The comparison of dispersal rate between invasive and native species varied by plant life form and functional traits.

A long dispersal distance is widely used to indicate high invasiveness, but it ignores the temporal dimensions of plant invasion. Faster dispersal rates (= distance/time) of invasive species than native ones have been widely used in modeling species invasion and planning control management. However, the comparison of dispersal rate between invasive and native plants, particularly for dispersal on a local or landscape scale, has not been tested with a comprehensive dataset. Moreover, both the effects of plant functional traits on the dispersal rate and variation in the functional-trait effects between invasive and native plants remain elusive. Compiling studies from 30 countries globally, we compared seed dispersal rates (km/year) on a local or landscape scale between 64 observations of invasive and 78 observations of native plants given effects of plant life forms, disturbance levels, and measurement methods. Furthermore, we compared the effects of functional traits on dispersal rate between invasive and native species. We found that: (1) Trait values were similar between the invasive and native plants except for the greater height of woody native plants than woody invasive ones; (2) Compared within the same plant life form, the faster dispersal rates of invasive species were found in herbaceous plants, not in woody plants, and disturbance level and measurement methods did not affect the rate comparison; (3) Plant height and seed length had significant effects on dispersal rates of both invasive and native plants, but the effect of leaf dry matter content (LDMC) was only significant on herbaceous invasive plants. The comparison of dispersal rate between invasive and native plants varied by plant life form. The convergent values but divergent dispersal effects of plant traits between invasive and native species suggest that the trait effects on invasiveness could be better understood by trait association with key factors in invasiveness, e.g., dispersal rate, than the direct trait comparison between invasive and native plants.

Examining the reproductive success of bull kelp (Nereocystis luetkeana, Phaeophyceae, Laminariales) in climate change conditions.

Climate change is affecting marine ecosystems in many ways, including raising temperatures and leading to ocean acidification. From 2014 to 2016, an extensive marine heat wave extended along the west coast of North America and had devastating effects on numerous species, including bull kelp (Nereocystis luetkeana). Bull kelp is an important foundation species in coastal ecosystems and can be affected by marine heat waves and ocean acidification; however, the impacts have not been investigated on sensitive early life stages. To determine the effects of changing temperatures and carbonate levels on Northern California's bull kelp populations, we collected sporophylls from mature bull kelp individuals in Point Arena, CA. At the Bodega Marine Laboratory, we released spores from field-collected bull kelp, and cultured microscopic gametophytes in a common garden experiment with a fully factorial design crossing modern conditions (11.63 ± 0.54°C and pH 7.93 ± 0.26) with observed extreme climate conditions (15.56 ± 0.83°C and 7.64 ± 0.32 pH). Our results indicated that both increased temperature and decreased pH influenced growth and egg production of bull kelp microscopic stages. Increased temperature resulted in decreased gametophyte survival and offspring production. In contrast, decreased pH had less of an effect but resulted in increased gametophyte survival and offspring production. Additionally, increased temperature significantly impacted reproductive timing by causing female gametophytes to produce offspring earlier than under ambient temperature conditions. Our findings can inform better predictions of the impacts of climate change on coastal ecosystems and provide key insights into environmental dynamics regulating the bull kelp lifecycle.

Biological invasions alter consumer-stress relationships along an estuarine gradient.

