Optimally managing under imperfect detection: a method for plant invasions

Early detection, herbicide resistance screening, and integrated management of invasive plant species: a review

Invasive plant species (IPS) are often considered weeds that cause high yield losses in crops, negatively affect the environment, and disrupt certain ecosystem services. The negative impact of IPS on biodiversity is increasing and disturbing native vegetation. The management of plant invasions can be divided in two phases (before and after invasion). Prior to introduction it is crucial to develop the knowledge base (biology, ecology, distribution, impact, management) on IPS, prevention measures and risk assessment. After introduction if eradication fails, the monitoring and the integrated management of IPS are imperative to prevent the naturalization and further dispersal. This review uses two major invasive weed species (Amaranthus palmeri S. Wats. and Solanum elaeagnifolium Cav.) as case studies to propose a framework for early detection, rapid herbicide resistance screening, and integrated management. The holistic framework that is presented exploits recent: (i) novel detection tools, (ii) rapid tests and assays for herbicide resistance, and (iii) biology, ecology, distribution traits, and management tools for the IPS. Farmers, advisors, researchers, and policymakers need briefing on IPS growth dynamics, adaptability rates, and response to conventional and novel treatments to prevent new invasions, eradicate isolated stands, and mitigate the impact of invasive weed species in the long term. © 2022 Society of Chemical Industry.

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.

Partial observability and management of ecological systems

The actual state of ecological systems is rarely known with certainty, but management actions must often be taken regardless of imperfect measurement (partial observability). Because of the difficulties in accounting for partial observability, it is usually treated in an ad hoc fashion, or simply ignored altogether. Yet incorporating partial observability into decision processes lends a realism that has the potential to improve ecological outcomes significantly. We review frameworks for dealing with partial observability, focusing specifically on dynamic ecological systems with Markovian transitions, i.e., transitions among system states that are influenced by the current system state and management action over time. Fully observable states are represented in an observable Markov decision process (MDP), whereas obscure or hidden states are represented in a partially observable process (POMDP). POMDPs can be seen as a natural extension of observable MDPs. Management under partial observability generalizes the situation for complete observability, by recognizing uncertainty about the system's state and incorporating sequential observations associated with, but not the same as, the states themselves. Decisions that otherwise would depend on the actual state must be based instead on state probability distributions (“belief states”). Partial observability requires adaptation of the entire decision process, including the use of belief states and Bayesian updates, valuation that includes expectations over observations, and optimal strategy that identifies actions for belief states over a continuous belief space. We compare MDPs and POMDPs and highlight POMDP applications to some common ecological problems. We clarify the structure and operations, approaches for finding solutions, and analytic challenges of POMDPs for practicing ecologists. Both observable and partially observable MDPs can use an inductive approach to identify optimal strategies and values, with a considerable increase in mathematical complexity with POMDPs. Better understanding of POMDPs can help decision makers manage imperfectly measured ecological systems more effectively.

Optimal management of stochastic invasion in a metapopulation with Allee effects

Invasive species account for incalculable damages worldwide, in both ecological and bioeconomic terms. The question of how a network of invasive populations can be optimally managed is one that deserves further exploration. A study accounting for partial observability and imperfect detection, in particular, could yield useful insights into species eradication efforts. Here, we generalized a simple model system that we developed in previous work. This model consists of three interacting populations with underlying strong Allee effects and stochastic dynamics, inhabiting distinct locations connected by dispersal, which can generate bistability. To explore the stochastic dynamics, we formulated an individual-based modeling approach. Next, using the theory of continuous-time Markov chains, we approximated the original high-dimensional model by a Markov chain with eight states, with each state corresponding to a combination of population thresholds. We then used the reduced model as the core for a powerful decision-making tool, referred to as a Partially Observable Markov Decision Process (POMDP). Analysis of this POMDP indicates when the system results in optimal management outcomes.

