Testing alien plant distribution and habitat invasibility in mountain ecosystems: growth form matters

Most studies focused on understanding habitat invasibility use the current levels of invasion as a direct proxy of habitat invasibility. This has shown to be biased by the influence of propagule pressure and climate. We suggest that plant growth forms need to be considered as an extra factor, as habitat preferences might not be equal for all potential invaders. We test the influence of propagule pressure, climate and habitat characteristics on the current level of invasion and habitat invasibility, specifically addressing whether an analysis focused on growth forms evidence different patterns than the total pool of alien species. We used 499 floristic vegetation plots located in Córdoba Mountains. We used proportional alien richness of the total pool and for each growth form as response variables. We identified models that best explained current levels of invasion. We used the residuals of the models with propagule pressure and climate as the response variable. Then, we performed linear models to test the relationship between habitat characteristics and the residuals of the models. We found different drivers of current alien distribution patterns for the total pool and each growth form. Habitat invasibility was not equal when quantified for the total pool or growth forms. Shrublands and outcrops were recorded as less susceptible to woody invasion, while grasslands and native woodlands were resistant to the invasion of grasses and none habitat type was resistant to the invasion of forbs. We highlight that the current level of invasion and habitat invasibility are highly growth form dependent.     

Defining invasiveness and invasibility in ecological networks

The success of a biological invasion is context dependent, and yet two key concepts—the invasiveness of species and the invasibility of recipient ecosystems—are often defined and considered separately. We propose a framework that can elucidate the complex relationship between invasibility and invasiveness. It is based on trait-mediated interactions between species and depicts the response of an ecological network to the intrusion of an alien species, drawing on the concept of community saturation. Here, invasiveness of an introduced species with a particular trait is measured by its per capita population growth rate when the initial propagule pressure of the introduced species is very low. The invasibility of the recipient habitat or ecosystem is dependent on the structure of the resident ecological network and is defined as the total width of an opportunity niche in the trait space susceptible to invasion. Invasibility is thus a measure of network instability. We also correlate invasibility with the asymptotic stability of resident ecological network, measured by the leading eigenvalue of the interaction matrix that depicts trait-based interaction intensity multiplied by encounter rate (a pairwise product of propagule pressure of all members in a community). We further examine the relationship between invasibility and network architecture, including network connectance, nestedness and modularity. We exemplify this framework with a trait-based assembly model under perturbations in ways to emulate fluctuating resources and random trait composition in ecological networks. The maximum invasiveness of a potential invader (greatest intrinsic population growth rate) was found to be positively correlated with invasibility of the recipient ecological network. Additionally, ecosystems with high network modularity and high ecological stability tend to exhibit high invasibility. Where quantitative data are lacking we propose using a qualitative interaction matrix of the ecological network perceived by a potential invader so that the structural network stability and invasibility can be estimated from the literature or from expert opinion. This approach links network structure, invasiveness and invasibility in the context of trait-mediated interactions, such as the invasion of insects into mutualistic and antagonistic networks.     

群落可侵入性及其影响因素

 可侵入性用于评价群落易遭受生物入侵的程度,受外来种死亡率、区域气候、干扰水平、生态系统抵抗入侵的能力、本地种竞争和抗干扰能力等因素的影响。当前对群落或区域间可侵入性的比较常以外来种数量或丰度为据,然而这两者仅代表了群落内单一的动态过程,不足以作为衡量群落可侵入性的广泛标准。借助一个描述外来种数量的简单模型阐明,由于影响可侵入性因素的复杂性,各地之间的可侵入性几乎不可比较。并从入侵过程、入侵种特性及本地种、本地群落对入侵的抵抗性几方面对群落可侵入性进行了阐述分析,其中着重介绍入侵生态中几个重要的概念,如可侵     

