Sudden Oak Death Material Decontamination

Nonnative, or exotic, invasive species introduce risks to forest ecosystems. Invasive species are altering fire regimes, hydrology, nutrient cycling, and productivity of ecosystems (Dukes and Mooney 2004). The invasive species issue is made especially complex because there are thousands of potential invasive species and new and established plants, plant material, pests, and pathogens are in constant movement. Adequate data are not always available to support rigorous quantitative modeling of the different stages of invasion. However, even a semiquantitative rule-based approach can help to identify locations that contain host species susceptible to specific pathogens or insect pests, and where propagules are more likely to enter based on the current locations of the invasive species, ports of entry, and methods of spread.

Unintentional exotic species invasions are often a function of ecological factors, often attacking forests compromised by other threats. Economic factors such as global travel and trade also play a role. In some instances, exotics are introduced intentionally to help irradicate other problematic species. In any case, a review of this section provides the reader with information about decision-making in invasive species management, as well as methods useful for evaluating risks from invasive species by modeling invasive plant, insect, and pathogen species.

To further review exotic invasive species, consider reading the following Environmental Threats Case Studies:

Uncertainty Estimation for Map-Based Analyses

Previsual Detection of Two Conifer-Infesting Adelgid Species in North American Forests

Estimating the Susceptibility to Phytophthora alni Globally Using Both Statistical Analyses and Expert Knowledge

A Landscape Scale Remote Sensing/GIS Tool to Assess Eastern Hemlock Vulnerability to Hemlock Woolly Adelgid Induced Decline

Assessment of Habitat Threats to Shrublands in the Great Basin

A Spatial Model for Predicting Effects of Climate Change on Swiss Needle Cast Disease Severity in Pacific Northwest Forests

Spread of Invasive Plants from Roads to River Systems in Alaska: A Network Model

Probabilistic regional risk assessment methodologies were reviewed to identify the methods that are currently in use and are capable of estimating threats to ecosystems from fire and fuels, invasive species, and their interactions with stressors. In a companion section, methods useful for evaluating risks from fire are highlighted. In this chapter, methods useful for evaluating risks from invasive species are highlighted.

The issue of invasive species is large and complex because there are thousands of potential invasive species, and constant movement of new and established plants, plant material, pests, and pathogens. Adequate data are not always available to support rigorous quantitative modeling of the different stages of invasion. However, even a semiquantitative rule-based approach can help to identify locations that contain host species susceptible to specific pathogens or insect pests, and where propagules are more likely to enter based on the current locations of the invasive species, ports of entry, and methods of spread. Predicting long-distance movement is much more difficult, as such events are rare, often poorly understood, and are often influenced by human behavior. Even so, published methods to make probabilistic predictions of pest establishment could be expanded to provide quantitative estimates of spread beyond an initial port of entry. Many invasive species are transported along roads, and so road networks provide some information about the likelihood of introduction into a new region.

Models based on fundamental biological and physical processes, such as population demographics and movement of organisms, can be more robust than purely statistical approaches. Process-based models may better support extrapolation beyond the range of available or historical data because they use predictor variables that represent physical and biological processes. However, even simple correlative approaches may be useful to quantify the overlap in spatial distribution of stressors and ecological receptors as a screening-level analysis. Furthermore, if predictors are chosen carefully, they may represent important processes. For example, data on non-indigenous species may be quite useful for predicting the occurrence of much rarer invasive species because the correlation is based on the key processes of human-influenced transport, establishment, reproduction, and dispersal of propagules. Ecological niche-modeling approaches are useful because they can use data from museum collections in other countries to make estimates of potential new range areas in the United States. Other spatial data such as road networks may also be useful to predict the number of nonindigenous species or presence of a particular species. Such relationships may also support extrapolation to future conditions if there will be more roads or a higher traffic volume.

As for any regional stressor, the use of multiple models and a weight of evidence approach would help to increase confidence in predictions of ecological risks from invasive species. Two approaches to predicting the risk of Asian long-horned beetle throughout United States forests make quite different predictions because they focus on different stages in the process of establishment and spread, thus combining such approaches should result in more robust predictions. Invasive species management should be addressed at multiple spatial scales, including reducing importation of new species at border crossings and ports, national and regional mapping of locations of invasive species, methods to reduce long distance transport, and methods to reduce local movement.

To further review modeling invasive species, consider reading the following Environmental Threats Case Studies:

Modeling Potential Movements of the Emerald Ash Borer: the Model Framework

This review provides an overview of issues in probabilistic risk modeling at the regional scale and suggestions for productive directions for future risk assessments and research.

Invasive nonindigenous species are a serious and increasing threat to many ecosystems throughout the United States. (NRC 2002, Pimentel 2005). For example, invasive species are implicated as threats for more than half of all endangered species in the United States (Wilcove and others 1998). Invasive species are also altering fire regimes, hydrology, nutrient cycling, and productivity of ecosystems in the Western United States, particularly rangelands and riparian areas (Dukes and Mooney 2004). Plant species such as yellow star-thistle (Centaurea solstitialis L.), other Centaurea species, and cheatgrass (Bromus tectorum L.) have overtaken large areas of native ecosystems in the Western United States (LeJeune and Seastedt 2001). Leafy spurge (Euphorbia esula L.), knapweeds (Centaurea L. sp.), tamarisk (also known as salt cedar, Tamarix ramosissima Ledeb.), nonnative thistles, purple loosestrife (Lythrum salicaria L.), and cheatgrass are some of the most severe problems on National Forest lands. For example, the number of counties in Washington, Oregon, Montana, and Wyoming where yellow star-thistle has been found has been increasing exponentially during the last 100 years (D'Antonio and others 2004). Furthermore, the number of new exotic species has increased roughly linearly over this time period, reaching a total of nearly 800 by 1997 (D'Antonio and others 2004). Annual costs of selected non-indigenous species in the United States have been estimated at $120 million (Pimentel and others 2005). However, this estimate does not account for all effects of invasive species on rangelands and forests (Dukes and Mooney 2004), and it is clear that such costs are substantial. Despite the difficulty in quantifying economic damage, there is substantial evidence suggesting that invasive species have many deleterious effects in ecosystems in the Western United States, and that improved management of invasive species in wildlands is crucial (D'Antonio and others 2004). For example, tamarisk alone has been estimated to cost $133 to $285 million per year (in 1998 United States dollars) for lost ecosystem services including irrigation water, municipal water, hydropower, and flood control (Zavaleta 2000).

Various aspects of invasive species biology and ecology, as well as policy and management issues (NRC 2002), are addressed in many published reviews. Review briefly are some key issues, but the focus in this piece is on modeling methods suitable for spatially explicit probabilistic risk assessments for invasive species. This section, and the companion section Modeling Fire, present results of a project sponsored by the United States Department of Agriculture (USDA) Forest Service, Western Wildlands Threat Assessment Center during its development; but these results should not be construed to represent the views of the Center nor its personnel. The overall goal of the project was to identify promising methods for analyzing ecological risks to forest, rangeland, and wildland ecosystems from multiple stressors. The results of such risk analyses are intended to provide information useful for strategic planning and management of wildlands including national forests. The specific goal of this section is to identify modeling approaches suitable for making spatially explicit, probabilistic estimates of ecological risks from invasive plant, insect, and pathogen species throughout large regions such as the Western United States. Such modeling approaches ideally should be capable of:

1. Calculating risk of a detrimental environmental effect.

2. Using spatially heterogeneous environmental data to drive calculation of risk at different points throughout a region. Spatial scales of interest include landscape, sub-State region, State, region of the United States, or the entire conterminous United States.

3. Relying primarily on available regional (in United States, state or multi-State) or national data.

4. Being useful for many species, not just a single invasive species.

5. Modeling effects of interaction among multiple stressors.

6. Modeling effects of changes in environmental conditions in the future.

Selected modeling approaches relevant to the goals listed above are reviewed, and more detailed analyses of specific aspects of invasive species assessment and management are provided by other sections within this broader review.

This section provides an overview of the stages of the invasion process, key factors that affect these stages, and different frameworks that can be used to assess risks due to invasive species. The process by which a nonindigenous species becomes an invasive species can be divided into the following 5 stages:

1. Uptake/entry into transport system

2. Survival and transport to the United States via land, air, or water, with or without vectors

3. Initial establishment—survival and reproduction

4. Local dispersion

5. Widespread dispersion

Three classes of key factors influence the likelihood that a potential invader will pass through each stage: (A) propagule pressure; (B) physicochemical requirements of the potential invader; and (C) community interactions (Colautti and MacIsaac 2004). However, even successful modeling of all stages of the invasion process still does not address the likelihood or degree of damage caused by the invasive species. For this purpose, an ecological risk assessment approach is required.

The topic of invasive species has begun to be addressed by practitioners of ecological risk assessment (Andersen and others 2004a, 2004b, Stohlgren and Schnase 2006). Andersen and others (2004a, 2004b) review the regulatory framework for invasive species in the United States and some of the issues in extending the approach to ecological risk assessment (originally developed for contaminants), in order to address biological stressors such as invasive species. They also provide information about a series of articles of the journal “Risk Analysis” that report the results of a joint workshop between the Society for Risk Analysis Ecological Risk Assessment Specialty Group and the Ecological Society of America Theoretical Ecology Section. In addition, they identify research needs for this field. Of relevance to this chapter, they suggest that ’Spatially explicit, multiscale decision support systems will contribute to better decision making through enhanced credibility, an explicit and direct relationship with managing for sustainability, and explicit illustration of trade-offs and the cost of inaction.’ Presented in one of the articles in this series is a model of establishment risks for Asian long-horned beetle (Anoplophora glabripennis Motschulsky) introduction via solid wood packing materials (Bartell and Nair 2004). This approach estimates both the probability of establishment at the port of entry and the probability of spread based on environmental factors, host availability, and traits of the invasive species. Uncertainty in key parameters is investigated by means of Monte Carlo analysis. Additionally, there is investigation of the efficacy of different management techniques. Integration of quantitative risk analysis and quantitative analysis of management options within a single analytical framework is much too rare and should be applied more widely. Another article in this series describes how the conceptual model in the relative risk model can be applied to predict the effects of invasive species (Landis 2003). This approach is promising in that it is capable of addressing multiple stressors simultaneously at the regional scale by means of a ranking procedure. Although complete risk assessments are not reported in this article, it illustrates how invasive species risk can be analyzed at the regional scale in the context of multiple stressors and multiple endpoints. A case study of this approach has been implemented for a European green crab (Carcinus maenas L.) for a region of Washington State (Colnar and Landis, in press).

Most exotic plant species have been introduced to the United States intentionally, whereas most insects and pathogens have entered the United States unintentionally (Mack and Erneberg 2002). Global travel and trade have increased the amount of plant material, wood, and wood products moving into United States ports, increasing the likelihood of introduction of invasive plants, insects, and pathogens. By 2020, it has been predicted that more than 100 new insect species and 5 new plant pathogens will become established (Levine and D'Antonio 2003). A particularly high-risk pathway for forest insects and pathogens is importation of raw logs (Tkacz 2002). As an example for the Pacific Northwest, surveys of ports, port areas, mills and businesses known to have received or handled imported wood or wood products from 1996 to 1998 found 7 species of wood-boring beetles from Asia, Europe, and the Eastern United States (Mudge and others 2001). For the United States as a whole, inspections of all types of products in four cargo pathways at ports and border crossings found the highest rate of insect introductions in refrigerated maritime cargo, with 1 new insect species found in every 54 inspections (Work and others 2005). It was estimated in this study that fewer than half of such new species are detected, and 42 insect species may have become established from 1997 to 2001. These species do not necessarily pose a high risk of widespread infestation or damage, but they do indicate that exotic species are entering the United States at an alarming rate. Many of the issues of invasive species transport and establishment from other countries to the United States also apply to establishment of new populations due to long-distance transport of invasive species among regions in the United States Gypsy moth (Lymantria dispar L.) is an example species known to cause severe infestation and damage in Eastern United States forests (Liebhold and Tobin 2006). Gypsy moth has been long established in the Eastern United States but has been prevented from establishing, to date, in the Pacific Northwest due to surveillance and eradication efforts (Hayes and Ragenovich 2001).

To manage invasions and reduce risks, it is vastly more cost-effective to prevent establishment, or eradicate an invasive species as soon after entry as possible (Simberloff 2003, Stocker 2004). However, most invasive species are difficult to locate and may not appear to present any significant risk to ecosystems until they have become well established, often many decades after introduction. Thus, most management and control efforts focus on severe known problems rather than preventing future severe problems. Also unfortunately, it is difficult to predict which nonindigenous species will become invasive, and which invasive species will become severe problems (Smith and others 1999). A number of initiatives have been undertaken in the United States to address various aspects of invasive species monitoring, risk assessment, and management due to the severity of problems caused by invasive species.

A number of international, national, and regional efforts are underway to attempt to reduce the risks posed by invasive species. Some of these efforts for the United States are discussed briefly below, with a focus on programs related to forest and rangeland ecosystems. It is beyond the scope of this review to discuss all international programs that may provide valuable information for invasive species in the United States. However, some sources of global information are mentioned in the subsequent section on invasive species databases.

The National Invasive Species Council (NISC) consists of eight Federal departments and was formed in 1999 by Executive Order 13112. The NISC 2001 National Management Plan called for development of a risk analysis system for non-native species by 2003. The NISC is intended to provide a gateway to information, programs, organizations, and services about invasive species. Their web site ( http://www.invasivespecies.gov) provides information about the impacts of invasive species and the Federal government's response, as well as select species profiles and links to agencies and organizations dealing with invasive species issues.