Robust Decision Analysis under Severe Uncertainty and Ambiguous Tradeoffs: An Invasive Species Case Study

Bayesian decision analysis is a useful method for risk management decisions, but is limited in its ability to consider severe uncertainty in knowledge, and value ambiguity in management objectives. We study the use of robust Bayesian decision analysis to handle problems where one or both of these issues arise. The robust Bayesian approach models severe uncertainty through bounds on probability distributions, and value ambiguity through bounds on utility functions. To incorporate data, standard Bayesian updating is applied on the entire set of distributions. To elicit our expert's utility representing the value of different management objectives, we use a modified version of the swing weighting procedure that can cope with severe value ambiguity. We demonstrate these methods on an environmental management problem to eradicate an alien invasive marmorkrebs recently discovered in Sweden, which needed a rapid response despite substantial knowledge gaps if the species was still present (i.e., severe uncertainty) and the need for difficult tradeoffs and competing interests (i.e., value ambiguity). We identify that the decision alternatives to drain the system and remove individuals in combination with dredging and sieving with or without a degradable biocide, or increasing pH, are consistently bad under the entire range of probability and utility bounds. This case study shows how robust Bayesian decision analysis provides a transparent methodology for integrating information in risk management problems where little data are available and/or where the tradeoffs are ambiguous.

Optimal invasive species surveillance in the real world: practical advances from research

When alien species make incursions into novel environments, early detection through surveillance is critical to minimizing their impacts and preserving the possibility of timely eradication. However, incipient populations can be difficult to detect, and usually, there are limited resources for surveillance or other response activities. Modern optimization techniques enable surveillance planning that accounts for the biology and expected behavior of an invasive species while exploring multiple scenarios to identify the most cost-effective options. Nevertheless, most optimization models omit some real-world limitations faced by practitioners during multi-day surveillance campaigns, such as daily working time constraints, the time and cost to access survey sites and personnel work schedules. Consequently, surveillance managers must rely on their own judgments to handle these logistical details, and default to their experience during implementation. This is sensible, but their decisions may fail to address all relevant factors and may not be cost-effective. A better planning strategy is to determine optimal routing to survey sites while accounting for common daily logistical constraints. Adding site access and other logistical constraints imposes restrictions on the scope and extent of the surveillance effort, yielding costlier but more realistic expectations of the surveillance outcomes than in a theoretical planning case.

Optimal spatial prioritization of control resources for elimination of invasive species under demographic uncertainty

Populations of invasive species often spread heterogeneously across a landscape, consisting of local populations that cluster in space but are connected by dispersal. A fundamental dilemma for invasive species control is how to optimally allocate limited fiscal resources across local populations. Theoretical work based on perfect knowledge of demographic connectivity suggests that targeting local populations from which migrants originate (sources) can be optimal. However, demographic processes such as abundance and dispersal can be highly uncertain, and the relationship between local population density and damage costs (damage function) is rarely known. We used a metapopulation model to understand how budget and uncertainty in abundance, connectivity, and the damage function, together impact return on investment (ROI) for optimal control strategies. Budget, observational uncertainty, and the damage function had strong effects on the optimal resource allocation strategy. Uncertainty in dispersal probability was the least important determinant of ROI. The damage function determined which resource prioritization strategy was optimal when connectivity was symmetric but not when it was asymmetric. When connectivity was asymmetric, prioritizing source populations had a higher ROI than allocating effort equally across local populations, regardless of the damage function, but uncertainty in connectivity structure and abundance reduced ROI of the optimal prioritization strategy by 57% on average depending on the control budget. With low budgets (monthly removal rate of 6.7% of population), there was little advantage to prioritizing resources, especially when connectivity was high or symmetric, and observational uncertainty had only minor effects on ROI. Allotting funding for improved monitoring appeared to be most important when budgets were moderate (monthly removal of 13-20% of the population). Our result showed that multiple sources of observational uncertainty should be considered concurrently for optimizing ROI. Accurate estimates of connectivity direction and abundance were more important than accurate estimates of dispersal rates. Developing cost-effective surveillance methods to reduce observational uncertainties, and quantitative frameworks for determining how resources should be spatially apportioned to multiple monitoring and control activities are important and challenging future directions for optimizing ROI for invasive species control programs.

