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Plans for expanding protected area systems (prioritizations) need to fulfill conservation objectives. They also need to account for other factors, such as economic feasibility and anthropogenic land‐use requirements. Although prioritizations are often generated with decision support tools, most tools have limitations that hinder their use for decision‐making. We outlined how the prioritizr R package (https://prioritizr.net) can be used for systematic conservation prioritization. This decision support tool provides a flexible interface to build conservation planning problems. It can leverage a variety of commercial (e.g., Gurobi) and open‐source (e.g., CBC and SYMPHONY) exact algorithm solvers to identify optimal solutions in a short period. It is also compatible with a variety of spatially explicit (e.g., ESRI Shapefile, GeoTIFF) and nonspatial tabular (e.g., Microsoft Excel Spreadsheet) data formats. Additionally, it provides functionality for evaluating prioritizations, such as assessing the relative importance of different places selected by a prioritization. To showcase the prioritizr R package, we applied it to a case study based in Washington state (United States) for which we developed a prioritization to improve protected area coverage of native avifauna. We accounted for land acquisition costs, existing protected areas, places that might not be suitable for protected area establishment, and spatial fragmentation. We also conducted a benchmark analysis to examine the performance of different solvers. The prioritization identified 12,400 km2 of priority areas for increasing the percentage of species’ distributions covered by protected areas. Although open source and commercial solvers were able to quickly solve large‐scale conservation planning problems, commercial solvers were required for complex, large‐scale problems.. The prioritizr R package is available on the Comprehensive R Archive Network (CRAN). In addition to reserve selection, it can inform habitat restoration, connectivity enhancement, and ecosystem service provisioning. It has been used in numerous conservation planning exercises to inform best practices and aid real‐world decision‐making. [ABSTRACT FROM AUTHOR]

Current rates of climate change and gloomy climate projections confront managers and conservation planners with the need to integrate climate change into already complex decision‐making processes. Predicting and prioritizing climatically stable areas and the areas likely to facilitate adaptive species’ range adjustments are important stages in maximizing conservation outcomes and rationalizing future land management. I determined, for the most threatened European terrestrial mammal species, the spatial adaptive trajectories (SATs) of highest expected persistence up to 2080. I devised simple spatial network indices for evaluation of species in those SATs: total persistence; proportion of SATs that offer in situ adaptation (i.e., stable refugia); number of SATs converging in a site; and relationship between SAT convergence and persistence and protected areas, the Natura 2000 and Emerald networks, and areas of low human disturbance. I compared the performance of high‐persistence SATs with a scenario in which each species remained in the areas with the best climatic conditions in the baseline period. The 1000 most persistence SATs for each of the 39 species covered one fifth of Europe. The areas with the largest adaptive potential (i.e., high persistence, stability, and SAT convergence) did not always overlap for all the species. Predominantly, these regions were located in southwestern Europe, Central Europe, and Scandinavia, with some occurrences in Eastern Europe. For most species, persistence in the most climatically suitable areas during the baseline period was lower than within SATs, underscoring their reliance on adaptive movements. Importantly, conservation areas (particularly protected areas) covered only minor fractions of species persistence among SATs, and hubs of spatial climate adaptation (i.e., areas of high SAT convergence) were seriously underrepresented in most conservation areas. These results highlight the need to perform analyses on spatial species’ dynamics under climate change. [ABSTRACT FROM AUTHOR]

