Optimal control of spatial-dynamic processes: The case of biological invasions

This study examines the spatial nature of optimal bioinvasion control. We develop and parameterize a spatially explicit two-dimensional model of species spread that allows for differential control across space and time, and we solve for optimal control strategies. We find that the qualitative nature of optimal strategies depend in interesting ways on aspects of landscape and invasion geometry. For example, we show that reducing the extent of exposed invasion edge, through spread, removal, or strategically employing landscape features, can be an optimal strategy because it reduces long-term containment costs. We also show that optimal invasion control is spatially and temporally “forward-looking” in the sense that strategies should be targeted to slow the spread of an invasion in the direction of greatest potential long-term damages. These and other novel findings contribute to the largely nonspatial literature on optimally controlling invasions and to understanding control of spatial-dynamic processes in general.invasive species, spatial-dynamic processes, spatial spread, reaction-diffusion, management, cellular automaton, eradication, containment, spatial control, integer programming, Environmental Economics and Policy, Land Economics/Use, Resource /Energy Economics and Policy, Q, Q1, Q2, Q5,

Harnessing enforcement leverage at the border to minimize biological risk from international live species trade

Allocating inspection resources over a diverse set of imports to prevent entry of plant pests and pathogens presents a substantial policy design challenge. We model inspections of live plant imports and producer responses to inspections using a “state-dependent” monitoring and enforcement model. We capture exporter abatement response to a set of feasible inspection policies from the regulator. Conditional on this behavioral response, we solve the regulator’s problem of selecting the parameters for the state-dependent monitoring regime to minimize entry of infested shipments. We account for exporter heterogeneity, fixed penalties for noncompliance, imperfect abatement control and imperfect inspections at the border. Overall, we estimate that state-dependent targeting (based on historical interceptions) cuts the rate of infested shipments that are accepted by one-fifth, relative to uniformly allocated inspections

Network metrics can guide nearly-optimal management of invasive species at large scales

Invasive species harm biodiversity and ecosystem services, with global economic costs of invasions exceeding $40 billion annually. Widespread invasions are a particular challenge because they involve large spatial scales with many interacting components. In these contexts, typical optimization-based approaches to management may fail due to computational or data constraints. Here we evaluate an alternative solution that leverages network science, representing the invasion as occurring across a network of connected sites and using network metrics to prioritize sites for intervention. Such heuristic network-guided methods require less data and are less computationally intensive than optimization methods, yet network-guided approaches have not been bench-marked against optimal solutions for real-world invasive species management problems. We provide the first comparison of the performance of network-guided management relative to optimal solutions for invasive species, examining the placement of watercraft inspection stations for preventing spread of invasive zebra mussels through recreational boat movement within 58 Minnesota counties in the United States. To additionally test the promise of network-based approaches in limited data contexts, we evaluate their performance when using only partial data on network structure and invaded status. Metric-based approaches can achieve a median of 100% of optimal performance with full data. Even with partial data, 80% of optimal performance is achievable. Finally, we show that performance of metric-guided management improves for counties with denser and larger networks, suggesting this approach is viable for large-scale invasions. Together, our results suggest network metrics are a promising approach to guiding management actions for large-scale invasions.Comment: 29 pages, 8 figures, 3 table

Coupled ecological and management connectivity across administrative boundaries in undeveloped landscapes

Human-induced ecological boundaries, or anthropogenic ecotones, may arise where administrative boundaries meet on undeveloped lands. Landscape-level ecological processes related to factors such as fire, invasive species, grazing, resource extraction, wildlife, and water may be affected due to unique management strategies adopted by each administrative unit. Over time, different management can result in discernible ecological differences (e.g., species composition or soil characteristics). Thus, fragmentation in the management landscape can correspond to ecological fragmentation. Different ecological patterns may emerge due to an increase in the number of management units in a region, or due to an increase in the number of different types of management units in the region. Temporal effects and collaboration history can also affect the emergence of ecotones. We use conceptual models to explore the relationship between these aspects of management fragmentation and the anthropogenic ecotones between management parcels. We then use examples of different management challenges to explore how anthropogenic ecotones can disrupt ecological flows. Our models suggest that cross-boundary collaboration that enhances management connectivity is likely essential to ecological connectivity in the face of environmental and social change

Quantifying ecological variation across jurisdictional boundaries in a management mosaic landscape