Frequencies of decision making and monitoring in adaptive resource management

Adaptive management involves learning-oriented decision making in the presence of uncertainty about the responses of a resource system to management. It is implemented through an iterative sequence of decision making, monitoring and assessment of system responses, and incorporating what is learned into future decision making. Decision making at each point is informed by a value or objective function, for example total harvest anticipated over some time frame. The value function expresses the value associated with decisions, and it is influenced by system status as updated through monitoring. Often, decision making follows shortly after a monitoring event. However, it is certainly possible for the cadence of decision making to differ from that of monitoring. In this paper we consider different combinations of annual and biennial decision making, along with annual and biennial monitoring. With biennial decision making decisions are changed only every other year; with biennial monitoring field data are collected only every other year. Different cadences of decision making combine with annual and biennial monitoring to define 4 scenarios. Under each scenario we describe optimal valuations for active and passive adaptive decision making. We highlight patterns in valuation among scenarios, depending on the occurrence of monitoring and decision making events. Differences between years are tied to the fact that every other year a new decision can be made no matter what the scenario, and state information is available to inform that decision. In the subsequent year, however, in 3 of the 4 scenarios either a decision is repeated or monitoring does not occur (or both). There are substantive differences in optimal values among the scenarios, as well as the optimal policies producing those values. Especially noteworthy is the influence of monitoring cadence on valuation in some years. We highlight patterns in policy and valuation among the scenarios, and discuss management implications and extensions.

Robust set-point regulation for ecological models with multiple management goals

Population managers will often have to deal with problems of meeting multiple goals, for example, keeping at specific levels both the total population and population abundances in given stage-classes of a stratified population. In control engineering, such set-point regulation problems are commonly tackled using multi-input, multi-output proportional and integral (PI) feedback controllers. Building on our recent results for population management with single goals, we develop a PI control approach in a context of multi-objective population management. We show that robust set-point regulation is achieved by using a modified PI controller with saturation and anti-windup elements, both described in the paper, and illustrate the theory with examples. Our results apply more generally to linear control systems with positive state variables, including a class of infinite-dimensional systems, and thus have broader appeal.

Adapting environmental management to uncertain but inevitable change

Implementation of adaptation actions to protect biodiversity is limited by uncertainty about the future. One reason for this is the fear of making the wrong decisions caused by the myriad future scenarios presented to decision-makers. We propose an adaptive management (AM) method for optimally managing a population under uncertain and changing habitat conditions. Our approach incorporates multiple future scenarios and continually learns the best management strategy from observations, even as conditions change. We demonstrate the performance of our AM approach by applying it to the spatial management of migratory shorebird habitats on the East Asian-Australasian flyway, predicted to be severely impacted by future sea-level rise. By accounting for non-stationary dynamics, our solution protects 25,000 more birds per year than the current best stationary approach. Our approach can be applied to many ecological systems that require efficient adaptation strategies for an uncertain future.

The optimal number of surveys when detectability varies

The survey of plant and animal populations is central to undertaking field ecology. However, detection is imperfect, so the absence of a species cannot be determined with certainty. Methods developed to account for imperfect detectability during surveys do not yet account for stochastic variation in detectability over time or space. When each survey entails a fixed cost that is not spent searching (e.g., time required to travel to the site), stochastic detection rates result in a trade-off between the number of surveys and the length of each survey when surveying a single site. We present a model that addresses this trade-off and use it to determine the number of surveys that: 1) maximizes the expected probability of detection over the entire survey period; and 2) is most likely to achieve a minimally-acceptable probability of detection. We illustrate the applicability of our approach using three practical examples (minimum survey effort protocols, number of frog surveys per season, and number of quadrats per site to detect a plant species) and test our model's predictions using data from experimental plant surveys. We find that when maximizing the expected probability of detection, the optimal survey design is most sensitive to the coefficient of variation in the rate of detection and the ratio of the search budget to the travel cost. When maximizing the likelihood of achieving a particular probability of detection, the optimal survey design is most sensitive to the required probability of detection, the expected number of detections if the budget were spent only on searching, and the expected number of detections that are missed due to travel costs. We find that accounting for stochasticity in detection rates is likely to be particularly important for designing surveys when detection rates are low. Our model provides a framework to do this.