The USDA Animal and Plant Health Inspection Service (APHIS) protects not only agricultural but also forest, rangeland, and wetland ecosystems. APHIS works closely with the USDA Forest Service and the U.S. Department of the Interior's Bureau of Land Management, National Park Service, and Fish and Wildlife Service. APHIS conducts risk assessments with a dual mission to promote international trade and prevent invasive species that may cause serious harm from entering the United States. Some APHIS activities focus on protecting and managing endangered species as well as migratory bird populations. APHIS maintains the Port Information Database, and there is great potential to strengthen and make broader use of this database for understanding the pathways taken by invasive species entering the United States (NRC 2002).

The USDA Forest Service, working in conjunction with Federal, State, Tribal, and private partners, has developed the Early Warning System (EWS) to detect and respond to environmental threats to forest lands in the United States. The EWS is composed of many existing programs, along with new initiatives such as the Western Wildland Environmental Threat Assessment Center and the Eastern Forest Environmental Threat Assessment Center. The EWS addresses potential catastrophic threats such as insects, diseases, invasive species, fire, weather-related risks, and other episodic events. The system is intended to:

1. improve understanding of the crucial elements involved in early detection and response to environmental threats
2. help identify and remedy weaknesses in the current system of early detection and response
3. aid for strategic planning and resource allocation

There are many groups both within and outside the Forest Service that participate in the process of detecting and responding to threats to forests. Further information about some component groups that conduct regional risk analyses is presented in other chapters in this volume. Further information about the EWS is available at the following web site: < http://www.fs.fed.us/foresthealth/programs/early_warning_system.shtml>.

The National Aeronautic and Space Administration (NASA) and the U.S. Geological Service (USGS) are developing a National Invasive Species Forecasting System (ISFS) for the management and control of invasive species on Department of Interior and adjacent lands. The system provides a framework for using USGS’s early detection and monitoring protocols and predictive models to process remote sensing data from the Moderate Resolution Imaging Spectroradiometer (MODIS), the Enhanced Thematic Mapper, and the Advanced Spaceborne Thermal Emission and Reflection Radiometer as well as commercial remote sensing data. The goal is to create on-demand, regional-scale assessments of invasive species patterns and vulnerable habitats. Additional information can be found at the following web site: http://bp.gsfc.nasa.gov/. This approach has recently been used to predict the relative suitability of all areas in the conterminous United States for tamarisk, an invasive woody shrub (Morisette and others 2006). This analysis is reviewed below under the heading of USGS & NASA Invasive Species MODIS-Regression Methodology.

Within the USDA Forest Service, the establishment of the two Threat Assessment Centers is a key part of the strategy for improving the management of invasive species. These efforts build upon ongoing programs and projects such as the Forest Inventory and Analysis Program (including Forest Health Monitoring) and Forest Health Protection. Further information about the strategies of these agencies for invasive species management is provided at the following web site: http://www.off-road.com/land/invasive_species_strategy.html. Recommendations for control of invasives in rangelands are provided at the following web site: http://www.fs.fed.us/rangelands/ecology/invasives.shtml

The USDA Forest Service’s Forest Health Technology Enterprise Team (FHTET) is using an expert opinion approach to model risks of invasive pests and tree pathogens at the national scale for national strategic planning purposes. Potential tree mortality risk is modeled based on expert opinion, forest inventory data, and other GIS (geographic information system) data (Marsden and others 2005), also see the following URL: http://www.fs.fed.us/foresthealth/technology/products.shtml. Further discussion of this approach is presented below under the heading of “FHTET national risk map”.

Many kinds of regional data may be useful for developing regional probabilistic risk assessments, including land cover and land use data, transportation networks, (e.g., roads and trails), hydrography, climate, digital elevation models, etc. Many such databases are available in GIS format from the National Atlas, which also includes data on selected invasive species (http://www.nationalatlas.gov/atlasftp.html). Data on land use is available from the National Land Cover Characterization database that is being compiled across States as a cooperative mapping effort of the Multi-Resolution Land Characteristics Consortium. Landcover databases are being developed by bioregion based on remotely sensed imagery acquired from 1999 to 2003 and are complete or nearly complete for most portions of the United States, including the West Coast and much of the Southeast ( http://www.mrlc.gov/mrlc2k_nlcd.asp). It is beyond the scope of this review to discuss all of these types of data, or even all types of databases specifically on invasive species, but a brief overview of invasive species survey data is presented below.

At the global scale, the Global Invasive Species Information Network is developing an online registry of datasets related to non-native species (Simpson 2004), and ongoing efforts are being made to develop linkages among national and multi-country invasive species databases (Simpson and others. 2006). The Global Invasive Species Programme (Mooney 1999) provides an online list of invasive species databases, including those covering the conterminous United States, Alaska, and Hawaii (http://www.gisp.org/links/index.asp). In the United States, a survey was undertaken recently to identify datasets of non-native species at county, State, region, national, and global scales (Crall and others 2006). Based on a literature survey, Internet search, and responses from surveys sent to 1,500 experts, a total of 319 datasets were identified, and metadata were collected for most datasets (79 percent). Of the total, 57 percent are available online (see the following web site for further information: http://www.niiss.org). Categories of datasets for which metadata are available consist of the following: 77 percent cover vegetation, 38 percent cover vertebrates, 77 percent cover invertebrates, 14 percent cover pathogens, and 9 percent cover fungi. Note that these percentages sum to greater than 100 percent because some datasets cover multiple taxa or categories. The scale of datasets for which metadata are available are as follows: 33 percent are at the county scale, 20 percent at the State scale, 17 percent at the multi-State regional scale, 15 percent are national, and 14 percent are global. Although this number of datasets is encouraging, the authors note that only 55 percent of the datasets have a quality assurance and quality control procedure, suggesting that the accuracy of many datasets may be questionable or undetermined.

Other sources of data useful for regional assessments of invasive species are databases developed by the Forest Inventory and Analysis (FIA) program of the USDA Forest Service (http://fia.fs.fed.us). The FIA program collects data for all land meeting a specific definition of forestland in 3 phases. Historically, Phase 1 has been based on aerial photography, but now satellite remote sensing imagery is being used. Phase 1 points are used to identify forested and nonforested locations. Phase 2 includes ground measurements such as tree species, height, diameter, disturbance, and stand age on more than 100,000 stratified sampling plots across the country. Historically, the focus was on timber resources that are available for potential harvest, but during recent decades there has been increased emphasis on a broader suite of forest characteristics including forest health and invasive species. In particular, Phase 3 sampling is done on a subset of plots to determine the species, abundance, and spatial arrangement of all trees, shrubs, herbs, grasses, ferns, and fern allies (horsetails and club mosses). This Phase 3 sampling was begun as a separate program called Forest Health Monitoring but is now administered through the FIA program. As an example, a pilot study collecting Phase 3 data on plots throughout Oregon found at least 1 non-native species on 70 percent of all forested plots, and 20 percent of plant cover was non-native in one of 10 forested plots (http://earthscape.org/r1/ES16479/pnrs_science%20update.pdf ), note: membership is required to access this web site, but free trial membership is available). In addition to data specifically on invasive species, the Phase 2 FIA data are a valuable source of vegetation data because they have been collected in statistically designed surveys for decades. Information on forest type, stand age, and disturbance history are available and can be used in conjunction with data on invasive species to predict vulnerability of forest stands to invasion. Such an approach is underway in the Southern United States (Ridley and others 2006). Phase 2 FIA data are also being used in conjunction with other data to develop regional and national vegetation databases in other research programs including LANDFIRE. See the topic "Conclusions concerning the use of fire modeling systems" in Weinstein and Woodbury (2007).

This section reviews selected modeling approaches relevant to the goals listed above in the Introduction section. The focus is on invasive species of concern for the Western United States, particularly forest and rangeland ecosystems. Examples were selected to cover a range of analytical techniques with an emphasis on the State or regional scale. In addition, examples were selected of two different methods applied to an invasive pathogen that is the causal agent of sudden oak death disease (Phytophthora ramorum Werres, de Cock & In’t Veld) and two methods applied to an invasive insect: the Asian long-horned beetle.

The most common and readily applied approaches to predicting the risk of invasive species occupying sites across a large region rely on biogeographical distribution models. These models are based on information about the biophysical factors that limit where a species can survive. Such models are known as bioclimatic envelope models, biogeographical distribution models, and (ecological) niche models. Such models are generally correlative and may be either statistically based or rule based. As applied to invasive species, such approaches typically attempt to map which parts of a region are suitable for the invading species, and suitability is typically based on habitat requirements. For pests and pathogens, the simplest approach is to map the presence or absence of suitable hosts. Such maps are typically developed from available regional data sets, which often provide relevant but not necessarily ideal data for a particular invasive species. Such maps may be useful for strategic planning at the regional scale, but may be of limited use for managing specific areas presuming that the managers of those areas already know where different species occur.

Niche models typically identify habitats for invasive species based on records of their presence at known locations. Such records can be obtained from museum collections such as herbaria, but currently only 5 to 10 percent of such data are available in electronic form worldwide (Graham and others 2004). To define the niche or bioclimatic envelope, biophysical data for each such location are often extracted from regional databases, usually in a GIS. The most important distinction among such approaches is whether they use absence data in addition to presence data. In other words, whether locations where the invasive species does not occur (absence) are used to define biophysical conditions that are outside of the niche. Either approach is problematic for invasive species because, typically, they have not yet occupied all possible sites. Thus, sites where the species doesn’t occur may not necessarily provide information about the species niche or requirements; instead, those may be sites that the invasive species haven’t yet reached. Presence and absence data can be obtained from the native region of the invasive species, but the species may have a different niche in the part of the world it is invading, as compared with its native region. However, use of data from the native region may be the only reasonable choice for species that have not become widely established in the United States. Even so, there may be substantial uncertainty in such predictions until a species becomes widely established. For example, an analysis of purple loosestrife (a common invasive species in Eastern United States wetland areas) determined that a reliable prediction of the current non-native distribution in North America was only possible 150 years after initial establishment (Welk 2004).

Many variations of the niche approach are used to predict the niche of the invasive species including:

1. simple ranges for factors based on mean climatic variables such as the widely used BIOCLIM and DOMAIN models
2. fuzzy rather than crisp calculations of the niche (Robertson and others 2004)
3. the use of spatial statistical techniques and newer computational approaches, such as genetic algorithms and support vector machines

A few examples of such approaches are evaluated in following sections, with a focus on the Western United States. For each of these examples, how they meet the criteria listed above is discussed.

In this family of approaches implemented in a software tool, the potential range of invasive species is predicted based on point data from the species native home range and spatial data including mean annual temperature, rainfall and elevation (Anderson and others 2003, Costa and others 2002, Godown and Peterson 2000, Peterson 2001, Peterson and Cohoon 1999, Peterson and Kluza 2003, Peterson and others 2003b, Stockwell and Peterson 2002, Underwood and others 2004; also see http://www.lifemapper.org/desktopgarp/). This approach shares many features with other approaches to predict ecological niches based on bioclimatic data, including climate envelope modeling and other methods for niche modeling. All of these approaches assume that bioclimatic predictor variables (for example, mean annual temperature and precipitation) control the native distribution of an invasive species, and these factors will also control the potential distribution in the United States This technique differs from others because it uses a machine learning method (also known as artificial intelligence) named Genetic Algorithm for Rule-Set Prediction (GARP). Based on only 15 to 20 records of locations of a species from its native home range (species input data), the method can predict the potential distribution (home range, or niche) of a species. This approach has been used by its developers to model the niche of both invasive species and noninvasive species. The user needs to provide species input data of known points where the species has been found in its native region. These data should be well distributed throughout the species native range and need to be georeferenced. The user also needs to provide environmental data covering the entire area for which predictions are desired, including mean annual temperature and precipitation (modeled surfaces). Potentially, many other input data could be used such as remote sensing images, but they might need to be available for both native region and the analysis region.

The software used is desktopGARP, which can be downloaded from the following web site: http://nhm.ku.edu/desktopgarp/. The user selects a type of inferential tool, such as logistic regression, or bioclimatic rules. The input data are then divided into training data and validation data. The software generates pseudodata via resampling, and then iteratively tries a large number of rule sets, continuing either until there is no further improvement in the predictions, or 1000 iterations. The output from the model is a map of species niche as presence/absence, with some confidence values. Modeling may be done for either counties or for grid cells (pixels). The primary prediction is whether a county or a pixel is contained in the species potential (fundamental) niche. A measure of likelihood is generated by using multiple models, and assigning higher likelihoods to counties or pixels predicted to be included in the niche by multiple models (Peterson and others 2004).

In the following citations, only one predicted value is made per county, although the approach could be extended for finer grain analyses if input data are available at finer scales. The methodology (Peterson 2003) and its use to predict the distribution of four alien plant species in North America for a single point in time (the fundamental niche) are described in the references reviewed herein. Invasive plant species analyzed to date include Hydrilla (Hydrilla L.C. Rich.), Russian olive (Elaeagnus angustifolia L.), sericea lespedeza (Lespedeza cuneata (Dum.-Cours.) G. Don), and garlic mustard (Alliaria petiolata (Bieb.) Cavara & Grande); (Peterson and others 2003a). To predict the spread of Asian long-horned beetle, the GARP approach has been combined with a spatial model of spread originally developed for forest fire (Peterson and others 2004).

The GARP approach has several strengths for the regional risk analysis of invasive species, which are as follows:

1. It has been applied to a number of taxa of invasive and noninvasive species in the United States and elsewhere
2. freely available software tool has been developed that implements this approach
3. Data requirements for this approach are modest.