Propagule Pressure: A Null Model for Biological Invasions

Invasion ecology has been criticised for its lack of general principles. To explore this criticism, we conducted a meta-analysis that examined characteristics of invasiveness (i.e. the ability of species to establish in, spread to, or become abundant in novel communities) and invasibility (i.e. the susceptibility of habitats to the establishment or proliferation of invaders). There were few consistencies among invasiveness characteristics (3 of 13): established and abundant invaders generally occupy similar habitats as native species, while abundant species tend to be less affected by enemies; germination success and reproductive output were significantly positively associated with invasiveness when results from both stages (establishment/spread and abundance/impact) were combined. Two of six invasibility characteristics were also significant: communities experiencing more disturbance and with higher resource availability sustained greater establishment and proliferation of invaders. We also found that even though ‘propagule pressure’ was considered in only ~29% of studies, it was a significant predictor of both invasiveness and invasibility (55 of 64 total cases). Given that nonindigenous species are likely introduced non-randomly, we contend that ‘propagule biases’ may confound current paradigms in invasion ecology. Examples of patterns that could be confounded by propagule biases include characteristics of good invaders and susceptible habitats, release from enemies, evolution of ‘invasiveness’, and invasional meltdown. We conclude that propagule pressure should serve as the basis of a null model for studies of biological invasions when inferring process from patterns of invasion. An erratum to this article can be found at     

群落可入侵性及环境胁迫

群落的可入侵性研究是入侵生态学的中心内容。从群落进化历史,群落结构,繁殖体压力。干扰和胁迫等5个影响入侵的主要因素综述了近年来群落可入侵性研究的工作进展和成果。其中重点阐述了群落结构对入侵的影响。包括群落物种组成,物种多样性和物种功能群多样性的诸多实验研究和相关假说,并用理论模型结合具体实验研究探讨了环境胁迫和可入侵性的关系。针对目前群落可入侵性研究存在的问题提出了自己的见解。     

Hotspots of plant invasion predicted by propagule pressure and ecosystem characteristics

Aim Biological invasions pose a major conservation threat and are occurring at an unprecedented rate. Disproportionate levels of invasion across the landscape indicate that propagule pressure and ecosystem characteristics can mediate invasion success. However, most invasion predictions relate to species’ characteristics (invasiveness) and habitat requirements. Given myriad invaders and the inability to generalize from single‐species studies, more general predictions about invasion are required. We present a simple new method for characterizing and predicting landscape susceptibility to invasion that is not species‐specific. Location Corangamite catchment (13,340 km²), south‐east Australia. Methods Using spatially referenced data on the locations of non‐native plant species, we modelled their expected proportional cover as a function of a site’s environmental conditions and geographic location. Models were built as boosted regression trees (BRTs). Results On average, the BRTs explained 38% of variation in occupancy and abundance of all exotic species and exotic forbs. Variables indicating propagule pressure, human impacts, abiotic and community characteristics were rated as the top four most influential variables in each model. Presumably reflecting higher propagule pressure and resource availability, invasion was highest near edges of vegetation fragments and areas of human activity. Sites with high vegetation cover had higher probability of occupancy but lower proportional cover of invaders, the latter trend suggesting a form of biotic resistance. Invasion patterns varied little in time despite the data spanning 34 years. Main conclusions To our knowledge, this is the first multispecies model based on occupancy and abundance data used to predict invasion risk at the landscape scale. Our approach is flexible and can be applied in different biomes, at multiple scales and for different taxonomic groups. Quantifying general patterns and processes of plant invasion will increase understanding of invasion and community ecology. Predicting invasion risk enables spatial prioritization of weed surveillance and control.     

Species-Rich Scandinavian Grasslands are Inherently Open to Invasion

Invasion of native habitats by alien or generalist species is recognized worldwide as one of the major causes behind species decline and extinction. One mechanism determining community invasibility, i.e. the susceptibility of a community to invasion, which has been supported by recent experimental studies, is species richness and functional diversity acting as barriers to invasion. We used Scandinavian semi-natural grasslands, exceptionally species-rich at small spatial scales, to examine this mechanism, using three grassland generalists and one alien species as experimental invaders. Removal of two putative functional groups, legumes and dominant non-legume forbs, had no effect on invasibility except a marginally insignificant effect of non-legume forb removal. The amount of removed biomass and original plot species richness had no effect on invasibility. Actually, invasibility was high already in the unmanipulated community, leading us to further examine the relationship between invasion and propagule pressure, i.e. the inflow of seeds into the community. Results from an additional experiment suggested that these species-rich grasslands are effectively open to invasion and that diversity may be immigration driven. Thus, species richness is no barrier to invasion. The high species diversity is probably in itself a result of the community being highly invasible, and species have accumulated at small scales during centuries of grassland management.     