Assessing the utility of statistical adjustments for imperfect detection in tropical conservation science

In recent years, there has been a fast development of models that adjust for imperfect detection. These models have revolutionized the analysis of field data, and their use has repeatedly demonstrated the importance of sampling design and data quality. There are, however, several practical limitations associated with the use of detectability models which restrict their relevance to tropical conservation science.

We outline the main advantages of detectability models, before examining their limitations associated with their applicability to the analysis of tropical communities, rare species and large‐scale data sets. Finally, we discuss whether detection probability needs to be controlled before and/or after data collection.

Models that adjust for imperfect detection allow ecologists to assess data quality by estimating uncertainty and to obtain adjusted ecological estimates of populations and communities. Importantly, these models have allowed informed decisions to be made about the conservation and management of target species.

Data requirements for obtaining unadjusted estimates are substantially lower than for detectability‐adjusted estimates, which require relatively high detection/recapture probabilities and a number of repeated surveys at each location. These requirements can be difficult to meet in large‐scale environmental studies where high levels of spatial replication are needed, or in the tropics where communities are composed of many naturally rare species. However, while imperfect detection can only be adjusted statistically, covariates of detection probability can also be controlled through study design. Using three study cases where we controlled for covariates of detection probability through sampling design, we show that the variation in unadjusted ecological estimates from nearly 100 species was qualitatively the same as that obtained from adjusted estimates. Finally, we discuss that the decision as to whether one should control for covariates of detection probability through study design or statistical analyses should be dependent on study objectives.

Synthesis and applications. Models that adjust for imperfect detection are an important part of an ecologist's toolkit, but they should not be uniformly adopted in all studies. Ecologists should never let the constraints of models dictate which questions should be pursued or how the data should be analysed, and detectability models are no exception. We argue for pluralism in scientific methods, particularly where cost‐effective applied ecological science is needed to inform conservation policy at a range of different scales and in many different systems.

Models that adjust for imperfect detection are an important part of an ecologist's toolkit, but they should not be uniformly adopted in all studies. Ecologists should never let the constraints of models dictate which questions should be pursued or how the data should be analysed, and detectability models are no exception. We argue for pluralism in scientific methods, particularly where cost‐effective applied ecological science is needed to inform conservation policy at a range of different scales and in many different systems.

Quantifying extinction probabilities from sighting records: inference and uncertainties

Methods are needed to estimate the probability that a population is extinct, whether to underpin decisions regarding the continuation of a invasive species eradication program, or to decide whether further searches for a rare and endangered species could be warranted. Current models for inferring extinction probability based on sighting data typically assume a constant or declining sighting rate. We develop methods to analyse these models in a Bayesian framework to estimate detection and survival probabilities of a population conditional on sighting data. We note, however, that the assumption of a constant or declining sighting rate may be hard to justify, especially for incursions of invasive species with potentially positive population growth rates. We therefore explored introducing additional process complexity via density-dependent survival and detection probabilities, with population density no longer constrained to be constant or decreasing. These models were applied to sparse carcass discoveries associated with the recent incursion of the European red fox (Vulpes vulpes) into Tasmania, Australia. While a simple model provided apparently precise estimates of parameters and extinction probability, estimates arising from the more complex model were much more uncertain, with the sparse data unable to clearly resolve the underlying population processes. The outcome of this analysis was a much higher possibility of population persistence. We conclude that if it is safe to assume detection and survival parameters are constant, then existing models can be readily applied to sighting data to estimate extinction probability. If not, methods reliant on these simple assumptions are likely overstating their accuracy, and their use to underpin decision-making potentially fraught. Instead, researchers will need to more carefully specify priors about possible population processes.