Conservation decisions are invariably made with incomplete data on species' distributions, habitats, and threats, but frameworks for allocating conservation investments rarely account for missing data. We examined how explicit consideration of missing data can boost return on investment in ecosystem restoration, focusing on the challenge of restoring aquatic ecosystem connectivity by removing dams and road crossings from rivers. A novel way of integrating the presence of unmapped barriers into a barrier optimization model was developed and applied to the U.S. state of Maine to maximize expected habitat gain for migratory fish. Failing to account for unmapped barriers during prioritization led to nearly 50% lower habitat gain than was anticipated using a conventional barrier optimization approach. Explicitly acknowledging that data are incomplete during project selection, however, boosted expected habitat gains by 20–273% on average, depending on the true number of unmapped barriers. Importantly, these gains occurred without additional data. Simply acknowledging that some barriers were unmapped, regardless of their precise number and location, improved conservation outcomes. Given incomplete data on ecosystems worldwide, our results demonstrate the value of accounting for data shortcomings during project selection. [ABSTRACT FROM AUTHOR]

Protected areas are a key instrument for conservation. Despite this, they are vulnerable to risks associated with weak governance, land‐use intensification, and climate change. We used a novel hierarchical optimization approach to identify priority areas for expanding the global protected area system that explicitly accounted for such risks while maximizing protection of all known terrestrial vertebrate species. To incorporate risk categories, we built on the minimum set problem, where the objective is to reach species distribution protection targets while accounting for 1 constraint, such as land cost or area. We expanded this approach to include multiple objectives accounting for risk in the problem formulation by treating each risk layer as a separate objective in the problem formulation. Reducing exposure to these risks required expanding the area of the global protected area system by 1.6% while still meeting conservation targets. Incorporating risks from weak governance drove the greatest changes in spatial priorities for protection, and incorporating risks from climate change required the largest increase (2.52%) in global protected area. Conserving wide‐ranging species required countries with relatively strong governance to protect more land when they bordered nations with comparatively weak governance. Our results underscore the need for cross‐jurisdictional coordination and demonstrate how risk can be efficiently incorporated into conservation planning. Planeación de las áreas protegidas para conservar la biodiversidad en un futuro incierto [ABSTRACT FROM AUTHOR]

Amphibians are severely affected by climate change, particularly in regions where droughts prevail and water availability is scarce. The extirpation of amphibians triggers cascading effects that disrupt the trophic structure of food webs and ecosystems. Dedicated assessments of the spatial adaptive potential of amphibian species under climate change are, therefore, essential to provide guidelines for their effective conservation. I used predictions about the location of suitable climates for 27 amphibian species in the Iberian Peninsula from a baseline period to 2080 to typify shifting species' ranges. The time at which these range types are expected to be functionally important for the adaptation of a species was used to identify full or partial refugia; areas most likely to be the home of populations moving into new climatically suitable grounds; areas most likely to receive populations after climate adaptive dispersal; and climatically unsuitable areas near suitable areas. I implemented an area prioritization protocol for each species to obtain a cohesive set of areas that would provide maximum adaptability and where management interventions should be prioritized. A connectivity assessment pinpointed where facilitative strategies would be most effective. Each of the 27 species had distinct spatial requirements but, common to all species, a bottleneck effect was predicted by 2050 because source areas for subsequent dispersal were small in extent. Three species emerged as difficult to maintain up to 2080. The Iberian northwest was predicted to capture adaptive range for most species. My study offers analytical guidelines for managers and decision makers to undertake systematic assessments on where and when to intervene to maximize the persistence of amphibian species and the functionality of the ecosystems that depend on them. [ABSTRACT FROM AUTHOR]