Estuaries represent steep stress gradients for aquatic organisms, with abiotic stress due to temperature and salinity typically increasing with distance into estuary. Invertebrate communities and their predators are strongly influenced by these stress gradients. The environmental stress model predicts that the importance of predation in structuring communities decreases with increasing environmental stress. Estuaries contain a stress gradient for marine organisms this includes salinity, temperature, and other abiotic properties. Additionally, estuaries are hotspots for biological invasions; increased stress tolerance among non-native species could change the predictions of the environmental stress model. In this study, we investigate how introduced species alter the predictions of the environmental stress model by examining the effects of predators on sessile invertebrates across an estuarine gradient. To do this, we deployed recruitment plates across the estuarine gradient of Tomales Bay, California, USA using various caging treatments over the summer of 2019. We found that the effect of predation changed across sites, with the mid-estuary site experiencing the greatest reductions in prey abundance and prey species richness when exposed to predators. This was likely to be due to higher proportions of non-native prey and predator taxa mid-estuary, including solitary ascidians, which are highly susceptible to predation. Overall, predation did not follow the predictions of the environmental stress model, but rather followed the abundance of functional groups with non-native species, whose distribution could be mediated by environmental stress gradients. We suggest that this may be a general result and that communities subject to large numbers of stress-tolerant invaders may have high rates of consumption in high stress areas, contrasting predictions by previous models.

Mapping oysters on the Pacific coast of North America: A coast-wide collaboration to inform enhanced conservation.

To conserve coastal foundation species, it is essential to understand patterns of distribution and abundance and how they change over time. We synthesized oyster distribution data across the west coast of North America to develop conservation strategies for the native Olympia oyster (Ostrea lurida), and to characterize populations of the non-native Pacific oyster (Magallana gigas). We designed a user-friendly portal for data entry into ArcGIS Online and collected oyster records from unpublished data submitted by oyster experts and from the published literature. We used the resulting 2,000+ records to examine spatial and temporal patterns and made an interactive web-based map publicly available. Comparing records from pre-2000 vs. post-2000, we found that O. lurida significantly decreased in abundance and distribution, while M. gigas increased significantly. Currently the distribution and abundance of the two species are fairly similar, despite one species being endemic to this region since the Pleistocene, and the other a new introduction. We mapped the networks of sites occupied by oysters based on estimates of larval dispersal distance, and found that these networks were larger in Canada, Washington, and southern California than in other regions. We recommend restoration to enhance O. lurida, particularly within small networks, and to increase abundance where it declined. We also recommend restoring natural biogenic beds on mudflats and sandflats especially in the southern range, where native oysters are currently found most often on riprap and other anthropogenic structures. This project can serve as a model for collaborative mapping projects that inform conservation strategies for imperiled species or habitats.

Balanced polymorphism fuels rapid selection in an invasive crab despite high gene flow and low genetic diversity.

Adaptation across environmental gradients has been demonstrated in numerous systems with extensive dispersal, despite high gene flow and consequently low genetic structure. The speed and mechanisms by which such adaptation occurs remain poorly resolved, but are critical to understanding species spread and persistence in a changing world. Here, we investigate these mechanisms in the European green crab Carcinus maenas, a globally distributed invader. We focus on a northwestern Pacific population that spread across >12 degrees of latitude in 10 years from a single source, following its introduction <35 years ago. Using six locations spanning >1500 km, we examine genetic structure using 9376 single nucleotide polymorphisms (SNPs). We find high connectivity among five locations, with significant structure between these locations and an enclosed lagoon with limited connectivity to the coast. Among the five highly connected locations, the only structure observed was a cline driven by a handful of SNPs strongly associated with latitude and winter temperature. These SNPs are almost exclusively found in a large cluster of genes in strong linkage disequilibrium that was previously identified as a candidate for cold tolerance adaptation in this species. This region may represent a balanced polymorphism that evolved to promote rapid adaptation in variable environments despite high gene flow, and which now contributes to successful invasion and spread in a novel environment. This research suggests an answer to the paradox of genetically depauperate yet successful invaders: populations may be able to adapt via a few variants of large effect despite low overall diversity.

Conservation aquaculture as a tool for imperiled marine species: Evaluation of opportunities and risks for Olympia oysters, Ostrea lurida.