Context Large landscapes exhibit natural heterogeneity. Land management can impose additional variation, altering ecosystem patterns. Habitat characteristics may reflect these management factors, potentially resulting in habitat differences that manifest along jurisdictional boundaries. Objectives We characterized the patchwork of habitats across a case study landscape, the Grand Canyon Protected Area-Centered Ecosystem. We asked: how do ecological conditions vary across different types of jurisdictional boundaries on public lands? We hypothesized that differences in fire and grazing, because they respond to differences in management over time, contribute to ecological differences by jurisdiction. Methods We collected plot-scale vegetation and soils data along boundaries between public lands units surrounding the Grand Canyon. We compared locations across boundaries of units managed differently, accounting for vegetation type and elevation differences that pre-date management unit designations. We used generalized mixed effects models to evaluate differences in disturbance and ecology across boundaries. Results Jurisdictions varied in evidence of grazing and fire. After accounting for these differences, some measured vegetation and soil properties also differed among jurisdictions. The greatest differences were between US Forest Service wilderness and Bureau of Land Management units. For most measured variables, US Forest Service non-wilderness units and National Park Service units were intermediate. Conclusions In this study, several ecological properties tracked jurisdictional boundaries, forming a predictable patchwork of habitats. These patterns likely reflect site differences that pre-date jurisdictions as well as those resulting from different management histories. Understanding how ecosystem differences manifest at jurisdictional boundaries can inform resource management, conservation, and cross-boundary collaborations

Optimizing management of invasions in an uncertain world using dynamic spatial models

Dispersal drives invasion dynamics of nonnative species and pathogens. Applying knowledge of dispersal to optimize the management of invasions can mean the difference between a failed and a successful control program and dramatically improve the return on investment of control efforts. A common approach to identifying optimal management solutions for invasions is to optimize dynamic spatial models that incorporate dispersal. Optimizing these spatial models can be very challenging because the interaction of time, space, and uncertainty rapidly amplifies the number of dimensions being considered. Addressing such problems requires advances in and the integration of techniques from multiple fields, including ecology, decision analysis, bioeconomics, natural resource management, and optimization. By synthesizing recent advances from these diverse fields, we provide a workflow for applying ecological theory to advance optimal management science and highlight priorities for optimizing the control of invasions. One of the striking gaps we identify is the extremely limited consideration of dispersal uncertainty in optimal management frameworks, even though dispersal estimates are highly uncertain and greatly influence invasion outcomes. In addition, optimization frameworks rarely consider multiple types of uncertainty (we describe five major types) and their interrelationships. Thus, feedbacks from management or other sources that could magnify uncertainty in dispersal are rarely considered. Incorporating uncertainty is crucial for improving transparency in decision risks and identifying optimal management strategies. We discuss gaps and solutions to the challenges of optimization using dynamic spatial models to increase the practical application of these important tools and improve the consistency and robustness of management recommendations for invasions

Analysis Benefits of invasion prevention: Effect of time lags, spread rates, and damage persistence

Quantifying economic damages caused by invasive species is crucial for cost-benefit analyses of biosecurity measures. Most studies focus on short-term damage estimates, but evaluating exclusion or prevention measures requires estimates of total anticipated damages from the time of establishment onward. The magnitude of such damages critically depends on the timing of damages relative to a species' arrival because costs are discounted back to the time of establishment. Using theoretical simulations, we illustrate how (ceteris paribus) total longterm damages, and hence the benefits of prevention efforts, are greater for species that a) have short lags between introduction and spread or between arrival at a location and initiation of damages, b) cause larger, short-lived damages (as opposed to smaller, persistent damages), and c) spread faster or earlier. We empirically estimate total long-term discounted impacts for three forest pests currently invading North America -gypsy moth (Lymantria dispar), hemlock woolly adelgid (Adelges tsugae), and emerald ash borer (Agrilus planipennis) -and discuss how damage persistence, lags between introduction and spread, and spread rates affect damages. Many temporal characteristics can be predicted for new invaders and should be considered in species risk analyses and economic evaluations of quarantine and eradication programs

Cooperation, Spatial-Dynamic Externalities, and Invasive Species Management

Most terrestrial biological invasions occur in landscapes comprising numerous, independently managed properties. Thus, control of invasion spread generally depends on the choices of many managers, each deciding the extent to control invasions on their property. Here we develop a spatially-explicit, integrated model of invasion spread and human behavior to examine how people’s control choices under laissez-faire affect patterns of invasion spread and the total costs and damages imposed by an invader. We evaluate how characteristics of the bioeconomic and social system, including the extent of cooperation among managers, affect the divergence between socially optimal and private control efforts. We find that system-wide invasion externalities generally increase with the potential range size of an invader and with marginal damages from invasion and decrease with marginal control costs and with the size of the invasion when it is discovered. As expected, private control decisions tend to under-control the invasion relative to socially optimal control. However, we also find that less extensive cooperation is needed to control invasions whose costs and damages otherwise lead to the largest externalities. This novel finding suggests that even small amounts of cooperation can avoid some of the worst invasion outcomes and coordination of control can provide large social benefits. This research highlights the importance of human behavior for affecting invasion spread and economic outcomes