Recovery of grassland birds in agricultural landscapes is a global imperative. Agricultural landscapes are complex, and the value of resource patches may vary substantially among species. The spatial extent at which landscape features affect populations (i.e., scale of effect) may also differ among species. There is a need for regional‐scale conservation planning that considers landscape‐scale and species‐specific responses of grassland birds to environmental change. We developed a spatially explicit approach to optimizing grassland conservation in the context of species‐specific landscapes and prioritization of species recovery and applied it to a conservation program in Kentucky (USA). We used a hierarchical distance‐sampling model with an embedded scale of effect predictor to estimate the relationship between landscape structure and abundance of eastern meadowlarks (Sturnella magna), field sparrows (Spizella pusilla), and northern bobwhites (Colinus virginianus). We used a novel spatially explicit optimization procedure rooted in multi‐attribute utility theory to design alternative conservation strategies (e.g., prioritize only northern bobwhite recovery or assign equal weight to each species' recovery). Eastern meadowlarks and field sparrows were more likely to respond to landscape‐scale resource patch adjacencies than landscape‐scale patch densities. Northern bobwhite responded to both landscape‐scale resource patch adjacencies and densities and responded strongly to increased grassland density. Effects of landscape features on local abundance decreased as distance increased and had negligible influence at 0.8 km for eastern meadowlarks (0.7–1.2 km 95% Bayesian credibility intervals [BCI]), 2.5 km for field sparrows (1.5–5.8 km 95% BCI), and 8.4 km for bobwhite (6.4–26 km 95% BCI). Northern bobwhites were predicted to benefit greatly from future grassland conservation regardless of conservation priorities, but eastern meadowlark and field sparrow were not. Our results suggest similar species can respond differently to broad‐scale conservation practices because of species‐specific, distance‐dependent relationships with landscape structure. Our framework is quantitative, conceptually simple, customizable, and predictive and can be used to optimize conservation in heterogeneous ecosystems while considering landscape‐scale processes and explicit prioritization of species recovery. Article impact statement: Multiattribute utility theory informs a spatially explicit method identifying alternative conservation strategies based on stakeholder values. [ABSTRACT FROM AUTHOR]

Keywords: decision analysis; introduced species; invasion; management priority; multiple choice knapsack problem; optimization; resource allocation; análisis de decisión; asignación de recursos; especie introducida; invasión; optimización; prioridad de manejo; problema de opción múltiple de la mochila EN decision analysis introduced species invasion management priority multiple choice knapsack problem optimization resource allocation análisis de decisión asignación de recursos especie introducida invasión optimización prioridad de manejo problema de opción múltiple de la mochila 1639 1649 11 10/05/21 20211001 NES 211001 INTRODUCTION Species and communities are often subject to numerous threats, which must be addressed to avoid poor conservation outcomes (Auerbach et al., 2014). We used number of hectares of vegetation in poor condition (>5% cover of introduced plant species) due to the presence of introduced plant species as a measure of candidate-action performance toward this management objective because workshop participants considered this level of cover likely to cause negative impacts and trigger a management response. Introduced plant species management in the Australian Alps We applied the decision framework to identify optimal strategies for managing multiple introduced plant species in two areas in the Australian Alps: alpine and subalpine areas of the Victorian Bogong High Plains (BHP) (36.9333° S, 147.3000° E) and New South Wales' Kosciuszko National Park's main range alpine area (KNP) (36.4492° S, 148.2672° E). Effectiveness is expressed as the proportion of impact remaining after management compared with the do-nothing case that results in the maximum impact and has no cost gl Species and actions identified for management changed with budget (Figure 3). [Extracted from the article]

Marxan is the most common decision‐support tool used to inform the design of protected‐area systems. The original version of Marxan does not consider risk and uncertainty associated with threatening processes affecting protected areas, including uncertainty about the location and condition of species' populations and habitats now and in the future. We described and examined the functionality of a modified version of Marxan, Marxan with Probability. This software explicitly considers 4 types of uncertainty: probability that a feature exists in a particular place (estimated based on species distribution models or spatially explicit population models); probability that features in a site will be lost in the future due to a threatening process, such as climate change, natural catastrophes, and uncontrolled human interventions; probability that a feature will exist in the future due to natural successional processes, such as a fire or flood; and probability the feature exists but has been degraded by threatening processes, such as overfishing or pollution, and thus cannot contribute to conservation goals. We summarized the results of 5 studies that illustrate how each type of uncertainty can be used to inform protected area design. If there were uncertainty in species or habitat distribution, users could maximize the chance that these features were represented by including uncertainty using Marxan with Probability. Similarly, if threatening processes were considered, users minimized the chance that species or habitats were lost or degraded by using Marxan with Probability. Marxan with Probability opens up substantial new avenues for systematic conservation planning research and application by agencies. [ABSTRACT FROM AUTHOR]