Bottom-up impact on the cecidomyiid leaf galler and its parasitism in a tropical rainforest

Although invasion risk is expected to increase with propagule pressure (PP), it is unclear whether PP-invasibility relationships follow an asymptotic or some other non-linear form and whether such relationships vary with underlying environmental conditions. Using manipulations of PP, soil fertility and disturbance, we tested how each influence PP-invasibility relationships for Lespedeza cuneata in a Kansas grassland and use recruitment curve models to determine how safe sites may contribute to plant invasions. After three growing seasons, we found that the PP-invasibility relationships best fit an asymptotic model of invasion reflecting a combination of density-independent and density-dependent processes and that seeds were aggregated within the plant community despite efforts to uniformly sow seeds. Consistent with some models, community invasibility decreased with enhanced soil fertility or reduced levels of disturbance in response to changes in the fraction of safe sites. Our results illustrate that disturbance and soil fertility can be a useful organizing principle for predicting community invasibility, asymptotic models are a reasonable starting point for modeling invasion, and new modeling techniques—coupled with classic experimental approaches—can enhance our understanding of the invasion process.     

What affects the probability of biological invasions in Antarctica? Using an expanded conceptual framework to anticipate the risk of alien species expansion

Successful alien species invasion depends on many factors studied mostly in post invasion habitats, and subsequently summarized in frameworks tailored to describe the studied invasion. We used an existing expanded framework with three groups of contributing factors: habitat invisibility, system context and species invasiveness, to analyze the probability of alien species invasions in terrestrial communities of Maritime Antarctic in the future. We focused on the first two factor groups. We tested if the expanded framework could be used under a different scenario. We chose Point Thomas Oasis on King George Island to perform our analysis. Strong geographical barrier, low potential bioclimatic suitability and resource availability associated with habitat invasibility significantly reduce the likelihood of biological invasion in Antarctica. An almost full enemy release (low pressure of consumers), the high patchiness of the habitat, and the prevalence of open gaps also associated with habitat invasibility increase the possibility of invasion. The dynamics of functional connectivity, propagule pressure and spatio-temporal patterns of propagule arrival associated with human activity and climate change belonging to the system context contribute to an increase in the threat of invasions. Due to the still low land transport activity migration pathways are limited and will reduce the spread of alien terrestrial organisms by land. An effective way of preventing invasions in Antarctica seems to lie in reducing propagule pressure and eliminating alien populations as early as possible. The expanded conceptual framework opens up wider possibilities in analyzing invasions taking place in different systems and with multiple taxa.     

Propagule pressure and native species richness effects drive invasibility in tropical dry forest seedling layers

Understanding the factors that encourage or inhibit plant invasions is vital to focusing limited invasive control efforts within areas where they are most practical and cost-effective. To extend the range of contexts in which invasibility is studied and aid the development of practical strategies to limit damaging plant invasions, we set out to test the relative importance of native species richness, native seedling density, and invasive propagule pressure, on the invasibility of artificial assemblages of naturally occurring tropical woody seedling communities. Our greenhouse mesocosms included a species pool of twelve trees and woody shrubs native to South Florida's tropical hardwood hammocks, and an increasingly prevalent noxious woody invader of this system, Ardisia elliptica. We found that invader propagule pressure was the single most important factor determining community invasibility. We also revealed a positive relationship between invasibility and native species richness in our polyculture mesocosms. Because A. elliptica biomass production significantly differed among different native monocultures and was not related to overyielding in native polycultures, we suggest that the effect of species richness on invasibility in this experiment was the result of sampling effects rather than a true effect of diversity.Three broad findings hold potential for application in preventing and controlling plant invasions, especially in the seedling layers of tropical dry forests: (1) effective invasive control efforts will likely benefit from measures to minimize propagule pressure; (2) managers might do well to prioritize invasive monitoring and removal efforts on the most diverse habitats within a management region; and (3) while more data are necessary to further understand our finding of a lack of association between productivity and invasibility, management regimes aimed at maximizing primary productivity might not increase invasibility, and in fact, strategies for controlling invasive plants via the management of ecosystem productivity may be ineffective.     