Most weaknesses of the GARP approach are shared by all niche modeling approaches, which include:

1. Not all of the stages of the invasion process are modeled
2. Only presence or absence of a species is predicted, not effects of invasive species
3. Results may be biased, depending on the source of data and the use of pseudo-absence data (Graham and others 2004)

Other approaches such as support vector machines and generalized additive model (GAM) approaches may be less biased and provide more optimal statistical solutions (Elith and others 2006, Stockwell 2005), but see also Anderson and others (2003) for improving on model selection methods.

This approach is also a family of related approaches to predict tree mortality risk due to an invasive insect or pathogen based on expert opinion, forest inventory data, and other GIS data (Marsden and others 2005) , and also consult FHTET products web site: http://www.fs.fed.us/foresthealth/technology/products.shtml). Specifically, predictions are made of the potential basal area loss of susceptible tree species due to an invasive insect or pathogen. The location of suitable host species is interpolated using inverse-distance weighting based on forest inventory data. A multi-criteria risk ranking model is developed based on expert opinion about the factors that influence pest or pathogen establishment, spread, and tree mortality. An iterative process is used to develop risk maps, so the experts and analysts can alter the weighting of difference factors to adjust the maps to match expert opinion. This approach has been used to predict the potential effect of oak wilt in the North Central States and of wood wasp (Sirex noctilio Fabricius) throughout the conterminous United States: (http://www.fs.fed.us/foresthealth/technology/invasives_sirexnoctilio_riskmaps.shtml).

The following are the key required input data and their sources:

1. Principal United States ports - Army Corps of Engineers, Waterborne Commerce, Foreign Cargo Statistics
2. Markets for wood products - Federal Highway Administration, Freight Management and Operations, Freight Analysis Framework, Highway Truck Volume and Environmental Systems Research Institute's (ESRI) polygon data
3. Distribution centers - National Transportation Atlas Database
4. Species occurrence and basal area of individual tree species - USDA Forest Service, Forest Inventory and Analysis, National and New York State Christmas Tree Association websites
5. Road density and distance to road – United States Geological Survey, Heterogeneous Distribution Indicator

Use of this approach requires one or more experts on the pest or pathogen, expertise in the use of FIA data, and expertise in GIS software. The spatial scope is the conterminous Unites States for a single time period. Required software includes ArcView 3.x, Spatial Analyst ModelBuilder (ESRI, Inc.), and IDRISI 32 (a raster GIS software package). Model output includes maps of predicted occurrence based on: (1) hosts known to be susceptibleand (2) hosts suspected to be susceptible.

For regional and national risk analysis, the approach of mapping factors that influence a stressor and then combining these factors with weightings derived from expert opinion are intuitively appealing and fairly common. This flexible, iterative expert opinion-based approach can be used for virtually any pest or pathogen, and a risk map can be generated fairly quickly because the system is already in place. Other strengths of this approach include the use of national FIA data and the quantification of potential damage in terms of tree mortality. However, the flexible expert opinion-based approach is also a weakness because it is so open-ended, subjective, and difficult to validate. To date, it does not appear that an attempt has been made to determine which environmental factors were actually associated with pest presence, or to quantify uncertainties in GIS layers or predictions. In contrast, a statistical inference approach that made quantitative predictions of pest occurrence would be more useful because it could be better tested against validation data.

Meentemeyer and others (2004) used a rule-based function to predict spread of sudden oak death pathogen distributions in grid cells (30m by 30m) throughout California. A prediction was made of the likelihood of presence of the disease based on rules derived from expert opinion and published data on plant species susceptibility, pathogen reproduction, and host climate. This method is focused on evaluating a single risk, the probability of oaks on a given site being infected by P. ramorum. More specifically, the method begins with mapping 5 predictor variables in a GIS and then using a set of rules to determine the risk of infection based on these predictor variables. The predictor variables are host species index, precipitation, maximum temperature, minimum temperature, and relative humidity. Host species index is weighted 3 times as strongly as precipitation and maximum temperature, which in turn are weighted twice as strongly as relative humidity and minimum temperature. Each variable is classified on a relative index, with host scored on a scale from 0 to 10, precipitation, maximum temperature, and humidity scored from 0 to 5, and minimum temperature scored from 0 to 1. The model was tested against 323 field observations in California. The model generally predicted higher risk for sites where P. ramorum is currently present and lower risk for sites where it is currently absent. However, it appears that approximately 20 percent of low-risk sites were infected.

Input data for the model include host susceptibility, pathogen reproduction, and host climate suitability. Like many modeling approaches, this approach requires expertise in GIS and database analysis. The model output is in the form of a map with estimated risk of occurrence of the pathogen at a single time period – movement of the pathogen is not modeled. The spatial scope includes all of California, and the map unit is landscape cell (30 by 30 m). The approach uses the CALVEG database (USDA Forest Service RSL 2003) for vegetation alliance and presence of P. ramorum and the Parameter-elevation Regressions on Independent Slopes Model (PRISM) for elevation-based regression extrapolations from base weather stations for climate data, which are available for the conterminous United States (http://www.wcc.nrcs.usda.gov/climate/prism.html).

The method meets the criterion of calculating the risk of detrimental environmental effect by mapping the probability of pathogen occurrence in each forest grid-cell and could be extended to predict the presence of pathogens in smaller regions or pixels. But the focus is assessment of effects over a region, specifically bioregions, rather than at all points within a region. The method meets the criterion of using spatially heterogeneous environmental data to drive calculation of risk at different points throughout the Western United States Potentially, it could be used to evaluate the risk from a number of stressors, but relationships between habitat conditions and probability of stressor occurrence would have to be developed. Potentially, the method could be extended to consider effects of interaction among multiple stressors, but interaction terms would need to be identified and parameterized in a regression model. The approach does not currently consider the effect of changes in environmental conditions over time.

Unfortunately, no attempt was made to determine which environmental factors were actually associated with disease presence. A statistical inference approach that made quantitative predictions of pathogen occurrence would be more useful because it could be better tested against validation data when they become available. The finding that 21 percent of sites predicted to be low risk, yet were found to be infected, suggests that the model has limited predictive power. This limited power is likely due to data limitations as well as lack of precision in rules and weights applied to them. The investigators do state that they plan to use FIA data to improve the predictions. This study was evaluated because it addressed an important risk factor in Western and potentially Eastern United States forests, but use of a method that makes more quantitative predictions would be useful in the future.

This approach predicts potential home range of an (invasive) insect or pathogen of trees by modeling the location of suitable host species based on forest inventory data (Nowak and others 2001, http://www.fs.fed.us/ne/syracuse/Data/Nation/InsectPoten.htm). A model of urban forests (UFORE) is used to predict urban forest composition based on data from a limited number of cities in the United States. Predictions are also made of the amount of tree cover that could be lost due to tree death and the costs of replacing killed trees. A simple model of spread (moving outward at a constant rate from one location) was used to predict the length of time required for invasion to occur in each major city. This approach has been used to predict the potential effect of Asian long-horned beetle throughout all urban areas in the United States (Nowak and others 2001), and preliminary predictions have been made for non-urban areas (http://www.fs.fed.us/ne/syracuse/Data/Nation/InsectPoten.htm). Preliminary predictions have also been made for the emerald ash borer (Agrilus planipennis Fairmaire) (http://www.fs.fed.us/ne/syracuse/Data/Nation/InsectPoten.htm). The main type of required input is appropriate forest inventory data. Model output is in the form of maps of predicted occurrence based on: (1) hosts known to be susceptible and (2) hosts suspected to be susceptible. The model has been used at the scale of the conterminous United States for a single point in time.

One strength of this approach is the use of FIA data in conjunction with a model that has been used for many years. Another strength of this approach is the quantification of damage in terms of economic losses of urban trees. For urban trees, such economic losses are quite high, though for wildlands they will be much lower for an individual tree and much harder to estimate for a forested region. A limitation for regional risk assessment and management is that the focus of the model is urban areas. Another limitation, typical of most niche modeling efforts, is that not all steps in the process of invasive dispersion and reproduction are modeled, and that predictions are primarily of the potential host range of the pathogen, not of effects of the pathogen other than economic losses due to the death of urban trees.

In this approach, a logistic regression is developed to predict the suitability of each 1 km pixel as habitat for tamarisk throughout the conterminous United States (Morisette and others 2006). Various ground surveys of tamarisk occurrence were integrated into a single database as presence or absence of tamarisk. Land cover, normalized difference vegetation index (NDVI), and enhanced vegetation index (EVI) were derived from MODIS data products. A discrete Fourier transform was used to model a constant amplitude yearly sine wave to each pixel, and the mean, amplitude, and phase of both NDVI and EVI were used as potential predictor variables along with a fitted parameter for each land cover class in a logistic regression model to predict the likelihood of habitat suitable for tamarisk. The ground data were split into a training set to fit the model (67 percent of data) and a validation set (33 percent of data). The best model included land cover, and seasonal variability in NDVI and EVI. The proportion of correctly predicted observations using a threshold of 0.5 was 0.90. The main model inputs are MODIS data and surveys of tamarisk presence. Because it is a regression procedure, many other input data could be used, such as human population density, trail networks, air temperature, etc. The main model output is a relative ranking of the likelihood of suitable habitat for an invasive species.

This general approach would be useful for regional assessments because it uses remotely sensed data that cover the entire conterminous United States. However, for each invasive species, a large database of ground survey data is required. If FIA or other systematic survey data could be used for this purpose, that would make the approach useful for many more invasive species. A limitation of this approach is that it uses statistical correlation to make predictions, thus it cannot readily predict the effect of future environmental conditions such as changes due to development, changes in hydrology, or changes in regional or global climate. Other examples of logistic regression to analyze invasive species include multiple species in South Africa (Higgins and others 1999) and Russian knapweed (Acroptilon repens (L.) DC.) in Colorado (Goslee and others 2003).

This approach uses spatial statistical analysis to predict the distribution of invasive and noninvasive alien plants throughout all bioregions in California (Dark 2004). Spatial autoregressive (SAR) models were used to assess the relationship between alien plant species distribution and native plant species richness, road density, population density, elevation, area of sample unit, and precipitation. Three predictors were found to be statistically significant for both invasive and non invasive plants: elevation, road density, and native plant species richness. The best model (with all predictors) explained about 80 percent of the variance in the number of alien species in each bioregion. Additionally, there was significant spatial correlation for both invasive and noninvasive alien plants. Both invasive and noninvasive alien plants are found in regions with low elevation, high road density, and high native-plant species richness. Spatial data input requirements include a digital elevation model, precipitation (a modeled surface), road networks, native species richness and occurrence of alien species. Because it is a regression procedure, many other input data could be used, such as population density, trail networks, air temperature, traffic volume, etc. The model has been applied to all of California for a single time, with bioregions as the map unit. Model outputs include maps of the number of invasive and noninvasive alien species by bioregion. The method could be extended to predict the presence of invasive species in smaller regions or pixels.

This general approach would be useful for regional probabilistic risk assessments because it uses widely available data in conjunction with a flexible spatial statistical approach. Additionally, it predicts the total number of nonindigenous (alien) species within a region. This technique could be feasibly extended to predict the probability of occurrence of invasive species based on the occurrence of noninvasive alien species. This would be very useful because noninvasive species were found to be roughly 10-fold more common than invasive species for the bioregions. This would be a useful first step for regional risk assessment for large regions such as the Western United States in order to identify areas with higher overall risk for invasive species. The approach could be improved by using more detailed data on vegetation types rather than bioregions. A limitation of this approach is that it uses statistical correlation to make predictions, thus it cannot readily predict the effect of future environmental conditions, such as changes due to development, changes in hydrology, or changes in regional or global climate. However, it might be feasible to develop statistically based extrapolations from existing data. For example, if the number of nonindigenous species in a region can be predicted based on some measure of the transportation network, or other environmental factor, one could extrapolate to future conditions with more roads or a higher traffic volume. A future scenario of new road development or greater traffic or both on existing transportation networks could be developed based on planned State and Federal transportation projects. This scenario could be used to predict the subsequent increase in occurrence of nonindigenous species and invasive species.

This method uses a type of machine learning algorithm called support vector machine (SVM) in a niche modeling approach to predict risk of occurrence of sudden oak death throughout California (Guo and others 2005). A useful comparison is made of presence-only (one class SVM) versus presence with pseudo-absence data (2-class SVM). Based on their results, the use of pseudo-absence data does not appear to be a good choice for modeling invasive species—they inherently lead to bias because they conflate environmentally determined absence with absence due to infestation not having occurred yet in a particular location. Input data include 14 environmental variables including mean annual temperature, mean annual precipitation, distance to roads, distance to patches of hosts, and presence of susceptible species. The use of this approach currently requires an analyst with not only GIS skills, but also substantial programming skill. Also, assistance may be needed from algorithm developers to modify code. Model output is a map of the potential location of the invasive species. The spatial scope includes all of California, and the map unit is a 1 km grid cell for a single time. Two regional databases are used as input data: California GAP and climate surfaces from the DAYMET model (http://www.daymet.org/). The software used is LIBSVM, which is a library of generic support vector machine functions developed by Chang and Lin 2001, as cited by Guo and others 2005. In this approach, risk is calculated only as potential presence of the disease. There are some probabilistic components, but many sources of uncertainty are not quantified.