Conservation aquaculture is becoming an important tool to support the recovery of declining marine species and meet human needs. However, this tool comes with risks as well as rewards, which must be assessed to guide aquaculture activities and recovery efforts. Olympia oysters (Ostrea lurida) provide key ecosystem functions and services along the west coast of North America, but populations have declined to the point of local extinction in some estuaries. Here, we present a species-level, range-wide approach to strategically planning the use of aquaculture to promote recovery of Olympia oysters. We identified 12 benefits of culturing Olympia oysters, including identifying climate-resilient phenotypes that add diversity to growers' portfolios. We also identified 11 key risks, including potential negative ecological and genetic consequences associated with the transfer of hatchery-raised oysters into wild populations. Informed by these trade-offs, we identified ten priority estuaries where aquaculture is most likely to benefit Olympia oyster recovery. The two highest scoring estuaries have isolated populations with extreme recruitment limitation-issues that can be addressed via aquaculture if hatchery capacity is expanded in priority areas. By integrating social criteria, we evaluated which project types would likely meet the goals of local stakeholders in each estuary. Community restoration was most broadly suited to the priority areas, with limited commercial aquaculture and no current community harvest of the species, although this is a future stakeholder goal. The framework we developed to evaluate aquaculture as a tool to support species recovery is transferable to other systems and species globally; we provide a guide to prioritizing local knowledge and developing recommendations for implementation by using transparent criteria. Our collaborative process engaging diverse stakeholders including managers, scientists, Indigenous Tribal representatives, and shellfish growers can be used elsewhere to seek win-win opportunities to expand conservation aquaculture where benefits are maximized for both people and imperiled species.

Scaling up experimental stress responses of grass invasion to predictions of continental-level range suitability.

Understanding how the biological invasion is driven by environmental factors will improve model prediction and advance early detection, especially in the context of accelerating anthropogenic ecological changes. Although a large body of studies has examined how favorable environments promote biological invasions, a more comprehensive and mechanistic understanding of invasive species response to unfavorable/stressful conditions is still developing. Grass invasion has been problematic across the globe; in particular, C4 grass invaders, with high drought tolerance, adaptations to high temperatures, and high water use efficiency, could become more severe. Here, we conducted a rigorous microcosm experiment, with one of the most damaging invasive C4 grass, cogongrass (Imperata cylindrica), to explore how cogongrass responds to soil water and nutrient stress. We further integrated the results of the microcosm study with a species distribution model to (1) corroborate greenhouse results with field observations and (2) validate the robustness of our findings at subcontinental scales. Both the microcosm experiments and species distribution model agreed that soil water stress had a stronger impact on cogongrass than the nutrient one. New vegetative growth of cogongrass continued to be inhibited by the prior water stress. The significant water effect on cogongrass total biomass was supported by the finding that both allometric and biochemical traits of cogongrass did not show significant responses to the changes in water treatment. Different to the conventional wisdom that nutrient enrichment plays a bigger role in facilitating biological invasions, this study highlighted the possibility that water conditions may have a more substantial effect on some aggressive invaders. Therefore, an important implication of this study on biological conservation is that field managers might take advantage of the negative effect of global drought on some invasive species to increase the efficiency of their controlling efforts because invasive species may become more vulnerable under drought effect.

Stage-specific overcompensation, the hydra effect, and the failure to eradicate an invasive predator.

As biological invasions continue to increase globally, eradication programs have been undertaken at significant cost, often without consideration of relevant ecological theory. Theoretical fisheries models have shown that harvest can actually increase the equilibrium size of a population, and uncontrolled studies and anecdotal reports have documented population increases in response to invasive species removal (akin to fisheries harvest). Both findings may be driven by high levels of juvenile survival associated with low adult abundance, often referred to as overcompensation. Here we show that in a coastal marine ecosystem, an eradication program resulted in stage-specific overcompensation and a 30-fold, single-year increase in the population of an introduced predator. Data collected concurrently from four adjacent regional bays without eradication efforts showed no similar population increase, indicating a local and not a regional increase. Specifically, the eradication program had inadvertently reduced the control of recruitment by adults via cannibalism, thereby facilitating the population explosion. Mesocosm experiments confirmed that adult cannibalism of recruits was size-dependent and could control recruitment. Genomic data show substantial isolation of this population and implicate internal population dynamics for the increase, rather than recruitment from other locations. More broadly, this controlled experimental demonstration of stage-specific overcompensation in an aquatic system provides an important cautionary message for eradication efforts of species with limited connectivity and similar life histories.