Addressing structural and observational uncertainty in resource management

Most natural resource management and conservation problems are plagued with high levels of uncertainties, which make good decision making difficult. Although some kinds of uncertainties are easily incorporated into decision making, two types of uncertainty present more formidable difficulties. The first, structural uncertainty, represents our imperfect knowledge about how a managed system behaves. The second, observational uncertainty, arises because the state of the system must be inferred from imperfect monitoring systems. The former type of uncertainty has been addressed in ecology using Adaptive Management (AM) and the latter using the Partially Observable Markov Decision Processes (POMDP) framework. Here we present a unifying framework that extends standard POMDPs and encompasses both standard POMDPs and AM. The approach allows any system variable to be observed or not observed and uses any relevant observed variable to update beliefs about unknown variables and parameters. This extends standard AM, which only uses realizations of the state variable to update beliefs and extends standard POMDP by allowing more general stochastic dependence among the observable variables and the state variables. This framework enables both structural and observational uncertainty to be simultaneously modeled. We illustrate the features of the extended POMDP framework with an example.

Dispersal and the design of effective management strategies for plant invasions: matching scales for success

Dispersal of propagules makes invasions a fundamentally spatial phenomenon, and to be effective, management actions to control or eradicate invasive species must take this spatial structure into account. While there is a vibrant literature linking detailed dispersal measurements to the rate of invasive spread, and a separate literature focused on incorporating management into invasive models in order to improve the control of weeds, there are relatively fewer manuscripts incorporating state-of-the-art dispersal modeling and management modeling together to provide on-ground recommendations for structuring effective management. In this paper, we perform a generalized analysis of a spatially explicit, individual-based simulation model of invasion management with empirically determined dispersal processes, illustrated with the example of Miconia calvescens in the Australian Wet Tropics rain forest, to explore how matching the spatial scale of management to the spatial scale of the dispersal processes underpinning invasion influences the success of management. We find that management strategies designed to maximize the number of weeds removed from the management region, either in the first year of management or over longer periods, provide a poor estimate of the spatial scale of management that maximizes the probability of eradication. We show that achieving a goal of certainty of eradication requires exceeding a minimal spatial scale of management and total management resourcing. We generalize these results to examine how the spatial scale of dispersal drives the spatial scale of effective management strategies. These results show that to be effective, management of dispersal-driven invasions must occur at spatial scales determined by the scale of dispersal processes, and resourced accordingly. It illustrates how those scales might be calculated for a specific case for which detailed dispersal data are available and generalizes the result to highlight how dispersal scale drives the scale of effective management. The results highlight the importance of understanding the ecological drivers of invasion to structure effective management.

Detection and plant monitoring programs: lessons from an intensive survey of Asclepias meadii with five observers

Monitoring programs, where numbers of individuals are followed through time, are central to conservation. Although incomplete detection is expected with wildlife surveys, this topic is rarely considered with plants. However, if plants are missed in surveys, raw count data can lead to biased estimates of population abundance and vital rates. To illustrate, we had five independent observers survey patches of the rare plant Asclepias meadii at two prairie sites. We analyzed data with two mark-recapture approaches. Using the program CAPTURE, the estimated number of patches equaled the detected number for a burned site, but exceeded detected numbers by 28% for an unburned site. Analyses of detected patches using Huggins models revealed important effects of observer, patch state (flowering/nonflowering), and patch size (number of stems) on probabilities of detection. Although some results were expected (i.e. greater detection of flowering than nonflowering patches), the importance of our approach is the ability to quantify the magnitude of detection problems. We also evaluated the degree to which increased observer numbers improved detection: smaller groups (3-4 observers) generally found 90 - 99% of the patches found by all five people, but pairs of observers or single observers had high error and detection depended on which individuals were involved. We conclude that an intensive study at the start of a long-term monitoring study provides essential information about probabilities of detection and what factors cause plants to be missed. This information can guide development of monitoring programs.