Invasion Dynamics of a Fish-Free Landscape by Brown Trout (Salmo trutta)

Metapopulation dynamics over the course of an invasion are usually difficult to grasp because they require large and reliable data collection, often unavailable. The invasion of the fish-free freshwater ecosystems of the remote sub-Antarctic Kerguelen Islands following man-made introductions of brown trout (Salmo trutta) in the 1950''s is an exception to this rule. Benefiting from a full long term environmental research monitoring of the invasion, we built a Bayesian dynamic metapopulation model to analyze the invasion dynamics of 85 river systems over 51 years. The model accounted for patch size (river length and connections to lakes), alternative dispersal pathways between rivers, temporal trends in dynamics, and uncertainty in colonization date. The results show that the model correctly represents the observed pattern of invasion, especially if we assume a coastal dispersal pathway between patches. Landscape attributes such as patch size influenced the colonization function, but had no effect on propagule pressure. Independently from patch size and distance between patches, propagule pressure and colonization function were not constant through time. Propagule pressure increased over the course of colonization, whereas the colonization function decreased, conditional on propagule pressure. The resulting pattern of this antagonistic interplay is an initial rapid invasion phase followed by a strong decrease in the invasion rate. These temporal trends may be due to either adaptive processes or environmental gradients encountered along the colonization front. It was not possible to distinguish these two hypotheses. Because invasibility of Kerguelen Is. freshwater ecosystems is very high due to the lack of a pre-existing fish fauna and minimal human interference, our estimates of invasion dynamics represent a blueprint for the potential of brown trout invasiveness in pristine environments. Our conclusions shed light on the future of polar regions where, because of climate change, fish-free ecosystems become increasingly accessible to invasion by fish species.     

Models of lake invasibility by Bythotrephes longimanus, a non-indigenous zooplankton

We built a family of hierarchical risk models for the spread of invasions by the spiny waterflea (Bythotrephes longimanus) in lakes in Ontario, Canada. Knowledge of covariates determining lake invasibility and ability to predict risk of future invasions may help to develop management policy and slow the invasions in the future. The models are based on two component submodels. The first component was a stochastic gravity submodel for the propagule pressure between lakes via recreational boaters. The second component was a submodel for establishment risk, given that the invader has already been introduced to a lake. This component was a logistic regression model, incorporating up to 17 measured covariates that describe the physical and chemical condition of the lake. Variants of the risk model, each incorporating different subsets of the covariates, were calibrated using presence/absence data from a 300-lake survey conducted in 2005?C2006 by the Canadian Aquatic Invasive Species Network (CAISN). The predictive capacity of the best model was high, giving AUC values close to 0.94. Of the model covariates considered, the most important predictors of existing invasions were propagule pressure and lake pH, and, to lesser extents, phosphorus (P) and lake elevation. Our fitting of the propagule pressure submodel demonstrated a significant Allee effect for Bythotrephes. Our development of the establishment risk predictor showed that it is essential to account for temporal variability in lake physico-chemistry. We demonstrated that invasions of lake networks by the spiny waterflea follow highly predictable patterns which can be understood with a properly calibrated, hierarchical risk model.     

Dealing with scarce data to understand how environmental gradients and propagule pressure shape fine‐scale alien distribution patterns on coastal dunes

Questions: On sandy coastal habitats, factors related to substrate and to wind action vary along the sea–inland ecotone, forming a marked directional disturbance and stress gradient. Further, input of propagules of alien plant species associated to touristic exploitation and development is intense. This has contributed to establishment and spread of aliens in coastal systems. Records of alien species in databases of such heterogeneous landscapes remain scarce, posing a challenge for statistical modelling. We address this issue and attempt to shed light on the role of environmental stress/disturbance gradients and propagule pressure on invasibility of plant communities in these typical model systems. Location: Sandy coasts of Lazio (Central Italy). Methods: We proposed an innovative methodology to deal with low prevalence of alien occurrence in a data set and high cost of field‐based sampling by taking advantage, through predictive modelling, of the strong interrelation between vegetation and abiotic features in coastal dunes. We fitted generalized additive models to analyse (1) overall patterns of alien occurrence and spread and (2) specific patterns of the most common alien species recorded. Conclusion: Even in the presence of strong propagule pressure, variation in local abiotic conditions can explain differences in invasibility within a local environment, and intermediate levels of natural disturbance and stress offer the best conditions for spread of alien species. However, in our model system, propagule pressure is actually the main determinant of alien species occurrence and spread. We demonstrated that extending the information of environmental features measured in a subsample of vegetation plots through predictive modelling allows complex questions in invasion biology to be addressed without requiring disproportionate funding and sampling effort.     