Local and regional variation in effects of burrowing crabs on plant community structure.

Burrowing animals can profoundly influence the structure of surrounding communities, as well as the performance of individual species. Changes in the community structure of burrowing animals or plants together with changing abiotic parameters could shift the influence of burrowers on surrounding habitats. For example, prior studies in salt marshes suggest that fiddler crabs stimulate cordgrass production, but leaf-grazing crabs suppress cordgrass production. Unfortunately, testing this prediction and others are impeded because few studies have examined crab impacts on the plant community and across multiple sites, multiple years, or both. This challenges our ability to predict how burrowing animals will influence plant community structure, and when and where these impacts will occur. We manipulated the densities of the dominant burrowing crabs in plant assemblages dominated by Pacific cordgrass (Spartina foliosa) and perennial pickleweed (Sarcocornia pacifica) at three sites in southern California for three years (2016, 2017, 2018). Crab impacts on plant community structure differed among each of our three sites. In contrast to our predictions, (1) leaf-grazing crabs (Pachygrapsus crassipes) had positive effects on cordgrass cover at one site and no effect on cordgrass production at a nearby site in the same marsh and (2) fiddler crabs (Uca crenulata) did not stimulate cordgrass production at another marsh. Because crabs affected traits of cordgrass, but not pickleweed, in the direction consistent with changes in cordgrass cover, we propose that marsh-specific crab effects on community structure were largely mediated through changes in cordgrass, as opposed to pickleweed. Importantly, crabs facilitated cordgrass during marsh-wide cordgrass loss, suggesting that crabs may mitigate environmental stress for this ecologically important plant. Because cordgrass abundance can be a critical measure of marsh functioning and is often a restoration target, we suggest that managing cordgrass populations would benefit from additional information about crab populations and their impacts among years, and among and within marshes.

Nutrients mitigate the impacts of extreme drought on plant invasions.

Extreme climate events, such as drought, are becoming increasingly important drivers of plant community change, yet little is known about their impacts on invasive plants. Further, drought impacts may be altered by other anthropogenic stressors, such as eutrophication. We found drought dramatically reduced density of invasive Lepidium latifolium in salt marshes, and this die-back was mitigated by nutrient addition. In a 3-yr field experiment (2014-2016) conducted during an unprecedented drought (2012-2015), we tracked the effects of drought and nutrient addition on the plant community. We conducted this research at four salt marshes across a salinity gradient in the San Francisco Bay, California, USA. We manipulated paired native and invaded plots, one-half of which were treated monthly with N and P for 1.5 yr during the most intense period of the drought and one subsequent wet winter. In addition, we monitored unmanipulated L. latifolium-invaded transects within our freshest and most saline sites throughout the three years of our manipulative experiment and one additional wet winter. We documented a dramatic die-back of invasive L. latifolium during extreme drought, with reductions in stem density (52-100%) and height (17-47%) that were more severe at low salinity sites than high salinity sites. We found nutrient application lessened the effect of drought on L. latifolium stem density, but not height. In native plots, extreme drought reduced native plant cover (4-24%), but nutrient addition mitigated this impact. Interestingly, native plants in invaded plots did not suffer reductions in cover due to drought, perhaps because they were simultaneously benefiting from the die-back of the invader. Our results show drought negatively impacted both native and invasive plants and this impact was stronger on the invader, which experienced persistent declines two years after the end of the drought. However, by mitigating the effect of drought on invasive plants, nutrient addition potentially erased the advantage drought provided native plants over invasive plants under ambient nutrient conditions.