Conserving biodiversity and combating ecological hazards require cost‐effective allocation of limited resources among potential management projects. Project priorities, however, can change over time as underlying social‐ecological systems progress, novel priorities emerge, and management capabilities evolve. Thus, reallocation of ongoing investments in response to shifting priorities could improve management outcomes and address urgent demands, especially when additional funding is not available immediately. Resource reallocation, however, could incur transaction costs, require additional monitoring and reassessment, and be constrained by ongoing project commitments. Such complexities may prevent managers from considering potentially beneficial reallocation strategies, reducing long‐term effectiveness. We propose an iterative project prioritization approach, based on marginal return‐on‐investment estimation and portfolio optimization, that guides resource reallocation among ongoing and new projects. Using simulation experiments in 2 case studies, we explored how this approach can improve efficacy under varying reallocation constraints, frequencies, costs, and rates of project portfolio change. Periodic budget reallocation could enhance the management of stochastically emerging invasive weeds in Australia and thus reduce the overall risk by up to 50% compared with a static budget. Reallocation frequency and the rate of new weed incursion synergistically increased the conservation gains achieved by allowing unconstrained reallocation. Conversely, budget reallocation would not improve the International Union for Conservation of Nature conservation status of threatened Australian birds due to slow rates of transition among conservation states; extinction risk could increase if portfolio reassessment is costly. Although other project prioritization studies may recommend periodic reassessment and reallocation, our findings revealed conditions when reallocation is valuable and demonstrated a structured approach that can help conservation agencies schedule and implement iterative budget‐allocation decisions cost‐effectively. Article impact statement: Reallocating funding among conservation projects in response to shifting or emerging priorities may improve outcomes. [ABSTRACT FROM AUTHOR]

Abstract: Controlling invasive species is critical for conservation but can have unintended consequences for native species and divert resources away from other efforts. This dilemma occurs on a grand scale in the North American Great Lakes, where dams and culverts block tributary access to habitat of desirable fish species and are a lynchpin of long‐standing efforts to limit ecological damage inflicted by the invasive, parasitic sea lamprey (Petromyzon marinus). Habitat restoration and sea‐lamprey control create conflicting goals for managing aging infrastructure. We used optimization to minimize opportunity costs of habitat gains for 37 desirable migratory fishes that arose from restricting sea lamprey access (0–25% increase) when selecting barriers for removal under a limited budget (US$1–105 million). Imposing limits on sea lamprey habitat reduced gains in tributary access for desirable species by 15–50% relative to an unconstrained scenario. Additional investment to offset the effect of limiting sea‐lamprey access resulted in high opportunity costs for 30 of 37 species (e.g., an additional US$20–80 million for lake sturgeon [Acipenser fulvescens]) and often required ≥5% increase in sea‐lamprey access to identify barrier‐removal solutions adhering to the budget and limiting access. Narrowly distributed species exhibited the highest opportunity costs but benefited more at less cost when small increases in sea‐lamprey access were allowed. Our results illustrate the value of optimization in limiting opportunity costs when balancing invasion control against restoration benefits for diverse desirable species. Such trade‐off analyses are essential to the restoration of connectivity within fragmented rivers without unleashing invaders. [ABSTRACT FROM AUTHOR]