This approach would be useful for regional probabilistic risk assessments because it is a generic machine learning technique applied to niche modeling. Thus, it could be used for invasive plants, insects, diseases, and possibly other stressors. One-class SVMs appear particularly attractive because they are statistically based and unbiased and theoretically optimum, unlike some other machine learning methods and don’t require a lot of model tuning. A weakness of the approach, at least for many potential users, is dependence on a library of computer code functions rather than a more mature and user-friendly software package, and assistance may be required from the library developers to apply the functions in an analysis. This approach also does not account for time, nor does it incorporate spatial processes such as dispersion. It may be difficult to specify weights for each variable. Like all niche models, it is dependent on data quality, and there will likely be issues of spatial support and spatial scaling.

The issue of invasive species is large and complex because there are thousands of potential invasive species and constant movement of plants, plant material, pests and pathogens, in addition to established invasive species. It seems clear that the most cost-effective approach is to control invasive species very early in the process of transport from the native range and entry to the United States. This issue has received national recognition as an important threat and should be addressed at the national scale (NRC 2002). Increased international trade is exacerbating the problem, and despite this increase, the budget for APHIS, the first line of defense, has been decreasing in recent decades as a function of the volume of imported material (D'Antonio and others 2004).

Despite the lack of complete data sets and complete information about the biology and ecology of invasive species, it is feasible to develop risk analyses of invasive species at the regional scale that should provide information useful for land managers. Even a semiquantitative rule-based approach can help to identify locations that contain susceptible host species for specific pathogens or insect pests and where propagules are more likely to enter, based on the current locations of the invasive species and methods of spread, (e.g., Meentemeyer and others 2004, Nowak and others 2001). As discussed in previous sections, the use of regional forest inventory data and detailed vegetation mapping based on these and other data provide an important starting point for regional risk assessments of invasive species.

A broad range of niche modeling approaches are useful because they can use data from museum collections in other countries to make estimates of potential new range areas in the United States. Such data provide information about the fundamental niche of the organism, although this information must be evaluated critically by scientists skilled in taxonomy and biogeography and applied with care (Graham and others 2004). The GARP approach would be useful for regional assessments because a software package is available specifically to apply this method to niche modeling. However, other approaches such as support vector machines and GAM approaches may be less biased and provide more optimal solutions (Elith 2006, Stockwell 2005).

As compared to predicting the fundamental ecological niche of a species, predicting the rate of long distance movement is much more difficult because such events are rare, may not be well understood, and may be affected by human behavior. The approach demonstrated recently by Bartell and Nair (2004) to examine pest establishment and spread could be expanded and adapted to provide quantitative estimates of spread beyond an initial port of entry. There is a large body of work in the spatial ecology literature addressing various aspects of the spread of populations and, more generally, the role of space in structuring populations and metapopulations (Tilman and Kareiva 1997). In recent years, there has been an increase in the number of publications using empirical data in conjunction with modeling approaches to predict the spread of invasive plant species. This process is complex because of the rare, but crucial events of long distance transport, including movement from the native range to the United States. Whereas simple diffusion models may be useful in some instances, the issue of long distance transport by human vectors needs to be addressed (Hastings and others 2005). Some of the methods discussed above included estimates of spread. One such analysis to assess the risk posed by Asian long-horned beetle combined the GARP niche modeling approach with a simple model of spread from likely ports of entry (Peterson and others 2004). This approach makes predictions quite different from those based on analysis of species host range, as discussed in a previous section (see “Nowak host range”).

Models based on fundamental biological and physical processes, such as population demographics and movement of organisms, generally are preferable to correlative statistical approaches. This does not mean that correlative approaches are not valuable for probabilistic regional risk assessments. They may be useful first steps for regional analysis; e.g., to quantify the overlap in spatial distribution of stressors and ecological receptors throughout the Western United States. Correlative models such as that of Dark (2004) may be extended with some confidence beyond the range of available data because they use predictor variables that represent physical and biological processes. For example, the distribution of nonindigenous and invasive species was found to be similar, because both must pass through the same environmental filters or stages. The approach of using data on locations of all nonindigenous species to predict the occurrence of much rarer problem-invasive species may be quite useful because the correlation is based on the key processes of human influenced transport, establishment, reproduction, and dispersal of propagules. In such cases, statistically based extrapolations from existing data should be quite credible and useful. In addition to extrapolating from all non-indigenous species to only invasive species, future environmental scenarios might be developed to predict future risks. For example, one could extrapolate to future conditions with more roads or a higher traffic volume, if the number of nonindigenous species in a region can be predicted based on some measure of the transportation network (Larson 2003, McKinney 2002), or other environmental factor. A future scenario of new road development or greater traffic or both on existing transportation networks could be developed based on planned State and Federal transportation projects. This scenario could be used to predict the subsequent increase in occurrence of non-indigenous species and invasive species.

Risk assessment for invasive species will be most useful if it helps provide information about the degree of potential harm, or damage. For certain invasive plant species, especially serious and common weeds of crop and rangelands, damage can be quantified in economic terms. However, it can be difficult to quantify the ecological effects of many invasive species, especially for effects on wildlands. For example, it has been assumed that purple loosestrife is a serious threat to wetlands in the Northeastern United States, and considerable effort has been made to eradicate it. However, an analysis of ecological effects found little evidence for damage to wetlands (Hager and McCoy 1998), although one recent publication did find some evidence that it can reduce native plant diversity (Schooler and others 2006). The lack of evidence of severe ecological effects in wildland ecosystems does not mean that such effects don’t exist. Rather, such a lack of evidence may indicate a lack of research on wildland ecosystem effects and the difficulty in quantifying such effects in wildland ecosystems as compared to highly managed ecosystems such as agricultural row crops. This difficulty in assessing economic damage of invasive species has been recognized as a key challenge for research (Andersen and others 2004a). Despite the challenge, such efforts may be useful, as they may provide evidence that even large expenditures required for removal of invasive species may provide a valuable economic return. For example, it has been estimated that the costs of eradication of tamarisk throughout the Western United States would be fully recouped within 17 years with continued ongoing benefits beyond that time (Zavaleta 2000).

As for any regional stressor, the use of multiple models and a weight of evidence approach would help to increase confidence in predictions of ecological risks from invasive species. As discussed previously, two approaches to predicting the risk of Asian long-horned beetle throughout United States forests make quite different predictions because they focus on different stages in the process of establishment and spread. All models have some level of uncertainty both in the data used to drive the model and in the calculations made within the model. A focus on uncertainty as an important type of information is crucial for meaningful assessments of invasive species risk. There is strong evidence of the potential for invasion and damage to occur for certain species such as those already on lists of noxious weeds. The strongest predictor for a species is if that species is already an invasive species causing substantial damage in another part of the world. For these species, there is generally quite a bit of information about aspects of their life history that are important for predicting risk, such as host range, reproductive potential, and phenotypic plasticity. However, for other species there is little or no information. For example, the causal agent of sudden oak death in California was only discovered because of unusual mortality and morbidity in California live oaks. Investigation revealed a new species; thus, there was virtually no information about the ecology of the species such as host range, climatic requirements, and reproductive potential. Until such information began to be gathered, it was not possible to make any meaningful prediction of invasiveness or ecological risk.

Finally, risk assessments will not be useful unless they provide guidance for management. Land managers could benefit in particular from regional risk assessments that provide information about potential future risks. Invasive species management should be addressed at multiple spatial scales such as:

1. reducing importation of new species at border crossings and ports
2. conducting national and regional mapping of locations of invasive species
3. developing procedures to reduce long distance transport if possible
4. developing local procedures to reduce movement of invasive species

Because many invasive species become established along roadways and trails, it may be easier to locate them and eradicate them before they spread. However, costs of eradication can be very high, and the most cost-effective approaches will be at the national and regional scale, rather than the scale of a single national forest. Quantitative approaches to estimate the costs and benefits of management options are needed. The feasibility of estimating such costs has been demonstrated (Bartell and Nair 2004, Zavaleta 2000), but much more work is required. Developing such estimates by bringing together risk assessors and land managers should be considered in developing regional risk assessments that will help focus on key issues for management.

In summary, the following suggestions may be considered when selecting modeling approaches for probabilistic risk assessment for invasive species at the regional scale:

1. Define management options and formulate the risk problem definition at the same time so that predictions will be useful for making management decisions.
2. Ecosystems are spatially explicit, so use spatially explicit data, such as vegetation type, topography, stream networks, and elevation.
3. Use both socioeconomic and ecological information.
4. Do not assume that the initial conditions of a landscape can all be captured by a few regionalized variables because of the large role that site history often plays in shaping future dynamics.
5. Whenever possible, make quantitative predictions of risks rather than using ranks (such as low, medium, and high). Ranked values can lead to erroneous interpretations because it may not be clear what is meant by a high risk and also because of uncertainty about what happens at the boundaries of the rank categories.
6. Quantify important spatial and nonspatial sources of data uncertainty and address these uncertainties in the analysis.
7. Quantify important sources of uncertainty in model equations, including aggregation and scaling issues, and address these uncertainties in the analysis.
8. Whenever feasible, use multiple models based on different approaches and data.

Invasive species management is closely entwined with the assessment and management of risk that arises from the inherently random nature of the invasion process. The theory and application of risk management for invasive species with an economic perspective is reviewed in this synthesis. Invasive species management can be delineated into three general categories: exclusion, detection, and control. Key ideas and approaches in current literature and potential applications of existing theory are presented in this synthesis. Economic literature tends to emphasize either individual management strategies, such as preventing invasive species from entering an ecosystem or controlling extant populations. There is also a growing focus on the optimal allocation between multiple activities for the same species such as between prevention and control. The key biological and economic relationships included vary across frameworks and objectives.

The synthesis is organized into sections covering the salient aspects of invasive species management by separating the major veins of economic literature on decision-making. Invasive species management is discussed and a brief overview of risk management and economic theory is provided. An overview of the key factors causing invasions is presented. Exclusion activities to prevent introductions is the focus in the third section. Control strategies after the species has been successfully introduced are emphasized. The trade-offs between multiple management strategies are addressed. Finally, a discussion concludes the synthesis.

An overview of decision-making under risk in invasive species management, with an emphasis on the economic literature, is provided in this synthesis, and the following topics are discussed: an overview of invasive species management; the key factors causing invasions; the exclusion activities aimed at preventing introductions; post-introduction control activities; and trade-offs between multiple management strategies. Scientists have studied the impacts of invasive species on non-native ecosystems for many years. Recently, the public has become more aware of the problems associated with invasive species, due largely to greater levels of media coverage and public information campaigns regarding the issue. Government agencies deal explicitly with risk in their on-going invasive species management programs; thus, risk management plays a crucial role in these programs.

Owing to the breadth of risk management, and discrepancies among discipline-specific terms, the sections below clarify the usage of terminology in this synthesis.

The word risk has three common definitions: (1) an [adverse] event (as in non-native invasive species are a risk to ecosystems); (2) the probability that the event will occur (as in the goal of management is to reduce the risk of invasive species introductions to new ecosystems) and (3) the probability that an event will occur weighted by the consequences of the event (as in the possibility that invasive species will harm oak forests is a substantial risk).

In economics, the term is most often used to describe situations in which the results of a decision follow some sort of probability distribution. The probability distribution may be objectively determined, either through a priori reasoning (such as the probability that a fair die will show the number 6) or through repeated experiments. Probabilities may also be subjectively determined without clear experimental evidence. These are known as beliefs. The term ambiguity applies when probabilities are not known with certainty. When probabilities are involved, it is possible to define (and maximize) objective functions that are weighted by these probabilities. We adopt the economics usage of the term risk, referring to a situation in which management decisions affect outcomes and their probabilities.

There may be cases when it is not possible to assign probabilities to outcomes. One example is the case of global climate change as discussed by Woodward and Bishop (1997). Although it is possible to assemble a panel of experts to glean their beliefs about possible dangers, and it is possible to delineate the range of possible options, Woodward and Bishop argue that it is not reasonable to assign probabilities to these options based on the number of experts sharing a particular belief. Woodward and Bishop call this pure uncertainty, following the distinction as defined by Frank Knight in 1921. Others term this ignorance (Arrow 1972). In these cases, it is not possible to define a function that is weighted by probabilities.

However, the term uncertainty has a number of different definitions, including simply: uncertainty arises whenever a decision can lead to more than one possible consequence (Hammond 1998). This definition includes situations such as lotteries where probabilities are well established. In the risk assessment literature, uncertainty arises due to the lack of precise knowledge about parameters, models, or scenarios. It can also come from differences among modelers (Linkov and Burmistrov 2003). We adopt the usage in the risk analysis literature, where uncertainty refers to this lack of precision, and use the term pure uncertainty to refer to the case where it is not possible to assign probabilities.

Risk analysis consists of risk assessment and risk management activities. Risk assessment is defined as ’the systematic, scientific characterization of potential adverse effects of human or ecological exposures to hazardous agents or activities’ (The Presidential/Congressional Commission on Risk Assessment and Risk Management 1997). Risk assessment informs risk management decisions by supplying this characterization of potential outcomes and probabilities. In invasive species management, risk assessment informs two specific areas: the risk surrounding introductions of new species, including vectors, species, and potential damages; and the risk associated with existing invasives, including the potential spread and damages caused by established species (Andersen and others 2004). For example, the date of the introduction of a pest, like the Siberian moth (Dendrolimus superans sibiricus) may not be known. However, numerous factors can be used to construct probabilities to characterize the chances of the Siberian moth being introduced at any particular date. These factors include the number of pathways that it has, the level of interaction between the U.S. and its native territory, and the introduction success of similar species. The frameworks for assessing invasive species risk vary substantially (Modeling Invasive Species).