Supporting Spartina: Interdisciplinary perspective shows Spartina as a distinct solid genus.

In 2014, a DNA-based phylogenetic study confirming the paraphyly of the grass subtribe Sporobolinae proposed the creation of a large monophyletic genus Sporobolus, including (among others) species previously included in the genera Spartina, Calamovilfa, and Sporobolus. Spartina species have contributed substantially (and continue contributing) to our knowledge in multiple disciplines, including ecology, evolutionary biology, molecular biology, biogeography, experimental ecology, biological invasions, environmental management, restoration ecology, history, economics, and sociology. There is no rationale so compelling to subsume the name Spartina as a subgenus that could rival the striking, global iconic history and use of the name Spartina for over 200 yr. We do not agree with the subjective arguments underlying the proposal to change Spartina to Sporobolus. We understand the importance of both the objective phylogenetic insights and of the subjective formalized nomenclature and hope that by opening this debate we will encourage positive feedback that will strengthen taxonomic decisions with an interdisciplinary perspective. We consider that the strongly distinct, monophyletic clade Spartina should simply and efficiently be treated as the genus Spartina.

Into the weeds: Matching importation history to genetic consequences and pathways in two widely used biological control agents.

The intentional introduction of exotic species through classical biological control programs provides unique opportunities to examine the consequences of population movement and ecological processes for the genetic diversity and population structure of introduced species. The weevils Neochetina bruchi and N. eichhorniae (Coleoptera: Curculionidae) have been introduced globally to control the invasive floating aquatic weed, Eichhornia crassipes, with variable outcomes. Here, we use the importation history and data from polymorphic microsatellite markers to examine the effects of introduction processes on population genetic diversity and structure. We report the first confirmation of hybridization between these species, which could have important consequences for the biological control program. For both species, there were more rare alleles in weevils from the native range than in weevils from the introduced range. N. eichhorniae also had higher allelic richness in the native range than in the introduced range. Neither the number of individuals initially introduced nor the number of introduction steps appeared to consistently affect genetic diversity. We found evidence of genetic drift, inbreeding, and admixture in several populations as well as significant population structure. Analyses estimated two populations and 11 sub-clusters for N. bruchi and four populations and 23 sub-clusters for N. eichhorniae, indicating divergence of populations during and after introduction. Genetic differentiation and allocation of introduced populations to source populations generally supported the documented importation history and clarified pathways in cases where multiple introductions occurred. In populations with multiple introductions, genetic admixture may have buffered against the negative effects of serial bottlenecks on genetic diversity. The genetic data combined with the introduction history from this biological control study system provide insight on the accuracy of predicting introduction pathways from genetic data and the consequences of these pathways for the genetic variation and structure of introduced species.

Timing of stressors alters interactive effects on a coastal foundation species.

The effects of climate-driven stressors on organismal performance and ecosystem functioning have been investigated across many systems; however, manipulative experiments generally apply stressors as constant and simultaneous treatments, rather than accurately reflecting temporal patterns in the natural environment. Here, we assessed the effects of temporal patterns of high aerial temperature and low salinity on survival of Olympia oysters (Ostrea lurida), a foundation species of conservation and restoration concern. As single stressors, low salinity (5 and 10 psu) and the highest air temperature (40°C) resulted in oyster mortality of 55.8, 11.3, and 23.5%, respectively. When applied on the same day, low salinity and high air temperature had synergistic negative effects that increased oyster mortality. This was true even for stressor levels that were relatively mild when applied alone (10 psu and 35°C). However, recovery times of two or four weeks between stressors eliminated the synergistic effects. Given that most natural systems threatened by climate change are subject to multiple stressors that vary in the timing of their occurrence, our results suggest that it is important to examine temporal variation of stressors in order to more accurately understand the possible biological responses to global change.

