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.     

Probabilistic approaches to scheduling reserve selection

Most existing reserve selection algorithms are static in that they assume that a reserve network is designed and patches are selected by decision-makers at a single point in time. In reality, however, selection processes are often dynamic and patches are selected one by one or in several groups because for example there are insufficient funds at the beginning of the process to put all the patches under protection. Finding an optimal dynamic selection strategy is tricky since due to the complementarity principle the value of a particular patch depends on the presence of other patches in the network - including those that have not yet been selected. As unprotected patches may be lost, e.g., through development, the long-term value of selecting a particular patch is uncertain. Existing dynamic selection algorithms are either ‘myopic’ and consider only those patches that have already been protected, totally ignoring future uncertainty, or they are based on stochastic dynamic programming, which delivers the optimal strategy taking uncertainty into account but is numerically too complex to be employed in actual selection problems. In this paper, a ‘foresighted’ selection strategy as well as a number of variants are developed using probability theory. The different strategies are compared for a large number of selection problems. All variants outperform the myopic strategy and perform close to the optimal strategy. However, the performances of all strategies, including the optimal and the myopic one, are not dramatic.     

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.     

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.     

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.     

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.     

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.     

Elephant-induced structural changes in the vegetation and habitat selection by large herbivores in an African savanna

African elephants can affect the quality of the habitat of other species by breaking or uprooting trees and shrubs in savannas. Their effect on vegetation has been widely studied but less is known about the effects of such vegetation changes on other animals. We studied how changes in the vegetation caused by elephants influence the selection of microhabitats by five African herbivore species (giraffe, kudu, steenbok, impala, and zebra) in Hwange National Park, Zimbabwe. There was no clear significant effect of overall elephant-induced vegetation changes on microhabitat selection except for the small species (steenbok and impala) that used vegetation modified by elephants preferentially. This is consistent with a medium-term browsing facilitation hypothesis. More subtle possible effects were detected for larger browsers (giraffe and kudu). They selected areas with broken and uprooted plants and avoided coppiced areas. All of the browsers selected sites characterized by plants uprooted and broken by elephants, which were associated with a higher visibility, and ultimately a better probability of detecting an approaching predator, suggesting that perceived predation risk plays an important role in microhabitat selection. These results illustrate how elephants can initiate indirect effects that influence microhabitat selection by other herbivores. Understanding the indirect effects of elephants through changes in food availability and predation risk thus needs further investigation. The results of this study do not provide support for the hypothesis that elephant-induced changes in the structure of habitats have caused the declines in the populations of the other herbivores in the study area.