Invading a mutualistic network: to be or not to be similar

Biological invasion remains a major threat to biodiversity in general and a disruptor to mutualistic interactions in particular. While a number of empirical studies have directly explored the role of invasion in mutualistic pollination networks, a clear picture is yet to emerge and a theoretical model for comprehension still lacking. Here, using an eco‐evolutionary model of bipartite mutualistic networks with trait‐mediated interactions, we explore invader trait, propagule pressure, and network features of recipient community that contribute importantly to the success and impact of an invasion. High level of invasiveness is observed when invader trait differs from those of the community average, and level of interaction generalization equals to that of the community average. Moreover, multiple introductions of invaders with declining propagules enhance invasiveness. Surprisingly, the most successful invader is not always the one having the biggest impact on the recipient community. The network structure of recipient community, such as nestedness and modularity, is not a primary indicator of its invasibility; rather, the invasibility is best correlated with measurements of network stability such as robustness, resilience, and disruptiveness (a measure of evolutionary instability). Our model encompasses more general scenarios than previously studied in predicting invasion success and impact in mutualistic networks, and our results highlight the need for coupling eco‐evolutionary processes to resolve the invasion dilemma.     

Prediction and error in multi‐stage models for spread of aquatic non‐indigenous species

Aim Predictions of spread of non‐indigenous species allow for greater efficiency in managing invasions by targeting areas for preventative measures. The invasion sequence is a useful concept in predictions of spread, as it allows us to test hypotheses about the transport and establishment of propagules in novel habitats. Our aims are twofold: (1) to develop and validate multi‐stage invasion models for the introduced fishhook waterflea, Cercopagis pengoi, and (2) to assess how variability in the transport patterns of the propagules influences the accuracy and spatial extent for predictions of spread. Location New York State, USA. Methods We developed a two‐stage model for the spread of C. pengoi. First, we developed a stochastic gravity model for dispersal based on surveys of recreational boat traffic in New York State as a proxy for propagule pressure. We then modelled the probability of establishment based on predicted levels of propagule pressure and measures of lakes’ physicochemistry. In addition, we used Monte Carlo simulations based on the gravity model to propagate variability in boater traffic through the establishment model to assess how uncertainty in dispersal influenced predictions of spread. Results The amount recreationalists were willing to spend, lake area and population size of the city nearest to the destination lake were significant factors affecting boater traffic. In turn, boater traffic, lake area, specific conductance and turbidity were significant predictors of establishment. The inclusion of stochastic dispersal reduced the rate of false positives (i.e. incorrect prediction of an invasion) in detecting invasions at the upper 95% prediction interval for the probability of establishment. Main conclusions Combinations of measures of propagule pressure, habitat suitability and stochastic dispersal allow for the most accurate predictions of spread. Further, multi‐stage spread models may overestimate the extent of spread if stochasticity in early stages of the models is not considered.     

Biological invasions and the neutral theory

Aim  The invasion of natural communities by alien species represents a serious threat, but creates opportunities to learn about community functions. Neutral theory proposes that the niche concept may not be needed to explain the assemblage and diversity of natural communities, challenging the classical view of community ecology and generating a lasting debate. Biological invasions, when considered as natural experiments, can be used to contrast some of the predictions of neutral and classic niche theories.
Location  Global.
Methods  We use data from biological invasions as natural experiments to contrast some of the fundamental predictions of neutral theory.
Results  Some emerging patterns did not differ from neutral model expectations (e.g. the relationship between native and exotic species richness, invasibility of resource-rich habitats, and the relationship between propagule release and invasion success). Nevertheless, other patterns (e.g. experimental evidence of the relationship between diversity and susceptibility to invasion, the invasion of communities with a low resource availability, invasiveness related to species traits) contrasted with the predictions that can be inferred from neutral theory.
Main conclusions  Neutral theory correctly highlights the need to include randomness in models of community structure. Biological invasion patterns show that neutral forces are important in structuring natural communities, but the patterns differ from those inferred from a complete neutral model. For biodiversity-conservation purposes, the implications of accepting or not accepting neutral theory as a process-based theory are very important.     

The more you introduce the more you get: the role of colonization pressure and propagule pressure in invasion ecology

Aim  We argue that 'propagule pressure', a key term in invasion biology, has been attributed at least three distinct definitions (with usage of a related term causing additional confusion). All of the definitions refer to fundamental concepts within the invasion process, with the result that the distinct importance of these different concepts has been at best diluted, and at worst lost.
Location  Global.
Methods  We reviewed pertinent literature on propagule pressure to resolve confusion about different uses of the term 'propagule pressure' and we introduced a new term for one variant, colonization pressure. We conducted a computer simulation whereby the introduction of species is represented as a simple sampling process to elucidate the relationship between propagule and colonization pressure.
Results  We defined colonization pressure as the number of species introduced or released to a single location, some of which will go on to establish a self-sustaining population and some of which will not. We subsequently argued that colonization pressure should serve as a null hypothesis for understanding temporal or spatial differences in exotic species richness, as the more species that are introduced, the more we should expect to establish. Finally, using a simple simulation, we showed that propagule pressure is related to colonization pressure, but in a non-linear manner.
Main conclusion  We suggest that the nature of the relationship between propagule pressure and colonization pressure, as well as the efficacy of various proxy measures of each, require more detailed exploration if invasion ecology is to continue to develop into a more predictive science.     