Coast-wide recruitment dynamics of Olympia oysters reveal limited synchrony and multiple predictors of failure.

Recruitment of new propagules into a population can be a critical determinant of adult density. We examined recruitment dynamics in the Olympia oyster (Ostrea lurida), a species occurring almost entirely in estuaries. We investigated spatial scales of interannual synchrony across 37 sites in eight estuaries along 2,500 km of Pacific North American coastline, predicting that high vs. low recruitment years would coincide among neighboring estuaries due to shared exposure to regional oceanographic factors. Such synchrony in recruitment has been found for many marine species and some migratory estuarine species, but has never been examined across estuaries in a species that can complete its entire life cycle within the same estuary. To inform ongoing restoration efforts for Olympia oysters, which have declined in abundance in many estuaries, we also investigated predictors of recruitment failure. We found striking contrasts in absolute recruitment rate and frequency of recruitment failure among sites, estuaries, and years. Although we found a positive relationship between upwelling and recruitment, there was little evidence of synchrony in recruitment among estuaries along the coast, and only limited synchrony of sites within estuaries, suggesting recruitment rates are affected more strongly by local dynamics within estuaries than by regional oceanographic factors operating at scales encompassing multiple estuaries. This highlights the importance of local wetland and watershed management for the demography of oysters, and perhaps other species that can complete their entire life cycle within estuaries. Estuaries with more homogeneous environmental conditions had greater synchrony among sites, and this led to the potential for estuary-wide failure when all sites had no recruitment in the same year. Environmental heterogeneity within estuaries may thus buffer against estuary-wide recruitment failure, analogous to the portfolio effect for diversity. Recruitment failure was correlated with lower summer water temperature, higher winter salinity, and shorter residence time: all indicators of stronger marine influence on estuaries. Recruitment failure was also more common in estuaries with limited networks of nearby adult oysters. Large existing oyster networks are thus of high conservation value, while estuaries that lack them would benefit from restoration efforts to increase the extent and connectivity of sites supporting oysters.

Global threats from invasive alien species in the twenty-first century and national response capacities.

Invasive alien species (IAS) threaten human livelihoods and biodiversity globally. Increasing globalization facilitates IAS arrival, and environmental changes, including climate change, facilitate IAS establishment. Here we provide the first global, spatial analysis of the terrestrial threat from IAS in light of twenty-first century globalization and environmental change, and evaluate national capacities to prevent and manage species invasions. We find that one-sixth of the global land surface is highly vulnerable to invasion, including substantial areas in developing economies and biodiversity hotspots. The dominant invasion vectors differ between high-income countries (imports, particularly of plants and pets) and low-income countries (air travel). Uniting data on the causes of introduction and establishment can improve early-warning and eradication schemes. Most countries have limited capacity to act against invasions. In particular, we reveal a clear need for proactive invasion strategies in areas with high poverty levels, high biodiversity and low historical levels of invasion.

Testing local and global stressor impacts on a coastal foundation species using an ecologically realistic framework.

Despite the abundance of literature on organismal responses to multiple environmental stressors, most studies have not matched the timing of experimental manipulations with the temporal pattern of stressors in nature. We test the interactive effects of diel-cycling hypoxia with both warming and decreased salinities using ecologically realistic exposures. Surprisingly, we found no evidence of negative synergistic effects on Olympia oyster growth; rather, we found only additive and opposing effects of hypoxia (detrimental) and warming (beneficial). We suspect that diel-cycling provided a temporal refuge that allowed physiological compensation. We also tested for latent effects of warming and hypoxia to low-salinity tolerance using a seasonal delay between stressor events. However, we did not find a latent effect, rather a threshold survival response to low salinity that was independent of early life-history exposure to warming or hypoxia. The absence of synergism is likely the result of stressor treatments that mirror the natural timing of environmental stressors. We provide environmental context for laboratory experimental data by examining field time series environmental data from four North American west coast estuaries and find heterogeneous environmental signals that characterize each estuary, suggesting that the potential stressor exposure to oysters will drastically differ over moderate spatial scales. This heterogeneity implies that efforts to conserve and restore oysters will require an adaptive approach that incorporates knowledge of local conditions. We conclude that studies of multiple environmental stressors can be greatly improved by integrating ecologically realistic exposure and timing of stressors found in nature with organismal life-history traits.