Conservation biologists recognize that a system of isolated protected areas will be necessary but insufficient to meet biodiversity objectives. Current approaches to connecting core conservation areas through corridors consider optimal corridor placement based on a single optimization goal: commonly, maximizing the movement for a target species across a network of protected areas. We show that designing corridors for single species based on purely ecological criteria leads to extremely expensive linkages that are suboptimal for multispecies connectivity objectives. Similarly, acquiring the least-expensive linkages leads to ecologically poor solutions. We developed algorithms for optimizing corridors for multispecies use given a specific budget. We applied our approach in western Montana to demonstrate how the solutions may be used to evaluate trade-offs in connectivity for 2 species with different habitat requirements, different core areas, and different conservation values under different budgets. We evaluated corridors that were optimal for each species individually and for both species jointly. Incorporating a budget constraint and jointly optimizing for both species resulted in corridors that were close to the individual species movement-potential optima but with substantial cost savings. Our approach produced corridors that were within 14% and 11% of the best possible corridor connectivity for grizzly bears (Ursus arctos) and wolverines (Gulo gulo), respectively, and saved 75% of the cost. Similarly, joint optimization under a combined budget resulted in improved connectivity for both species relative to splitting the budget in 2 to optimize for each species individually. Our results demonstrate economies of scale and complementarities conservation planners can achieve by optimizing corridor designs for financial costs and for multiple species connectivity jointly. We believe that our approach will facilitate corridor conservation by reducing acquisition costs and by allowing derived corridors to more closely reflect conservation priorities. [ABSTRACT FROM AUTHOR]

A common goal in conservation planning is to acquire areas that are critical to realizing biodiversity goals in the most cost-effective manner. The way monetary acquisition costs are represented in such planning is an understudied but vital component to realizing cost efficiencies. We sought to design a protected-area network within a forested urban region that would protect 17 birds of conservation concern. We compared the total costs and spatial structure of the optimal protected-area networks produced using three acquisition-cost surrogates (area, agricultural land value, and tax-assessed land value). Using the tax-assessed land values there was a 73% and 78% cost savings relative to networks derived using area or agricultural land value, respectively. This cost reduction was due to the considerable heterogeneity in acquisition costs revealed in tax-assessed land values, especially for small land parcels, and the corresponding ability of the optimization algorithm to identify lower-cost parcels for inclusion that had equal value to our target species. Tax-assessed land values also reflected the strong spatial differences in acquisition costs (US$0.33/m2-$55/m2) and thus allowed the algorithm to avoid inclusion of high-cost parcels when possible. Our results add to a nascent but growing literature that suggests conservation planners must consider the cost surrogate they use when designing protected-area networks. We suggest that choosing cost surrogates that capture spatial- and size-dependent heterogeneity in acquisition costs may be relevant to establishing protected areas in urbanizing ecosystems. [ABSTRACT FROM AUTHOR]

Systematic conservation planning optimizes trade-offs between biodiversity conservation and human activities by accounting for socioeconomic costs while aiming to achieve prescribed conservation objectives. However, the most cost-efficient conservation plan can be very dissimilar to any other plan achieving the set of conservation objectives. This is problematic under conditions of implementation uncertainty (e.g., if all or part of the plan becomes unattainable). We determined through simulations of parallel implementation of conservation plans and habitat loss the conditions under which optimal plans have limited chances of implementation and where implementation attempts would fail to meet objectives. We then devised a new, flexible method for identifying conservation priorities and scheduling conservation actions. This method entails generating a number of alternative plans, calculating the similarity in site composition among all plans, and selecting the plan with the highest density of neighboring plans in similarity space. We compared our method with the classic method that maximizes cost efficiency with synthetic and real data sets. When implementation was uncertain-a common reality-our method provided higher likelihood of achieving conservation targets. We found that χ, a measure of the shortfall in objectives achieved by a conservation plan if the plan could not be implemented entirely, was the main factor determining the relative performance of a flexibility enhanced approach to conservation prioritization. Our findings should help planning authorities prioritize conservation efforts in the face of uncertainty about future condition and availability of sites. [ABSTRACT FROM AUTHOR]