Risk management, as the Presidential Commission (1997) states, is “the process of identifying, evaluating, selecting, and implementing actions to reduce risk to human health and to ecosystems.” Risk management relies heavily on underlying risk assessments to establish the potential for adverse events occurring as a consequence of a particular action. In addition, risk management must account for resource, social, ethical, political, and legal constraints. In this synthesis, with a focus on the economic literature, particular attention is paid to how resource constraints guide risk management decisions.

Some common economic concepts and terms used throughout the review are briefly covered in this section. Welfare economics focuses on the implications of alternative resource allocation methods on social welfare, both in market and nonmarket settings. One criterion used to judge whether an outcome is efficient is Pareto optimality; a Pareto optimal allocation is one in which no one can be made better off without making someone else worse off. A competitive equilibrium will be Pareto optimal unless there are market failures. One example of a market failure is an externality, where a consumer or producer generates costs that they do not bear themselves. Invasive species represent an externality in that accidental introductions of invasives impose a cost to society and can occur as a consequence of consumption or production activities. Therefore, one role of management is to align individual incentives with social goals—to internalize external costs—so that a Pareto-optimal allocation will result. One possible tool that can be used to align incentives is a tax on the externality, calculated as the difference between private cost and social cost at the optimum. This is known as a Pigovian tax. Another tool is a system of tradable permits in which an agency sets the total allowable level of the externality, but the allocation of that level emerges out of a permit market. Both of these have been suggested as ways to handle the invasive species that are introduced as a byproduct of economic activity.

When situations are risky, it may not be possible to guarantee a particular outcome, but it may be possible to choose among alternative probability distributions by choosing the level of conditioning variables. Economists have developed theories of rational choice that are appropriate in risky situations, including the Expected Utility theory of von Neumann and Morgenstern (1944) for objective probabilities and the Subjective Expected Utility Theory of Savage (1954) for subjective probabilities. For example, it may be possible to reduce the probability of species introductions by altering trade levels. Expected utility Theory is one framework that can guide these choices. The objective function consists of the expected level of utility, where utility represents an individual’s satisfaction derived from their preferences for consuming or experiencing goods and services. Utility functions, or numerical representations of individual preferences, can account for costs and benefits that accrue under unknown future events. The von-Neumann-Morgenstern utility function offers one characterization of an individual’s preferences over all potential outcomes. Expected utility theory essentially states that such a characterization exists if an individual's preferences conform to certain axioms. Such representations allow for identification of optimal behavior that maximizes expected utility. They also provide a basis to compare different risk preferences, or attitudes toward risky situations. For example, an individual may be risk-averse, i.e., he or she prefers a situation with little or no risk to a more risky situation even if the expected outcome in the risky situation is higher.

When probabilities cannot be assigned to possible outcomes—situations of Knightian pure uncertainty—it is possible to use other criteria, such as maxi-min (choose the course of action that leads to the best case when the worst state of nature occurs) or mini max-regret (choose the course of action that leads to the lowest possible regret, Loomes and Sugden 1982). Ciriacy-Wantrup (1964) promoted the Safe Minimum Standard criterion, which suggest that irreversible losses should be avoided. This is echoed in the Precautionary Principle of Perrings (1991). These criteria can be justified as rational in situations where possible future outcomes are knowable, but the probabilities of those outcomes are not.

The theme of optimization over time is prominent in the area of natural resource economics, and the balance of the productivity of natural assets with that of other assets typically characterizes an optimal solution. In the context of renewable resources, the optimal harvest rate is one that equates the returns from the stock of the resource to the returns one could achieve in an alternative investment. Extinction can be an optimal outcome, particularly if there are no nonmarket benefits associated with the resource. This theme is echoed in the literature on invasive species, where both corner solutions (eradication) and interior solutions (control at some positive population level), are possible. The probability of random catastrophic events has been shown to increase the appropriate discount rate (risk adjusted discounting) and accelerate harvest (Reed 1984). It is also possible to factor in the stochasticity associated with population growth (Pindyck 1984), and this can either introduce caution or intensify harvest pressure. An alternative approach is to specify some probability of extinction and then set management levers so that this probability is not exceeded; for example, one possible criterion is that the probability of extinction should never be higher than 1 percent (Haight 1995, Montgomery and others 1994). Analogous criteria can be used in invasive species management.

Management activities and corresponding invasion

Invasive species management spans a variety of activities that can be grouped into three areas: exclusion, detection, and control (see figure at right). The management activities concentrate on different parts of the invasion process, which comprises three main stages: introduction, establishment, and spread. Even though agencies engage in additional activities, these categories capture the majority of decisions facing managers. Thus, the synthesis is arranged according to the general management categories. Although the theory behind the risk management models is discussed, the emphasis is on the potential outcomes.

Various species may be in different stages of the invasion process so that management agencies engage in exclusion, detection, and control activities simultaneously. Additionally, the dynamic nature of the invasion process implies that it is optimal to make management decisions in a forward-looking manner by accounting for future stages in current actions. Existing literature often analyzes such aspects of the relationships between the management activities. Many papers in the economic literature, for example, consider the optimal allocation between exclusion and management activities for the same species.

This section focuses on the key factors that are thought to contribute to the risk of invasions, including factors that can be controlled for the purposes of risk management. One commonly-held view is the disturbance hypothesis (Dalmazzone 2000), which asserts human activities and their accompanying disturbances to the environment primarily cause both species’ introductions and their subsequent invasions of new ecosystems. In addition, human and commodity movement provide the major vectors for species to enter new ecosystems. Risk management requires the knowledge of which vectors pose the greatest chance for new introductions of invasives, and this translates to a reliance on comprehensive risk assessment (e.g., Representing Human-Mediated Pathways in Forest Pest Risk Mapping). Current risk assessments typically do not use an economic framework and economic data to understand the relationship between trade and invasion risk. Costello and others (2005) provide one of the few examples of such a framework when they parameterize a model based on data of invasive species introductions to find that the threat of new invasions depends on the past trade level with a region and the past exposure to invasive species. Using invasion data from the San Francisco Bay over a period of 138 years, they identify trade partners from the Atlantic/Mediterranean and West Pacific regions as posing the greatest risk of introductions to the San Francisco Bay Area. Explicitly incorporating economic aspects can potentially alter the results of a risk assessment and, in turn, change suggested approaches to risk management. In this case, risk management can potentially reduce risks through targeted trade restrictions and economic mechanisms. However, such restrictions can produce unintended negative consequences if inappropriately targeted or implemented.

Economic activities can produce other externalities such as land disturbance and the loss of biodiversity. Scientists have long argued that biodiversity loss increases an ecosystem’s susceptibility to invasion. This idea stems from a theory postulated by Elton (1958) that diverse habitats can better fend off invasions. The potential relationship between biodiversity loss and invasions arises from the interactions between native and non-native species. Many experts believe that interactions between native and exotic species are generally detrimental, often stemming from competition over limited space or food, (e.g., Shigesada and Kawasaki 1997, Tilman 1982, Tilman 2004). However, studies have shown that the relationship between native and non-native species is quite complex, and some species may actually benefit due to mutualism (Bruno and others 2003). Hence, a simple classification based on the number of species in a geographic area can not necessarily predict the susceptibility to new invasions; instead, the effects of the interaction often depend on the spatial scale (Fridley and others 2004, Meiners and others 2004).

Apart from the externalities from economic activities, each species’ unique biological traits largely affect their impacts in a new ecosystem. Thus, risk assessment emphasizes biological traits of potential invasive species as indicators of potential risk (Downing and others 2007, Iverson and others 2007, Pontius and others 2007). However, given the numerous possible factors and characteristics that contribute to a species’ invasiveness, the selection of appropriate characteristics poses much difficulty. For example, Rejmanek (1999) posits that all salient biological characteristics provide some information on the potential risk posed by a species. Besides the species specific biological traits, the following sections show that landscape characteristics of the potential habitat also provide important indicators:

• Soil Quality is Fundamental to Ensuring Healthy Forests
• The Formation of Dense Understory Layers in Forests Worldwide: Consequences and Implications for Forest Dynamics, Biodiversity, and Succession
• Methods to Assess Landscape-Scale Risk of Bark Beetle Infestation to Support Forest Management Decisions)

Other researchers, such as Williamson (1996), believe that very few characteristics provide suitable predictors for invasions. Williamson (1996) argues that most invasion patterns elude generalization over wide taxonomic ranges due to the specificity of success factors. Still, propagule pressure, habitat suitability, and prior invasion success serve as rough indicators of invasion success. Of these, propagule pressure, or the number of organisms in an area, is the variable that can be most directly altered through risk management. As the propagule pressure increases, the chances of survival increase whereas the effects of predators, stochasticity, and the Allee effect diminish (see Eradication as an Optimal Strategy). Unsurprisingly, a positive correlation exists between propagule pressure and disturbed land. Disturbed land tends to have greater economic activity, which translates to increased exposure to vectors for exotic species.

In addition to establishing general predictive factors, Williamson (1996) formulates the Tens’ Rule, which postulates that of the exotic species introduced to an area, 10 percent will become established and 10 percent of those will spread (approximately 1 percent of introduced species). Although this is a very general rule-of-thumb, assigning probabilities with educated guesses for the underlying probability distributions can produce an approximation of the actual invasion process, (e.g., Lockwood and others 2001). Using such approximations, a decision-maker can perform a more structured analysis, which potentially widens the possible management options available (Perrings 2005, see Understanding Risk Mitigation Versus Adaptation). However, whereas general rules, such as the Tens’ Rule, serve as useful benchmarks to provide a sense of the magnitude of potential invasions at the aggregate level, they do not predict outcomes at a micro-level scale. The pine shoot beetle (Tomicus piniperda) is an example of how aggregate level predictions can fail at the regional level. Pine-shoot beetle sightings were met with strict quarantines due to its classification as a high-risk pest causing potentially high economic damages. The pine-shoot beetle actually produced relatively low damages, but the quarantine measures resulted in significant losses to the pine industry in the affected areas (Haack and Poland 2001). As the authors state, ‘… it is difficult for agencies like APHIS to change course once they have enacted a federal quarantine given that the concerns of the uninfested states have been heightened by the initial establishment of the quarantine.’ Thus, whereas risk assessment can inform risk management, it could potentially exclude key impacts such as in the economic consequences of quarantines on industry or the irreversibility of certain actions.

Risk management frameworks incorporate these relationships into the decision-making problem facing the agency manager along with the spatial, temporal and stochastic dimensions. However, there is no clear rule dictating which relationships must be included or how they should be included. Inclusion of specific relationships depends largely on the agency manager’s objective, and the choice of relationships will impact the model’s outcome.

Exclusion strategies occupy much of the limelight in risk management for invasive species because the majority of species introductions have been attributed to human activities (see Factors Fueling the Invasion Process). Reducing the risk of species introduction involves managing the potential pathways that species use to enter a new ecosystem. Market-based mechanisms, such as tariffs or permits, can regulate trade behavior and produce socially optimal outcomes (see Policy and Market-Based Mechanisms to Manage the Risk of Introductions). Whether or not the probability distribution of the invasion process is known can substantially affect the optimal strategy necessary to prevent a species introduction (see Pure Uncertainty Versus Risk in Assessing Prevention Strategies).

The varying policies and market-based mechanisms aimed at reducing introductions produce substantially different outcomes and can lead to unintended effects such as economic losses. Increased trade volume creates greater opportunities for species to engage in "ecosystem-hopping", leading some to argue for tighter trade restrictions to reduce this risk (Jenkins 1999). However, the sheer volume of trade coupled with strong political resistance and social welfare losses requires a targeted approach. The first step is identifying the high risks within trade (see Factors Fueling the Invasion Process). The next step involves evaluating mechanisms which reduce this risk. Market-based mechanisms can ensure socially optimal outcomes, but their implementation is often confounded by political issues and the inability to properly capture the full implications of these mechanisms. Optimal tariff policy is discussed in a majority of these papers, but the role of politics should not be overlooked. Several policies, such as phytosanitary measures (http://www.ippc.int/IPP/En/default.jsp), aim to reduce the potential damages of pests that arrive through trade. However, it can be argued that extant tariffs and trade policies often stem more from political motives than the conscious desire to mitigate environmental damages produced by trade. As Margolis and others (2005) illustrate, delineating protectionist tariffs from those designed to mitigate invasion risk requires knowledge regarding the social costs inflicted by invasive species and the value the government places on societal welfare. Without this information, it is hard to gauge the consequences of tariffs. Achieving socially optimal outcomes involves two steps: (1) identifying the mechanisms that induce behavior to produce the socially optimal outcome, as demonstrated in the papers in the following sections, and (2) implementing these mechanisms. The first step pertains to this synthesis; however, the obstacles that arise during implementation must also be kept in mind while evaluating these mechanisms.

Models that utilize taxes to manage invasive species introductions are discussed in this section. Although the economic focus on invasive species is relatively new, frameworks from the environmental economics literature can inform decision-making models. For example, Costello and McAusland 2003, Knowler and Barbier 2005, and McAusland and Costello 2004 draw from the pollution literature by treating invasives as a negative externality comparable to pollution. Knowler and Barbier (2005) evaluate the extent to which market-based mechanisms, such as taxes, can produce a socially optimal level of exotic plant imports. Private industry and agriculture rely heavily on exotic species for a range of purposes (McNeely 1999). To address the unintended consequences of intentional introductions, Knowler and Barbier assess the effects of Pigovian taxes for the private nursery industry. Pigovian taxes impose a penalty on the loss associated with an agent’s actions; in the pollution literature, Pigovian taxes are levied against firms based on the amount that they pollute (see A (Brief) Primer in Economic Theory). Setting optimal levels of Pigovian taxes requires perfect information on firm practices and, more importantly, the impacts of those actions. Assessing the contribution of individual firms on overall species’ introductions is difficult. However, from a social welfare perspective, optimal Pigovian taxes provide a better alternative than total prohibition of exotic imports. As shown in the pollution literature, market-based mechanisms such as Pigovian taxes can internalize the externalities of private actions to result in a socially optimal outcome.

