple stakeholders and their contested value judgments have to be considered simultaneously to explore uncertainties around value trade-offs.     

Approaches for performing uncertainty analysis in large-scale energy/economic policy models

A number of key policy insights have emerged from the application of large-scale economic/energy models, such as integrated assessment models for climate change. These insights have been particularly powerful in those instances when they are shared by all or most of the existing models. On the other hand, some results and policy recommendations obtained from integrated assessment models vary widely from model to model. This can limit their usability for policy analysis. The differences between model results are mostly due to different underlying assumptions about exogenous processes, about endogenous processes and the dynamics among them, differences in value judgments, and different approaches for simplifying model structure for computational purposes. Uncertainty analyses should be performed for the dual purpose of clarifying the uncertainties inherent in model results and improving decision making under uncertainty. This paper develops a unifying framework for comparing the different types of uncertainty analyses through their objective functions, categorizes types of uncertainty analyses that can be performed on large models, and compares different approaches to uncertainty analysis by explaining underlying assumptions, suitability for different model types, and advantages and disadvantages. The appendix presents a summary of integrated assessment models for climate change that explicitly account for uncertainty.     

Development of a Pollination Service Measurement (PSM) method using potted plant phytometry

The value of pollination to human society is not limited to agricultural production, but also in the sustainability of ecosystems and the services that they provide. Seed set can be used as a comparative measure of pollination effectiveness, with minimum variability expected when other resources are not limiting. Six species of self-incompatible fall asters (Symphyotrichum) were used to evaluate pollination service at 12 sites across a spectrum of expected levels of pollination. Seed set per inflorescence was generally lower at sites with lower pollinator numbers and diversity, although as expected pollinator assemblage characteristics were highly variable within and between sites. However, rankings of sites showed consistency of response across phytometer species and between years; the summed ranks across multiple species appears to have as the greatest value in Pollination Service Measurement (PSM). Abundance, richness, and Shannon diversity of pollinator assemblages were highly autocorrelated and showed variable relationships with seed set depending on plant species and temporal scale of pollinator assemblage assessment. Use of seed set to directly measure pollination service at a site was consistent and cost effective when compared to less certain and more labour-intensive methods of pollinator collection and identification, and shows promise for implementation in pollination monitoring and bioassessment practices.     

Confronting Management Challenges in Highly Uncertain Natural Resource Systems: a Robustness–Vulnerability Trade-off Approach

This paper presents a framework for the study of policy implementation in highly uncertain natural resource systems in which uncertainty cannot be characterized by probability distributions. We apply the framework to parametric uncertainty in the traditional Gordon–Schaefer model of a fishery to illustrate how performance can be sacrificed (traded-off) for reduced sensitivity and hence increased robustness, with respect to model parameter uncertainty. With sufficient data, our robustness–vulnerability analysis provides tools to discuss policy options. When less data are available, it can be used to inform the early stages of a learning process. Several key insights emerge from this analysis: (1) the classic optimal control policy can be very sensitive to parametric uncertainty, (2) even mild robustness properties are difficult to achieve for the simple Gordon–Schaefer model, and (3) achieving increased robustness with respect to some parameters (e.g., biological parameters) necessarily results in increased sensitivity (decreased robustness) with respect to other parameters (e.g., economic parameters). We thus illustrate fundamental robustness–vulnerability trade-offs and the limits to robust natural resource management. Finally, we use the framework to explore the effects of infrequent sampling and delays on policy performance.     

A comparison of fixed-site and non-fixed-site approaches for species protection

The efficacy of simultaneously advancing two distinct conceptual designs (referred to here as fixed-site and non-fixed-site) for species conservation and protection is addressed. In the literature, numerous models can be found that typically stem from a particular design, but rarely are comparisons made between approaches. This paper presents a more integrated optimization framework that models landowner behavior and species viabilities at a landscape scale. Regional demand for resource extraction is used as the economic driver, a variant of simulated annealing is used to solve the model under different species protection approaches, and a detailed species population simulator is utilized to measure biological responses. When directly comparing the outcomes of different species protection strategies from a case study in Oregon (USA), it was found that neither approach was universally superior in terms of financial value or degree of protection for two late seral forest dependent species.     

Assessment of ecosystem health based on fish assemblages in the Wei River basin,China

In the Wei River basin, the ecosystem is gradually deteriorating due to the rapid growth of the population and the development of economies. It is thus important to assess the ecosystem health and take measures to restore the damaged ecosystem. In this study, an index of biotic integrity (IBI) for fish was developed to aid the conservation of the ecosystem based on a calibration data set. An index of water and habitat quality (IWHQ) was calculated based on environmental variables and habitat quality (QHEI) to identify the environmental degradation in the studied sites. The least degraded sites (IWHQ?≤?2; W1, W5, W10, W12, W13, W14, and W16) were chosen as the reference sites. Six metrics that are sensitive to environmental degradation were utilized to differentiate the reference and the impaired sites using statistical methods. These metrics included the number of species (P1), the total biomass (P2), the number of Cobitidae species (P8), the proportion of species in the middle and low tiers (P10), the proportion of individuals that were classified as sensitive species (P25), and number of individuals in the sample (P39). A continuous scoring method was used to score the six metrics, and four classes were defined to characterize the ecosystem health of the Wei River basin. The fact that the overall IBI scores were negatively correlated with the index of environmental quality (IWHQ) based on the validation data set indicated that the index should be useful for biomonitoring and the conservation of biodiversity. According to the results, more than half of the sites were classified as poor or very poor. The ecosystem health in the Wei River was better than that in the Jing River and the Beiluo River, and this study will be a great reference for water resources management and ecosystem restoration in the Wei River basin.     

A New Statistical Dynamic Analysis of Ecosystem Patterns

While phenomenological investigations of ecosystem patterns often fail to reveal underlying dynamic mechanisms, we highlight a universal principle for pattern formation in ecosystems. We consider ecosystems to be typical complex adaptive systems that seek an optimal process to obtain maximized flux under given constraints. An analysis of the optimal process reveals underlying microscopic dynamic mechanisms that induce complex patterns in ecosystems. We emulate ecosystem patterns using a Self-Organization Feature Map: an artificial neural network theoretical model by which evolution processes, structural classifications, and the fractal growth of ecosystem patterns can be simulated. The results help us analyze the formation and dynamics of ecosystem patterns, with attending implications for the classification, protection, and optimization of ecosystems.     

Addressing statistical and operational challenges in designing large-scale stream condition surveys

Implementing a statistically valid and practical monitoring design for large-scale stream condition monitoring and assessment programs can be difficult due to factors including the likely existence of a diversity of ecosystem types such as ephemeral streams over the sampling domain; limited resources to undertake detailed monitoring surveys and address knowledge gaps; and operational constraints on effective sampling at monitoring sites. In statistical speak, these issues translate to defining appropriate target populations and sampling units; designing appropriate spatial and temporal sample site selection methods; selection and use of appropriate indicators; and setting effect sizes with limited ecological and statistical information about the indicators of interest. We identify the statistical and operational challenges in designing large-scale stream condition surveys and discuss general approaches for addressing them. The ultimate aim in drawing attention to these challenges is to ensure operational practicality in carrying out future monitoring programs and that the resulting inferences about stream condition are statistically valid and relevant.