Our knowledge of cryptogam taxonomy and species distributions is currently too poor to directly plan for their conservation. We used inventory data from four distinct vegetation types, near Hobart Tasmania, to address the proposition that vegetation type, vascular plant taxon composition, and environmental variables can act as surrogates for mosses and macrofungi in reservation planning. The four vegetation types proved distinct in their taxon composition for all macrofungi, mosses, and vascular plants. We tested the strength of the relationships between the composition of cryptogam taxonomic groups and vascular plant composition and between the environmental variables and canopy cover. Taxon composition of woody vascular plants and vascular plants was the best predictor of the taxon composition of mosses and macrofungi. Combinations of environmental variables and canopy cover were also strong predictors of the taxon composition of mosses and macrofungi. We used an optimization routine for vascular plant taxa and woody plant species and determined the representation of cryptogam taxa in these selections. We identified sites with approximately 10% and 30% of the greatest proportions of vascular plants and woody vascular plants and calculated representation of mosses and macrofungi at these sites. We compared the results of these site selections with random site selections and random selections stratified by vegetation type. Random selection of sites by vegetation type generally captured more cryptogams than site selection by vascular plants at the 10% level. Vascular plant and woody plant taxon composition, vegetation type, and environmental and structural characteristics, all showed promise as surrogates for capturing common cryptogams in reserve systems. [ABSTRACT FROM AUTHOR]

Uncertainty in the implementation and outcomes of conservation actions that is not accounted for leaves conservation plans vulnerable to potential changes in future conditions. We used a decision-theoretic approach to investigate the effects of two types of investment uncertainty on the optimal allocation of global conservation resources for land acquisition in the Mediterranean Basin. We considered uncertainty about (1) whether investment will continue and (2) whether the acquired biodiversity assets are secure, which we termed transaction uncertainty and performance uncertainty, respectively. We also developed and tested the robustness of different rules of thumb for guiding the allocation of conservation resources when these sources of uncertainty exist. In the presence of uncertainty in future investment ability (transaction uncertainty), the optimal strategy was opportunistic, meaning the investment priority should be to act where uncertainty is highest while investment remains possible. When there was a probability that investments would fail (performance uncertainty), the optimal solution became a complex trade-off between the immediate biodiversity benefits of acting in a region and the perceived longevity of the investment. In general, regions were prioritized for investment when they had the greatest performance certainty, even if an alternative region was highly threatened or had higher biodiversity value. The improved performance of rules of thumb when accounting for uncertainty highlights the importance of explicitly incorporating sources of investment uncertainty and evaluating potential conservation investments in the context of their likely long-term success. [ABSTRACT FROM AUTHOR]

The first step in conservation planning is to identify objectives. Most stated objectives for conservation, such as to maximize biodiversity outcomes, are too vague to be useful within a decision-making framework. One way to clarify the issue is to define objectives in terms of the risk of extinction for multiple species. Although the assessment of extinction risk for single species is common, few researchers have formulated an objective function that combines the extinction risks of multiple species. We sought to translate the broad goal of maximizing the viability of species into explicit objectives for use in a decision-theoretic approach to conservation planning. We formulated several objective functions based on extinction risk across many species and illustrated the differences between these objectives with simple examples. Each objective function was the mathematical representation of an approach to conservation and emphasized different levels of threat. Our objectives included minimizing the joint probability of one or more extinctions, minimizing the expected number of extinctions, and minimizing the increase in risk of extinction from the best-case scenario. With objective functions based on joint probabilities of extinction across species, any correlations in extinction probabilities had to be known or the resultant decisions were potentially misleading. Additive objectives, such as the expected number of extinctions, did not produce the same anomalies. We demonstrated that the choice of objective function is central to the decision-making process because alternative objective functions can lead to a different ranking of management options. Therefore, decision makers need to think carefully in selecting and defining their conservation goals. [ABSTRACT FROM AUTHOR]