To assess the impacts of a Pigouvian tax, Knowler and Barbier develop a model to analyze the decision facing a policymaker regulating a private industry. Specifically, they study the commercial nursery industry, where importing, breeding and selling behaviors often occur without consideration of the potential loss to society from unintended spread following the sale of the exotic species. The social benefits of plant imports are represented by the discounted aggregate profits of the private nursery industry. The expected losses depend on the quantity of land invaded by the species once the invasion occurs. The overall net benefits are the total profits until the time when the invasion occurs minus the discounted losses following the invasion. A hazard function characterizes the probability that the species will arrive by a particular date. This hazard function incorporates the salient factors driving invasions, such as the invasiveness of the species and the number of firms in the industry. Solving the dynamic optimization problem yields a time path of the optimal number of firms in the industry. The application of this model requires empirical analysis. However, the uncertainty in several relationships, such as potential damages, potential invasiveness, and the time of the invasions, necessitate assumptions based on educated guesses and a priori beliefs. To facilitate the model implementation, Knowler and Barbier make several simplifying assumptions in their analysis of the saltcedar (Tamarisk spp.), an ornamental shrub, which became invasive. The hazard function is estimated from a survey of decision-makers on their perceived risk of invasiveness. Based on USDA data for the horticultural industry, the industry’s profit function is fitted at the state-level using a second-order polynomial equation. The analysis of four model specifications for different treatments of the relationship between the number of firms and the hazard function, coupled with varying specifications of the hazard level (low- and high-hazard) and four levels of profitability illustrate two key points: (1) the optimal number of firms is always lower than the optimal long-run equilibrium without invasion risk and (2) the optimal number of firms and level of Pigovian taxes is sensitive to the hazard level. Under some conditions, the optimal number of firms is zero; i.e., it is optimal to prohibit all imports of the exotic species.

Conventional wisdom states that tariffs, or any protectionism, will reduce invasion risk as a consequence of a reduction in trade; Costello and McAusland (2003) demonstrate that this may not be the case. Protectionist policies can achieve a reduction in overall invasive species introductions. However, the failure to account for the role of agricultural damages skews the interpretation of the true efficacy of protectionist policies, which may actually increase invasion risk. This result is an example of the aforementioned disturbance hypothesis (see Factors Fueling the Invasion Process), and, in this case, human disturbance is often believed to increase the chance of invasion. Higher tariffs on agriculture will reduce agricultural imports, so domestic producers will increase production. This, in turn, increases land disturbance as more land is converted to agricultural production. This increase in land disturbances facilitates invasions by extant invasives as well as new ones, thus, any reductions in invasion risk from the tariffs are offset by increased risk from land disturbance. A complex theoretical framework presented in their paper incorporates the potential damages from different trade levels and commodities, the supply and demand elasticities for various commodities, and the level of protectionism on these commodities. Though their model is theoretical and difficult to parameterize, the analysis illustrates that setting policy based on conventional beliefs may lead to suboptimal results. As Costello and McAusland state:

"…the rate of introduction causing crop damages provides minimal (if not outright misleading) information about the rate of ecologically damaging invasions. This has important implications for the use of existing estimates of invasion related damage; while existing estimates are staggering, they omit invasion related costs to biodiversity and other non-monetized assets."

Whereas Costello and McAusland’s model does not incorporate averting behavior by farmers or the role of invasive species management activities, several salient observations are provided in their paper such as the usefulness of current introduction estimates and the impact of using incorrect empirical models. Also illustrated is the value of expanding the breadth of the analysis to better inform decision-making by including both direct and indirect consequences of incentive mechanisms, in addition to the underlying stochastic relationships. The crucial component is acknowledging and incorporating the economic aspects, such as price distortions and demand and supply responses to import changes. An often overlooked aspect of invasive species policies is addressed—the potential behavioral responses by the import-competing industries who respond to the supply changes resulting from the tariffs impact on the importing firms. Tariffs may produce positive effects for some firms while concurrently altering production choices by other firms, which can lead to other changes such as an increase in domestic agriculture intensity. The need for analysis to encompass the full extent of changes resulting from a policy is illustrated in this paper.

In a subsequent paper, McAusland and Costello (2004) analyze the combination of tariffs and monitoring practices to achieve the socially optimal level of prevention activities. The assumption that all components are known is shown in their model. Whereas tariffs and cargo inspections reduce the introductions of invasive species, the omission of explicit stochastic elements excludes this model from frameworks that can be implemented directly for risk management. The results of the analysis, though, are worth mentioning as they can provide insight for risk management practices: (1) it is always optimal to have a positive tariff although it may be optimal not to have inspections in some situations; (i.e., if the level of infection of the partner is so high that it is optimal to not inspect but instead to set a high tariff); (2) higher infection rates necessitate higher tariffs but not necessarily greater inspections; and (3) extending the time horizon results in greater inspections but not necessarily higher tariffs. They draw an analogy between this situation and the one involving pollution emissions, which requires monitoring to determine the pollution levels to levy the correct taxes. Here, the monitoring entails inspections that sort the uninfected goods from the infected ones. The findings from the inspections determine the amount of monitoring needed in the future and the level of taxes that should be set. At sufficiently high levels of infection, the optimal strategy is to discontinue monitoring and rely solely on taxes to repay the costs of invasives.

Horan and Lupi (2005) explore a tradable permit program as an alternative to current regulation of ballast water to reduce the number of invasive species entering the Great Lakes. Permits allow commercial vessels to release ballast water, which carries species. However, releases are unobservable; thus, they must be estimated as a function of vessel characteristics and management practices. The authors find that although permit trading produces the most efficient outcomes, appropriately targeted technology regulations can lead to similar results. Emission permits are considered more efficient than regulation because they provide a performance-based mechanism, which is why permits are preferred for pollution control. However, unlike pollution emissions, the existence of invasive species in ballast water is unknown beforehand, and, even after the species have been released, the species introductions are not observed due to a lack of appropriate monitoring technology. Also a potentially lengthy lag between introductions and spread (Crooks and Soulé 1999) further obfuscates the ability to pinpoint the individual polluter. This means that a specific vessel cannot be connected to a specific species introduction, because the outcome of a vessel’s actions is not directly observable. To overcome this lack of information, tradable permits can act as a proxy for the potential risk posed by each vessel via a performance measure that incorporates vessel-specific characteristics and firm actions aimed at reducing introduction risk.

Horan and Lupi’s permit trading model (2005) relates to a previous one introduced in Horan and others (2002) regarding prevention strategies in risky and uncertain scenarios (see Pure Uncertainty Versus Risk in Assessing Prevention Strategies). In this recent model, each firm introduces a range of species, measured by their biomass, through their vessels. The potential biosecurity actions that a firm can employ to reduce the risk of transporting species are considered inputs. There are two stochastic relationships: (1) the size of the biomass, which depends upon the biosecurity inputs and the firm’s characteristics, and (2) the post-introduction probability of establishment and spread, which depends on the given control strategy, the biomass, and the biosecurity inputs. Combining these two separate stochastic relationships characterizes the probability of a firm introducing an invasive species. The authors characterize the total probability of an individual species introduction as the sum of the separate probabilities of introduction over all firms. This total invasion probability drives the expected damages resulting from a species invasion. The policymaker’s objective is to minimize the social costs, which are represented by the costs of biosecurity inputs for all firms plus the expected damages resulting from successful invasions. Focusing on ballast water released by vessels in the Great Lakes, Horan and Lupi illustrate the model using data and estimates for probability of introduction and successful invasion, firm characteristics, biosecurity inputs, and costs.

Optimally, the marginal cost of an action (choice of biosecurity input) for each firm equals the expected marginal benefits of that action, or the decrease in expected damages. Permit trading requires much information including vessel- and firm-specific characteristics and actions, all potential invaders and expected damages, and probabilities for introductions and successful invasions as they relate to new habitats and firm behavior. Creating permits based on the specific characteristics of each vessel and firm and for each specific species would be the first-best option. However, with this scheme, the multiple permits for each species and each vessel would result in a cumbersome system. A second-best permit trading scheme, related to the first-best option, produces a desirable outcome but with only one permit for all species, instead of several different ones targeting different species. Whereas less efficient than the first-best approach, a single permit reduces the information requirements because the policymaker does not require detailed information for each specific firm and vessel. This approach finds that the first-best scheme provides the least costly option followed by the second-best trading scheme when simulating three risk scenarios for different mechanisms: (1) the first-best trading scheme with varying permits, (2) the second-best scheme with one permit, and (3) various technology regulations. This result holds for relatively moderate permitted levels of invasive species introductions; the difference between the regulation mechanisms fades with stricter permitted levels. Interestingly, their outcomes suggest that technology regulations can inexpensively mitigate risks if suitable technology is chosen and appropriately regulated. Although direct implementation requires several assumptions, this model offers a useful tool to analyze potential regulatory policies while accounting for the major stochastic relationships. Also, it takes the Knowler and Barbier (2005) analysis (see Trade Policy) one step further by demonstrating the potential loss incurred by simplifying assumptions to address information gaps.

By characterizing the unknown elements of any situation, managers can employ explicit frameworks to evaluate the potential outcomes of various policy mechanisms as illustrated in these papers. The authors were forced to make several simplifying assumptions to deal with a lack of data or to address the stochastic elements, but they still provide valuable analysis. They also illustrate the importance of evaluating policies in an explicit economic framework to capture the fullextent of the repercussions such as the social welfare loss from posing industry-wide taxes or implementing tariffs without accounting for the changes in industrial behavior.

Whereas it is assumed most  decision-makers have some information that can help characterize risk in invasive species management, there may be cases (Knightian pure uncertainty) where it is misleading to assign probabilities, and information is lost when the true lack of knowledge is overlooked. Horan and others (2002) tackle this issue using an aggregate model to capture pre-invasion decisions by firms whose actions can introduce invasive species. Horan and others (2002) argue that invasions cannot be analyzed using standard economic theory, which assigns probabilities to all situations regardless of the level of uncertainty. Traditional risk-management models function similarly by characterizing all risk, irrespective of the level of uncertainty, with probability distributions. The authors argue that standard expected utility theory (or traditional risk-management) does not apply to low probability events, especially when the events are catastrophic, as they could be in the case of invasive species. Non-native species invasions can be considered catastrophic since irreversibility of invasions poses potentially very high costs and irrevocable damage to native ecosystems. To illustrate the effects of incorporating differing levels of uncertainty into the decision-making framework, the authors identify optimal prevention strategies by firms under the traditional risk-management framework (with assumed probabilities) versus an ignorance model (full uncertainty, which is not characterized by probabilities), which appropriately reflects the circumstances before the invasion occurs.

In the traditional risk management model, the probability of introducing a species depends on the firm’s characteristics and the control strategies chosen by each individual firm. A species’ successful invasion depends on the biomass of the introduced species, the characteristics of the environment, and the firm’s characteristics. From the perspective of a policymaker regulating firms in an industry, the concept presented in the paper by Horan and others (2002) creates a framework where the stochastic elements are the species introductions and the success of the invasion. The framework, which focuses on general aggregate-level decisions, is fairly theoretical and the information necessary to implement this model directly may not be available. The probability of an invasion follows a Bernoulli distribution that depends on the actions of all firms in the industry. As the number of firms increase, the probability of an invasion approaches one. The present value of damages facing society depends on expected damages, expected costs, and the possible set of all species that may be introduced. The risk management problem is static meaning the state-of-the-world remains the same for the single planning period. The firm minimizes expected damages caused by the species plus the control, or abatement, costs that lessen the probability of a species introduction. The major distinction between the traditional framework and the ignorance model is the potential set of invading species; in the traditional framework, all species that can invade are known whereas under the ignorance model, the set of potential species contains a subset of species that is completely unknown. This approach gives rise to the idea that events are associated with different levels of potential surprise.

According to the traditional risk-management framework, (i.e., the expected value approach), the policymaker has two potential optimal strategies: (1) all firms should be unregulated or (2) all firms should undertake expensive measures so that the probability of an invasion is driven down to zero. Also, with a large number of firms, abatement is not optimal because the chances of invasion are high regardless of the control strategies pursued by individual firms. In both frameworks, the optimal strategy is to set marginal costs equal to expected marginal benefits, or the negative of damages. Under ignorance, though, firms will evaluate the marginal impacts of the events and subsequent potential outcomes quite differently. The difference in valuations of the marginal costs and damages leads to different outcomes for the two approaches. In the expected value scenario, low abatement is an optimum strategy for all firms whereas that is not the case for full uncertainty because the firms’ values are significantly different. Subsequently, policies using the uncertainty framework establish uniform performance limits for all firms as opposed to the risk management framework where limits vary for each firm. Straightforward application of this framework is unlikely; however, the theoretical model, which illustrates the importance of considering alternative decision frameworks when elements of the model are unknown is the greater contribution of this paper. Due to the importance of uncertainty in the invasion process, continued reliance on the traditional approach for characterizing risk could lead to a severely restricted view of the true situation. This does not mean that the expected value approach is not valuable, but it is crucial to be aware of other characterizations and unspoken caveats of these models.