Setting realistic recovery targets for two interacting endangered species, sea otter and northern abalone

Failure to account for interactions between endangered species may lead to unexpected population dynamics, inefficient management strategies, waste of scarce resources, and, at worst, increased extinction risk. The importance of species interactions is undisputed, yet recovery targets generally do not account for such interactions. This shortcoming is a consequence of species-centered legislation, but also of uncertainty surrounding the dynamics of species interactions and the complexity of modeling such interactions. The northern sea otter (Enhydra lutris kenyoni) and one of its preferred prey, northern abalone (Haliotis kamtschatkana), are endangered species for which recovery strategies have been developed without consideration of their strong predator-prey interactions. Using simulation-based optimization procedures from artificial intelligence, namely reinforcement learning and stochastic dynamic programming, we combined sea otter and northern abalone population models with functional-response models and examined how different management actions affect population dynamics and the likelihood of achieving recovery targets for each species through time. Recovery targets for these interacting species were difficult to achieve simultaneously in the absence of management. Although sea otters were predicted to recover, achieving abalone recovery targets failed even when threats to abalone such as predation and poaching were reduced. A management strategy entailing a 50% reduction in the poaching of northern abalone was a minimum requirement to reach short-term recovery goals for northern abalone when sea otters were present. Removing sea otters had a marginally positive effect on the abalone population but only when we assumed a functional response with strong predation pressure. Our optimization method could be applied more generally to any interacting threatened or invasive species for which there are multiple conservation objectives.

Quantifying levels of biological invasion: towards the objective classification of invaded and invasible ecosystems

Biological invasions are a global phenomenon that threatens biodiversity, and few, if any, ecosystems are free from alien species. The outcome of human-mediated introductions is affected by the invasiveness of species and invasibility of ecosystems, but research has primarily focused on defining, characterizing and identifying invasive species; ecosystem invasibility has received much less attention. A prerequisite for characterizing invasibility is the ability to compare levels of invasion across ecosystems. In this paper, we aim to identify the best way to quantify the level of invasion by nonnative animals and plants by reviewing the advantages and disadvantages of different metrics. We explore how interpretation and choice of these measures can depend on the objective of a study or management intervention. Based on our review, we recommend two invasion indices and illustrate their use by applying them to two case studies. Relative alien species richness and relative alien species abundance indicate the contribution that alien species make to a community. They are easy to measure, can be applied to various taxa, are independent of scale and are comparable across regions and ecosystems, and historical data are often available. The relationship between relative alien richness and abundance can indicate the presence of dominant alien species and the trajectory of invasion over time, and can highlight ecosystems and sites that are heavily invaded or especially susceptible to invasion. Splitting species into functional groups and examining invasion patterns of transformer species may be particularly instructive for gauging effects of alien invasion on ecosystem structure and function. Establishing standard, transparent ways to define and quantify invasion level will facilitate meaningful comparisons among studies, ecosystem types and regions. It is essential for progress in ecology and will help guide ecosystem restoration and management.

General rules for managing and surveying networks of pests, diseases, and endangered species

The efficient management of diseases, pests, or endangered species is an important global issue faced by agencies constrained by limited resources. The management challenge is even greater when organisms are difficult to detect. We show how to prioritize management and survey effort across time and space for networks of susceptible-infected-susceptible subpopulations. We present simple and robust rules of thumb for protecting desirable, or eradicating undesirable, subpopulations connected in typical network patterns (motifs). We further demonstrate that these rules can be generalized to larger networks when motifs are combined in more complex formations. Results show that the best location to manage or survey a pest or a disease on a network is also the best location to protect or survey an endangered species. The optimal starting point in a network is the fastest motif to manage, where line, star, island, and cluster motifs range from fast to slow. Managing the most connected node at the right time and maintaining the same management direction provide advantages over previously recommended outside-in strategies. When a species or disease is not detected and our belief in persistence decreases, our results recommend shifting resources toward management or surveillance of the most connected nodes. Our analytic approximation provides guidance on how long we should manage or survey networks for hard-to-detect organisms. Our rules take into account management success, dispersal, economic cost, and imperfect detection and offer managers a practical basis for managing networks relevant to many significant environmental, biosecurity, and human health issues.