The elephant in the room: the role of failed invasions in understanding invasion biology

Most species introductions are not expected to result in invasion, and species that are invasive in one area are frequently not invasive in others. However, cases of introduced organisms that failed to invade are reported in many instances as anecdotes or are simply ignored. In this analysis, we aimed to find common characteristics between non‐invasive populations of known invasive species and evaluated how the study of failed invasions can contribute to research on biological invasions. We found intraspecific variation in invasion success and several recurring explanations for why non‐native species fail to invade; these included low propagule pressure, abiotic resistance, biotic resistance, genetic constraints and mutualist release. Furthermore, we identified key research topics where ignoring failed invasions could produce misleading results; these include studies on historical factors associated with invasions, distribution models of invasive species, the effect of species traits on invasiveness, genetic effects, biotic resistance and habitat invasibility. In conclusion, we found failed invasions can provide fundamental information on the relative importance of factors determining invasions and might be a key component of several research topics. Therefore, our analysis suggests that more specific and detailed studies on invasion failures are necessary.     

Freshwater invasibility level depends on the population age structure of the invading mussel species

Environmental conditions may affect invasibility and potentially prevent successful invasions of the freshwater bivalve Limnoperna fortunei Dunker, 1857. However, even though the larval stage may be considered an important species’ characteristic, the invasion processes of L. fortunei are mainly evaluated using only the adult stage. Therefore, the aim of this study was to identify what, and how, environmental filters might predict the likelihood of occurrence of each of the L. fortunei larval stages. Logistic regressions were applied using the larval stages of L. fortunei as a surrogate of population age structure and the environmental variables as the main filters that potentially predicted the likelihood of the occurrence of each larval stage of L. fortunei. The turbidity predicted the occurrence of the D-shaped larvae and straight-hinged veliger stages, while the umbonated-veliger and pediveliger stages were predicted by the pH and conductivity. Finally, the phytoplankton density (diatoms) predicted the occurrence of the umbonated-veliger, pediveliger and mainly the plantigrade stages. Our findings suggested that, during larvae development, from younger to older stages, the main environmental predictor of larvae occurrence shifted from abiotic to biotic variables, indicating that larval stages are indeed an important factor that helps in the evaluation of freshwater invasibility. These findings are particularly important for floodplain systems, where flood pulse dynamics may increase propagule pressure, leading to a successful spread among habitats. Then, even though environmental filters were important to predict successful invasions, we highlight that a successful invasion might depend on the population age structure of the invading species arriving in the new habitat. Thus, successful L. fortunei invasions in floodplain systems may depend on the interaction between invasiveness, invasibility and propagule pressure.     

Allee Effects, Propagule Pressure and the Probability of Establishment: Risk Analysis for Biological Invasions

Colonization is of longstanding interest in theoretical ecology and biogeography, and in the management of weeds and other invasive species, including insect pests and emerging infectious diseases. Due to accelerating invasion rates and widespread economic costs and environmental damages caused by invasive species, colonization theory has lately become a matter of considerable interest. Here we review the concept of propagule pressure to inquire if colonization theory might provide quantitative tools for risk assessment of biological invasions. By formalizing the concept of propagule pressure in terms of stochastic differential equation models of population growth, we seek a synthesis of invasion biology and theoretical population biology. We focus on two components of propagule pressure that affect the chance of invasion: (1) the number of individuals initially introduced, and (2) the rate of subsequent immigration. We also examine how Allee effects, which are expected to be common in newly introduced populations, may inhibit establishment of introduced propagules. We find that the establishment curve (i.e., the chance of invasion as a function of initial population size), can take a variety of shapes depending on immigration rate, carrying capacity, and the severity of Allee effects. Additionally, Allee effects can cause the stationary distribution of population sizes to be bimodal, which we suggest is a possible explanation for time lags commonly observed between the detection of an introduced population and widespread invasion of the landscape.