After the species successfully establishes, the decision-maker may employ several control strategies: eradicate the population, slow the spread of the population through spatial control strategies, or take no action. As in the other stages of the invasion process, a species’ ability to successfully spread relates to its biological characteristics and the interaction with its surrounding habitat and species. Unlike previous stages, there may be more available information on the species’ characteristics at this stage, which can inform decision-making. From an ecological perspective, eradication may yield the most desirable outcome. However, it may be costly to achieve under conditions such as larger spatial scales or substantial population sizes. Consequently, eradication attempts often fail to reach their objectives. Sections that follow focus on the spatial aspects of control and the efficacy of eradication as a control strategy.

Invasive species management is inherently about the management of land, or space. Ecological literature provides the theoretical framework to capture the spatial aspects, (e.g., Shigesada and Kawasaki 1997); however, the majority of the economic literature fails to explicitly incorporate the spatial aspect. Discussion of the spatial effects on management is only found in the literature pertaining to control strategies following successful establishment. This literature is quite limited and does not include any stochastic aspects.

Barrier zones reduce the spread of species either through eradication of small populations or quarantining a population. Using a dynamic framework, Sharov and Liebhold (1998a) assess the management of barrier zones for gypsy moths in the U.S. To assess the efficacy of barrier zones, the authors construct a model of pest dispersal, which factors in the monetary damages and benefits of control. Model application requires information about the specific population: the length of the population front, the shape of the population, the spread rate, the cost of the barrier zone, the damages caused by the species, and the discount rate. The conceptual framework (based on the spatial, economic, and biological components) is evaluated for three different spatial population spread scenarios: a strip with a constant width, a rectangular area, and a circular area. Parameterizing this framework with gypsy moth data and information from the Slow-the-Spread program (http://www.gmsts.org/operations/) the authors demonstrate the benefits produced by containment and eradication strategies over disparate geographic areas.

The authors indicate that eradication is viable for a species with a limited range whereas slowing the species spread can be optimal in several scenarios. Using gypsy moth data as a case study, the model analysis shows eradication is optimal for certain small or isolated populations or both whereas slowing the spread is better for larger, more established populations. Slowing the spread, as a control strategy, can yield substantial reductions in population spread (Sharov and Liebhold 1998b). The merger of economic and ecological relationships into a spatial model is demonstrated for one of the first times in this paper. Hof (1998) constructs a spatial model to illustrate how the effectiveness of barrier zones is reduced by the dynamics of the managed population. As the population grows, it can extend the size of the barrier zone or splinter, thus reducing the viability of barrier zones as an optimal management tool. However, an important caveat is pointed out in these two papers that, as with most papers reviewed in this synthesis, implementing such a framework has certain limitations. The choice of functional forms, model structure, and the data greatly influence the outcomes. Altering assumptions on these functional forms or other relationships included in the model can lead to varying outcomes. However, Sharov and Liebhold’s model provides a spatial framework with explicit economic aspects that can be expanded to incorporate several scenarios and could potentially be extended to analyze decisions before the species begins spreading.

Building upon the framework set forth by Sharov and Liebhold (1998a), Cacho and others (2004) analyze the critical points that govern the optimal control strategy: eradication, containment, or doing nothing. Their model focuses on plants and includes several parameters such as maximum rate of spread, seed longevity, and costs of control. The authors represent the unknown length of seed longevity in differing environments by using a range of values in the biological parameters. They determine the switching points at which eradication and control are no longer optimal strategies by employing Scotch broom (Cytisus scoparius, L.) data and estimates. Based on this analysis, the salient characteristics are seed longevity and the spread rate. As the spread rate increases, the two switching points move closer together indicating that management should emphasize eradication.

Useful frameworks for incorporating the spatial dimensions into risk management strategies are proposed in these papers. Sharov and Liebhold (1998a) provide a caution in their paper, which is applicable to all models: ’Control of natural resources may depend considerably on social factors; thus the model…cannot automatically generate decisions.’ Further work to understand and incorporate societal and other factors will increase the viability of these frameworks. Overall, very little literature explicitly analyzes the spatial aspects, and future work should definitely focus on the spatial dimension as it is one of the most crucial components in the invasive species management problem. Perhaps researchers can learn from areas with substantial existing spatial research such as wildfire prevention or land conservation.

Eradication as a control strategy yields the most desirable outcome—total elimination of the invasive species from the habitat—but this strategy often fails due to numerous obstacles that impede complete removal, leading many to question the circumstances when eradication is feasible and optimal. Myers and others (2000) cited several successful eradication cases noting that success relies upon certain key conditions. Simberloff (2001) argues that eradication in itself is not impossible, but is idiosyncratic and contingent upon several criteria: (1) sufficient resources to successfully complete the project, (2) clear and identifiable authority to oversee the project, and (3) fairly good information regarding the biological characteristics of the species; i.e., the same basic criteria needed for successfully implementing any activity involved in invasive species management. He mentions resource constraints but without explicitly employing economic frameworks to assess the management options in the control stage. Several authors have addressed this gap by identifying the economic conditions under which eradication is optimal, (e.g., Eiswerth and van Kooten 2002, Olson and Roy 2002, Regan and others 2006, Taylor and Hastings 2004).

Olson and Roy (2002) focus on the costs of control and damages of species currently under management; i.e., they capture the decision of a manager who must choose future strategies for an existing population. The policymaker minimizes the expected discounted control costs plus the damages caused by the remaining population conditional upon the species’ growth function. The growth function incorporates environmental disturbances as a random process. As these disturbances increase, so do the chances of the population growing. Using this framework, they develop a rough guide of conditions favoring eradication. For small populations with marginal damages greater than marginal control costs, eradication is always optimal. When marginal damages are less than marginal costs, eradication is still optimal if the growth rate is sufficiently high. Irrespective of population size, eradication is optimal if the damages significantly outweigh the control costs in the worst possible scenario of environmental disturbances. Whereas this stylized framework is fairly general and cannot be directly implemented, it provides an approximate rule-of-thumb to ascertain the optimality of eradication as a management strategy. The one drawback is the information requirements; the marginal costs relative to the marginal damages must be known fairly well to determine the optimal management strategy.

Eradication not only depends on the relative costs and damages of controlling the population, but also upon the tenuous relationships between the population and its habitat. Environmental and demographic stochasticity and the Allee effect can drive low-density populations towards extinction (Liebhold and Bascompte 2003). The Allee effect works similarly to the critical depensation point or a threshold under which a population cannot survive. The Allee effect has been observed for low-density populations, but could apply to other populations as well. This effect contributes to an extinction threshold; if a species’ population is low enough, extinction will automatically occur. All species exhibit this effect, except asexual organisms like some plants. In general, management methods should be aimed at increasing the probability of extinction. Extinction is highly likely if an adequate number of the population is removed, although achieving 100-percent eradication is difficult. Taylor and Hastings (2004) utilize Spartina alterniflora (a non-native grass in Washington that exhibits a weak Allee effect) to test this theory while accounting for economic aspects. Their analysis of the Spartina alterniflora data indicates that, in the absence of an Allee effect, the optimal strategy involves the removal of isolated, high-growth, low-density species. The model analysis establishes a relationship between budget and optimal strategy: lower budgets necessitated the removal of low-density plants, and the optimal strategy with larger budgets is to focus on eradicating high-density areas. For this particular species, the Allee effect does not lead to cheaper eradication. Hence, the Allee effect plays a role in determining eradication strategies, but it must be considered on a species-specific basis and in conjunction with budget constraints.

Regan and others (2006) construct a theory to analyze the optimal time needed to survey an area before declaring that an eradication attempt has been successful. Evaluating the efficacy of eradication strategies depends on the reliability of survey strategies, which in turn, depends on the amount of time and resources devoted to detection. These authors postulate that managers facing budget constraints may prematurely cease surveying, which could result in a new eruption of the pest if the species was not fully eradicated. The authors develop a simple rule of thumb for the optimal number of consecutive zero surveys by minimizing the sum of survey costs and expected damages. They compare this rule of thumb with the results of an optimal forward-looking solution derived using stochastic dynamic programming. The key difference between the two approaches is that stochastic dynamic programming incorporates all the possibilities that can occur in the future, including the possibility that the plant will re-emerge and a new attempt at eradication will have to be undertaken, and then finds the best decision. The authors parameterize these two seemingly different approaches—the rule-of-thumb and the stochastic dynamic problem—using bitterweed (Helenium amarum) data. The authors state that this rule-of-thumb can reduce variability in decision strategies while increasing the sensitivity of their decisions to various parameters in the eradication programs.

Eiswerth and van Kooten (2002) argue that the categorization of risk in subjective terms necessitates the use of fuzzy membership functions, which differ from the traditional expected value approaches (similar to Horan and others 2002, see Pure Uncertainty Versus Risk in Assessing Prevention Strategies). Subjective risk assessments can produce widely varying outcomes depending on the scientists or experts administering the assessment, (e.g., Woodward and Bishop 1997). The paper presents a stochastic dynamic model maximizing the agricultural producers’ discounted present value of net returns. The objective function consists of the agricultural production, which depends on the size of the invasion and the choice of control technology. The objective function is conditional upon the species growth function, which includes a stochastic term. As part of this research, the authors surveyed land managers to gauge their management choices under risk. The authors parameterize this model using results of this survey and extant data for the yellow starthistle (Centaurea solstitialis). The analysis illustrates that land managers tend to aggressively control a species even when the economic criteria do not warrant such a stringent control regime. The optimal control strategy involves managing the spread of yellow starthistle instead of full eradication, even though this weed has significantly impacted agriculture.

Management activities in one stage have direct consequences on other stages, thus it is important to analyze several stages concurrently. For example, scarce resources necessitate allocation between several activities. Decision-makers determine these allocations concurrently, thus the framework should incorporate the relationships between these stages. Economic literature often focuses on the introduction and post-establishment stages of the invasion process to identify the optimal strategies between exclusion and control activities. The allocation between control and other activities, such as post-introduction detection, is the focus of some papers reviewed here. The interaction between mitigation and adaptation activities is discussed in Understanding Risk Mitigation Versus Adaptation. Optimal resource allocation strategies amongst differing activities are addressed in the other sections that follow.

Risk analysis often treats mitigation and adaptation separately, but invasive species risk analysis needs to account for both of these actions for effective management practices. Shogren (2000) discusses the distinction between mitigation— actions where people actively reduce the probability of a bad state, and adaptation— actions which reduce the magnitude of a bad state if it happens (as with insurance). He proposes the need to account for both of these actions simultaneously due to the fact that an action to reduce risk affects the consequences if the species does invade. His model is based on endogenous risk theory to analyze risk-benefit tradeoffs for explosive invaders, and it depicts the problem facing a representative policy maker allocating scarce resources. These ideas stem from economic theory on decision-making under risk and uncertainty as addressed in previous sections of this review (de Finetti 1974, Drèze 1987, Savage 1954, Von Neumann and Morgenstern 1944).

Perrings (2005) builds upon Shogren’s framework and extends it to examine decision-making practices aimed at allocating resources between these two strategies. He classifies management strategies addressing risk into the same categories: mitigation and adaptation. Mitigation refers to actions that alter the chances of an event occurring. In invasive species literature, mitigation activities reduce the likelihood of invasions. Adaptation refers to actions that alter the value of the outcome. These activities would reduce the impact cost of invasions without changing the probability of the invasions themselves. Decisions regarding mitigation and adaptation activities often occur simultaneously. The chosen strategy relates to where the species is in the invasion process; i.e., whether the species has just been introduced or whether it has already established. The manager must also assess whether the situation is observable or controllable. Perrings points out that there are two schools of thought regarding the predictability of invasions (see Factors Fueling the Invasion Process). The first school, including Williamson (1996), argues that invasions can rarely be predicted beyond a few indicators such as propagule pressure and the past invasion history of the species. Others, such as Rejmánek (1999), believe that the invasiveness of a species and the susceptibility of the land can be predicted by analyzing a wider range of salient characteristics.

Using probability transition matrices that follow a Markov Chain, Perrings evaluates four possible outcomes once a species has been introduced: (1) it may not establish, (2) it may establish irrespective of management activities, (3) it may establish, and its population will depend on the state of nature (including management activities), or (4) it may establish and have an unstable population in the long run. The probabilities in the transition matrices represent the overall resilience of the land against invasion. If these probabilities are known, a model of the system’s dynamics and the value function (both dependent on the probability transition matrix) can guide the optimal choice of strategies. In addition to the probabilities, the model requires knowledge of the expected net benefits and costs of different control regimes, and a feedback matrix that links control choices to the probability transition matrix. If this information is known, the outcomes of control measures; e.g., those that only reduce population size, can be assessed for their long-run effectiveness.

Mitigation is an appropriate option if the expected outcomes of management activities can be assigned some probabilities. In situations where probabilities for the connections between actions and outcomes are unknown, mitigation cannot occur, and managers are left with adaptation as the only possible strategy. Perrings’ main objective is to draw attention to the need to quantify unknown aspects as he states at the end of his paper, ’In an environment in which decision-making is increasingly dominated by non-probabilistic ‘scenarios’ which drive decision-makers to focus on adaptation, it is important to remind ourselves that this may be both inefficient and inequitable’. This argument arises from the idea that any structured analysis based on some quantitative information is better than the alternative because conventional wisdom does not necessarily lead to optimal strategies, such as the case of tariffs to reduce invasion risk (see Policy and Market-Based Mechanisms to Manage the Risk of Introductions).