Traditional sensitivity and elasticity analyses of matrix population models have been used to inform management decisions, but they ignore the economic costs of manipulating vital rates. For example, the growth rate of a population is often most sensitive to changes in adult survival rate, but this does not mean that increasing that rate is the best option for managing the population because it may be much more expensive than other options. To explore how managers should optimize their manipulation of vital rates, we incorporated the cost of changing those rates into matrix population models. We derived analytic expressions for locations in parameter space where managers should shift between management of fecundity and survival, for the balance between fecundity and survival management at those boundaries, and for the allocation of management resources to sustain that optimal balance. For simple matrices, the optimal budget allocation can often be expressed as simple functions of vital rates and the relative costs of changing them. We applied our method to management of the Helmeted Honeyeater (Lichenostomus melanops cassidix ; an endangered Australian bird) and the koala (Phascolarctos cinereus ) as examples. Our method showed that cost-efficient management of the Helmeted Honeyeater should focus on increasing fecundity via nest protection, whereas optimal koala management should focus on manipulating both fecundity and survival simultaneously. These findings are contrary to the cost-negligent recommendations of elasticity analysis, which would suggest focusing on managing survival in both cases. A further investigation of Helmeted Honeyeater management options, based on an individual-based model incorporating density dependence, spatial structure, and environmental stochasticity, confirmed that fecundity management was the most cost-effective strategy. Our results demonstrate that decisions that ignore economic factors will reduce management efficiency. [ABSTRACT FROM AUTHOR]

Urban planners acquire open space to protect natural areas and provide public access to recreation opportunities. Because of limited budgets and dynamic land markets, acquisitions take place sequentially depending on available funds and sites. To address these planning features, we formulated a two-period site selection model with two objectives: maximize the expected number of species represented in protected sites and maximize the expected number of people with access to protected sites. These objectives were both maximized subject to an upper bound on area protected over two periods. The trade-off between species representation and public access was generated by the weighting method of multiobjective programming. Uncertainty was represented with a set of probabilistic scenarios of site availability in a linear-integer formulation. We used data for 27 rare species in 31 candidate sites in western Lake County, near the city of Chicago, to illustrate the model. Each trade-off curve had a concave shape in which species representation dropped at an increasing rate as public accessibility increased, with the trade-off being smaller at higher levels of the area budget. Several sites were included in optimal solutions regardless of objective function weights, and these core sites had high species richness and public access per unit area. The area protected in period one depended on current site availability and on the probabilities of sites being undeveloped and available in the second period. Although the numerical results are specific for our study, the methodology is general and applicable elsewhere. [ABSTRACT FROM AUTHOR]

We developed a simple model of Pinus strobus L. stand dynamics to compare the impacts of different temporal arrangements of surface fires designed to reflect the application of fire as both an essential ecosystem process (natural-fire) and as an efficient means of producing specific habitat features or other values (optimal fire). We used a stochastic simulation model of fire processes to estimate the mean fire-return interval that would maximize stand structural diversity. We investigated trade-offs between structural diversity and temporal population stability associated with changes in the fire interval and used a deterministic version of the model to explore the effects of scheduling fires at fixed intervals. In stochastic simulations, maximum structural diversity occurred at intermediate levels of disturbance (40-year mean fire interval). When fires were scheduled at fixed intervals, a longer, 100-year return interval maximized diversity. Mean fire-return interval was a mitigating factor in the diversity-stability relationship, which changed from positive to negative as the fire interval was reduced progressively from 250 to 5 years. As an alternative to scheduling fires at specified mean intervals, we developed a goal-programming model (a form of linear programming model) and used it to identify an optimal fire schedule for achieving habitat and visual-quality objectives. In comparison with the 40-year stochastic mean fire interval, which maximized structural diversity, the optimal schedule produced comparable levels of both diversity and fire frequency. Our results show how simulation and goal-programming models can be used to evaluate prescribed fire-scheduling alternatives and to explore the comparative advantages of natural and optimal fire-management approaches. [ABSTRACT FROM AUTHOR]