Optimal approaches for balancing invasive species eradication and endangered species management.

Resolving conflicting ecosystem management goals-such as maintaining fisheries while conserving marine species or harvesting timber while preserving habitat-is a widely recognized challenge. Even more challenging may be conflicts between two conservation goals that are typically considered complementary. Here, we model a case where eradication of an invasive plant, hybrid Spartina, threatens the recovery of an endangered bird that uses Spartina for nesting. Achieving both goals requires restoration of native Spartina. We show that the optimal management entails less intensive treatment over longer time scales to fit with the time scale of natural processes. In contrast, both eradication and restoration, when considered separately, would optimally proceed as fast as possible. Thus, managers should simultaneously consider multiple, potentially conflicting goals, which may require flexibility in the timing of expenditures.

Integrated assessment of biological invasions.

As the main witnesses of the ecological and economic impacts of invasions on ecosystems around the world, ecologists seek to provide the relevant science that informs managers about the potential for invasion of specific organisms in their region(s) of interest. Yet, the assorted literature that could inform such forecasts is rarely integrated to do so, and further, the diverse nature of the data available complicates synthesis and quantitative prediction. Here we present a set of analytical tools for synthesizing different levels of distributional and/or demographic data to produce meaningful assessments of invasion potential that can guide management at multiple phases of ongoing invasions, from dispersal to colonization to proliferation. We illustrate the utility of data-synthesis and data-model assimilation approaches with case studies of three well-known invasive species--a vine, a marine mussel, and a freshwater crayfish--under current and projected future climatic conditions. Results from the integrated assessments reflect the complexity of the invasion process and show that the most relevant climatic variables can have contrasting effects or operate at different intensities across habitat types. As a consequence, for two of the study species climate trends will increase the likelihood of invasion in some habitats and decrease it in others. Our results identified and quantified both bottlenecks and windows of opportunity for invasion, mainly related to the role of human uses of the landscape or to disruption of the flow of resources. The approach we describe has a high potential to enhance model realism, explanatory insight, and predictive capability, generating information that can inform management decisions and optimize phase-specific prevention and control efforts for a wide range of biological invasions.

Modeling the relationship between propagule pressure and invasion risk to inform policy and management.

Predicting population establishment based on initial population size is a theoretically and empirically challenging problem whose resolution informs a multitude of applications. Indeed, it is a central problem in the management of introduced, endangered, harvested, and pathogenic organisms. We focus here on introduced species. We synthesize the current state of modeling in this predictive enterprise and outline future directions in the application of these models to developing regulations intended to prevent the establishment of invaders. Descriptive and mechanistic models of single-population introductions are fairly well developed and have provided insight into invasion risk in laboratory and field conditions. However, many invasions stem from large-scale and repeated releases of a multitude of species from relatively indiscriminate invasion vectors associated with international trade and travel. Vector-scale models of invasion risk are less well developed and are characterized largely by the use of untested proxy variables for propagule pressure. We illustrate the problems associated with proxy variables and introduce a more mechanistic theoretical formulation characterizing vector-scale invasion pressure in terms of propagule pressure (number of introduced individuals) and colonization pressure (number of introduced species). We outline key questions to be addressed in applying both single-population and vector-scale models to the development of threshold-based invasion regulations. We illustrate these ecological and applied questions using examples from terrestrial, aquatic, and marine systems. We develop in detail examples from ballast-water transport that, as one of the best-characterized global invasion vectors and one that is subject to emerging international threshold-based biosecurity regulations, provides a rich case study.