Unlike the previous papers in this synthesis, the focus in this section is on the trade-offs between management strategies and their social benefits and costs. Welfare functions allow the analyst to capture the overall benefits and losses of a management decision. Several papers employ the use of welfare functions in their objective functions to assess optimal resource allocation strategies, (e.g., Finnoff and Tschirhart 2005, Finnoff and others 2005, Leung and others 2002).

Leung and others (2002) show that prevention is more cost effective than control. Stochastic dynamic programming captures the situation facing a policymaker allocating resources between prevention and control activities on an aggregate-level. Welfare consists of the profit function minus the costs of invasive species management activities. The invasive species grows according to a logistic function plus some stochastic term representing uncertainty in species growth patterns in the new environment. The planner’s maximization problem optimizes welfare over a probability transition matrix that reflects the probability of moving across states, (i.e., different invasion outcomes) given various allocations between exclusion and control strategies.

Implementing the Leung and others (2002) model requires the following: data on a species’ growth function, the costs of controlling that particular invasive species, the efficacy of control, the total inputs and costs for the industry, the total outputs and prices for the industry, the monetary loss caused by the invasive species, and the probability of invasion. Data on zebra mussels and power plants, coupled with estimates of certain biological characteristics and the probability of invasion, are used to simulate three possible scenarios for lakes: uninvaded over a 25-year time horizon, invaded over 25 years and uninvaded for 5 years. The simulations determine the optimal allocation for prevention strategies given two control options (do nothing or do something) for 10 years. The optimal expenditures for prevention activities yield the greatest welfare. However, the difference in cumulative welfare resulting from optimal expenditures, suboptimal expenditures, and taking no action is relatively small. Engaging in optimal prevention activities is ideal over the longer time horizon (25 years), whereas the optimal strategy with the shorter time horizon (5 years) is to not take any action. As in several other papers, Leung and others (2002) employ data from a highly invasive species with high growth rates and high damages (in this case, the zebra mussel). Using such a species illustrates the worst case scenario for invasives. Applying this model to less insidious invasive species may produce different outcomes. The advantage of this model is the explicit linkage between private industry and management activities. Whereas actual data may not exist for all components of the model, estimates can be used to analyze the potential scenarios facing the policymaker for diverse industries and invasive species.

Leung and others (2005) follow up their previous work with an attempt to bridge the gap between theory and application by proffering a framework to identify general rules-of-thumb for resource allocation over various invasive species management activities. Extending the concepts in their earlier paper, the authors establish the relationships underlying optimal choice of exclusion and control strategies. The policymaker endeavors to maximize cumulative social welfare conditional on several factors: (1) the welfare in an invaded state, (2) the welfare in an uninvaded state, and (3) the probability of invasion dependent on the prevention strategy, invasion parameters, and the efficacy of prevention. Based on the model analysis, optimal control expenditure increases with the system’s value and decreases with uncontrollable damages (amongst other rules). The optimal prevention expenditure is closely tied to the preventability of invasions. Several rules characterize the optimal expenditure including one stating expenditures decrease as the probability of unpreventable invasions increases. The authors provide a detailed list of data required to implement the model as well as a thorough comparative statics analysis of the interaction between the various parameters and variables. This model’s strength lies in its application using available data. However, the simplified framework comes at a cost— several strong assumptions (e.g., the specific functional forms, the relationships included or excluded in the framework, the availability of data necessary to implement the framework, etc.) underlie the model. The loss of specificity translates to a gain in the ease of implementation and a decrease in the time needed to reach general management rules.

Building upon the underlying trade-off between prevention and control, Finnoff and others (2007) evaluate the effect of manager’s risk preferences on the optimal investment in management activities. Risk preferences dictate the valuation and incorporation of risk into decision-making frameworks. The authors postulate that, based on their endogenous risk model (an extension of Shogren 2000, see Understanding Risk Mitigation Versus Adaptation), risk averse models tend to over-invest in control while under-investing in prevention. As a manager’s risk aversion increases, so does the propensity to implement control activities. This behavior results in increased invasions as indicated in their paper. This paper was based upon an earlier one (Finnoff and others 2005) where a similar endogenous risk framework analyzed the role of feedback between decision-makers, (i.e., the firms or the manager) and biological and economic aspects associated with invasions. Here, feedback refers to the ability of the decision-makers to update beliefs based on changes in the situation. If decision-makers neglect to respond to these changes, the results could range from minor efficiency loss to severe biological and economic consequences as a result of invasions.

Like humans, plants can be thought of as welfare maximizing organisms whose survival success depends on certain biological traits which can predict outcomes from interaction with other plants, humans, and their environment (Finnoff and Tschirhart 2005). Contrary to previous papers on species management, the focus in this paper is on the species, (i.e., the plant) as an optimizing agent, which aims to maximize its biomass conditional on specified parameters and the presence of competitors in the habitat. Finnoff and Tschirhart explain the uniqueness of this model compared to previous ones: "In the plant community model herein, the theory starts prior to population updates by first assuming the individual plant behaves as if it is choosing its optimum biomass. Optimization is done given the plant’s parameters and the presence of other competing plants in its own and other species." Using this model, the authors evaluate individual plant behavior and species interactions as they result from plant-specific traits, environmental factors such as temperature, and human interaction. Each scenario analysis offers a rough guideline for plant behavior given certain conditions.

The authors classify invasive species as redundant or successful. Redundant species fail to invade successfully but remain in the habitat as biological insurance until environmental conditions become favorable for them. Successful species effectively invade the new habitat from the start. These two categories are mutually exclusive, but species can switch groups over time as the environmental circumstances change. The plant’s efficient energy usage dictates its growth function, which updates the model. An individual plant’s optimization problem—maximizing net energy—includes the leaf size, the flow of solar radiation, the biomass, and the energy expended for the plant’s functioning. Additionally, as a member of a plant community, the population size and growth vis-à-vis the available land capacity combine to enter as a space constraint that also influences the individual plant’s optimization. The model of plant behavior is then incorporated to a policy-maker’s welfare maximization problem because there is feedback between human decisions such as agricultural management and species success. Through this framework, the authors capture the interconnection between ecological and economic relationships in a situation with multiple species. The policymaker chooses prevention and control efforts to manage an invasive species. The probability of invasion depends solely on prevention efforts. Accounting for human effects on species population, the plant’s growth function has altered to now include population reductions through harvest and control measures.

Based on the relationships and factors in just the plant relationships, the analysis determines that the optimum plant biomass in the steady state depends largely on plant-specific traits, namely those related to respiration activity. Expanding this result to multiple species provides criteria to predict species success in steady-state scenarios. Factors beyond the plant-specific parameters, such as temperature, also drive the optimization behavior. After augmenting the aforementioned plant relationships by temperature, the authors analyze the optimization behavior to find that any number of species can co-exist regardless of the resource constraints in this model. This outcome deviates from previous papers in that the number of resources dictates the maximum number of coexisting species populations. The authors construct a conceptual framework encompassing the major economic and ecological factors that impact plant success. Although the authors do not apply empirical data to the model, this can be done using data for current species and estimates for potential species. The majority of the model is deterministic except for the probability of invasions, thus the information necessary to implement the model should be available. By explicitly incorporating complex species interactions, a creative, albeit unorthodox, approach for evaluating the ecological consequences of human actions is proffered in this paper.

Optimal strategies for multiple activities can be found by focusing on the trade-offs between the management costs and the species’ damages deterred by engaging in the particular management activity. The optimal resource allocation between prevention and control activities with a stochastic initial population size depends on the marginal damage function of the invading species (Olson and Roy 2005). Whereas this model cannot be directly implemented due to the theoretical nature of the framework, their analysis produces general rule-of-thumb principles for optimal resource allocation between prevention and control activities. The framework represents a situation where an invasive species has been controlled, and the decision-maker must allocate resources for potential management strategies for the same species. As an example, the gypsy moth (Lymantria dispar) presents such circumstances; it has been controlled in certain areas and requires continuous management. The management options can vary from exclusionary activities for preventing new introductions of the gypsy moth, to control strategies for managing remaining gypsy moth populations.

The policymaker chooses the level of prevention and control activities. The costs of control and prevention are assumed to be known, but the damages from the resulting invasion are driven by a stochastic relationship representing the risk of an unknown invasion. The policymaker selects the prevention and control strategies simultaneously prior to the invasion, which reflects the decision-making process in risk management. However, the established population size is known indicating that the invasion had already occurred and these management decisions focus on potential invasions going forward from either the same species or other species.

The role of risk on optimal resource allocations is highlighted in this paper. An increase in risk is represented by an increase in the variability associated with the chance of an invasion. The optimal choice between prevention and control following such an increase in risk depends mainly on the shape of the marginal damage function. Thus, the species’ damage function must be known to apply this framework. Data on past damages from the species can be used to estimate the damage function, which can then determine the optimal management strategy for the species in an uninvaded area or a reoccurrence of the species in the same area.

Whereas most papers focus on the introduction and spread stages, few explicitly consider the detection stage between the introduction of the species and the subsequent establishment and spread. The unclear relationship between species that are intercepted or discovered during the introduction stage and the established species being found in ecosystems is due to the fact that successful introductions do not often translate to successful invasions (Williamson 1996). Even those species that successfully establish often begin to spread after long lag periods (Crooks and Soulé 1999). Lags occur for many reasons such as natural lags in population dynamics or changes in the environment and the genetic composition of extant species. Additionally, past experiences with species do not provide good indicators of their future invasiveness due to an ever-changing environment and the response to and by other species. Also, species introduced many years ago may now have populations that are sizeable enough to detect (Costello and Solow 2003). These factors contribute to the uncertainty surrounding the establishment stage of the invasion process.

If populations are detected early in the invasion process, either before they fully establish or as they are establishing, control strategies can commence sooner and, possibly, at a lower cost. Some species, such as the black-striped mussel (Mytilopsis sp.) in Australia, have been eradicated due to detection activities, which included constant surveying followed by quick mobilization upon detection (Myers and others 2000). Mehta and others (2007) capture the stochastic and dynamic aspects of this trade-off between detection and control activities. The model focuses on a decision-maker minimizing costs and expected damages for a single invasive species by choosing a constant optimal search level at the detection stage. The time of detection is stochastic and depends on the effort devoted to search activities and how easy it is to detect the species. Based on simulations representing four types of species, the model analysis indicates that it is often optimal to devote significant resources to detection efforts for species causing high damages, even if the species is difficult to detect. The optimal strategy for species that do not have a high-damage potential involves undertaking no action if the population is sufficiently small, if the detection is quite difficult, or if post-detection control activities are costly. Even if a species causes a high level of damage, it may not be optimal to invest in detection when the post-detection control strategy is relatively costly; (i.e., the control costs are near or greater than the damages produced by the species). The simulations show that the biological parameters are more influential than the economic parameters. This may be an artifact of the specific model but it is a point worthy of further exploration. It is demonstrated in the paper that the optimal detection strategy relies greatly on the detectability of the species, similar to findings from Cacho and others (2006) who apply search theory to a spatial model aimed at analyzing detection and control strategies. Whereas the Cacho and other's (2006) model does not include any economic aspects, it does incorporate the risk underlying these activities and the role of detection on subsequent eradication strategies to illustrate the importance of detectability in the optimal detection strategies for weeds.

Some characterizations of the trade-off between the costs of managing invasive species and the damages inflicted by them are provided in these papers. The variety of potential methods of addressing resource allocation amongst several activities is also touched upon. General guidelines for resource allocation are established as well. However, direct application of these models is fairly difficult. Specific models, or examples, of these strategies in practice would be quite instructive and useful for pragmatic application.

An overview of some of the existing frameworks for evaluating risk management from an economic perspective is provided in this synthesis, as the field of invasive species management literature continues to evolve and expand. New collaborations and new knowledge have spawned, and will continue to create, a wide range of methodologies aimed at identifying optimal strategies and mechanisms for diverse management cases and objectives. The individual sections illustrate that several creative and insightful decision-making frameworks have already been explored. Nonetheless, there are numerous potential research areas that need to be investigated.

Space and invasive species are closely intertwined. Models, which explicitly incorporate the spatial and economic aspects are crucial to the invasive species management problem, yet very few currently exist. Also, current economic models focus on only three major management activities. Other management activities, such as restoration and public outreach, offer high returns for invasive species management and ought to be considered in the risk management framework as they occupy a place in the decision-making framework for agency managers. The set of activities included in risk management framework should be expanded, as well as the number of activities included in resource allocation frameworks. Realistically, management activities are undertaken concurrently and the theoretical frameworks should reflect this.

Only a few models incorporate multiple species, so this should be expanded to understand the interaction between species as well as optimal resource allocations across species. Approaches that transcend the traditional risk management, or expected values and framework are employed in some papers; they highlight crucial issues involving the levels of risk facing managers. Increasing an awareness of different methodologies for incorporating stochastic elements will help agency managers and expand the number of tools available for characterizing management risk. Overall, these models tend to be general. Whereas that is important for establishing overall frameworks and guidelines, future work should focus on specific species to emphasize the link between theory and application. Also, the focus tends to be solely on insidious species in some papers whereas agencies face a wide gamut of invasive species. These frameworks should be applied to a variety of different types of species, and the first step towards this has been taken through the range of simulations used in these papers.

The interdisciplinary body of literature in this field is constantly growing. As such, certain key papers have been focused on in this synthesis while acknowledging that other recent or related papers may have been omitted. The purpose of the synthesis is to provide a basic overview of the existing state of invasive species risk management literature from an economic perspective. Hopefully, this review will encourage readers to continue to push the boundaries of this research by engaging across the disciplines to discover novel and exciting approaches for decision-making tools for invasive species.