Allee effects in biological invasions

Understanding the dynamics of small populations is obviously important for declining or rare species but is also particularly important for invading species. The Allee effect, where fitness is reduced when conspecific density is low, can dramatically affect the dynamics of biological invasions. Here, we summarize the literature of Allee effects in biological invasions, revealing an extensive theory of the consequences of the Allee effect in invading species and some empirical support for the theory. Allee effects cause longer lag times, slower spread and decreased establishment likelihood of invasive species. Expected spatial ranges, distributions and patterns of species may be altered when an Allee effect is present. We examine how the theory can and has been used to detect Allee effects in invasive species and we discuss how the presence of an Allee effect and its successful or unsuccessful detection may affect management of invasives. The Allee effect has been shown to change optimal control decisions, costs of control and the estimation of the risk posed by potentially invasive species. Numerous ways in which the Allee effect can influence the efficacy of biological control are discussed.     

The role of Allee effects in gypsy moth, <Emphasis Type="Italic">Lymantria dispar</Emphasis> (L.), invasions

Allee effects have been applied historically in efforts to understand the low-density population dynamics of rare and endangered species. Many biological invasions likewise experience the phenomenon of decreasing population growth rates at low population densities because most founding populations of introduced nonnative species occur at low densities. In range expansion of established species, the initial colonizers of habitat beyond the organism’s current range are usually at low density, and thus could be subject to Allee dynamics. There has been consistent empirical and theoretical evidence demonstrating, and in some cases quantifying, the role of Allee dynamics in the gypsy moth, Lymantria dispar (L.), invasion of North America. In this review, we examine the potential causes of the Allee effect in the gypsy moth and highlight the importance of mate-finding failure as a primary mechanism behind an Allee effect, while the degree to which generalist predators induce an Allee effect remains unclear. We then explore the role of Allee effects in the establishment and spread dynamics of the gypsy moth system, which conceptually could serve as a model system for understanding how Allee effects manifest themselves in the dynamics of biological invasions.     

Pathogens can Slow Down or Reverse Invasion Fronts of their Hosts

Infectious diseases are often regarded as possible explanations for the sudden collapse of biological invasions. This phenomenon is characterized by a host species, which firstly can successfully establish in a non-native habitat, but then spontaneously disappears again. This study proposes a reaction-diffusion model consisting of a simple SI disease with vital dynamics of Allee effect type. By way of travelling wave analysis, conditions are derived under which the invasion of the host population is slowed down, stopped or reversed as a consequence of a subsequently introduced disease. Hence, pathogens can dramatically control the rate of spread of invasive species.     

Invasion speed is affected by geographical variation in the strength of Allee effects

Allee effects can play a critical role in slowing or preventing the establishment of low density founder populations of non-indigenous species. Similarly, the spread of established invaders into new habitats can be influenced by the degree to which small founder populations ahead of the invasion front are suppressed through Allee effects. We develop an approach to use empirical data on the gypsy moth, a non-indigenous invader in North America, to quantify the Allee threshold across geographical regions, and we report that the strength of the Allee effect is subject to spatial and temporal variability. Moreover, we present what is to our knowledge the first empirical evidence that geographical regions with higher Allee thresholds are associated with slower speeds of invasion.     

Dangerously few liaisons: a review of mate-finding Allee effects

In this paper, we review mate-finding Allee effects from ecological and evolutionary points of view. We define ‘mate-finding’ as mate searching in mobile animals, and also as the meeting of gametes for sessile animals and plants (pollination). We consider related issues such as mate quality and choice, sperm limitation and physiological stimulation of reproduction by conspecifics, as well as discussing the role of demographic stochasticity in generating mate-finding Allee effects. We consider the role of component Allee effects due to mate-finding in generating demographic Allee effects (at the population level). Compelling evidence for demographic Allee effects due to mate-finding (as well as via other mechanisms) is still limited, due to difficulties in censusing rare populations or a failure to identify underlying mechanisms, but also because of fitness trade-offs, population spatial structure and metapopulation dynamics, and because the strength of component Allee effects may vary in time and space. Mate-finding Allee effects act on individual fitness and are thus susceptible to change via natural selection. We believe it is useful to distinguish two routes by which evolution can act to mitigate mate-finding Allee effects. The first is evolution of characteristics such as calls, pheromones, hermaphroditism, etc. which make mate-finding more efficient at low density, thus eliminating the Allee effect. Such adaptations are very abundant in the natural world, and may have arisen to avoid Allee effects, although other hypotheses are also possible. The second route is to avoid low density via adaptations such as permanent or periodic aggregation. In this case, the Allee effect is still present, but its effects are avoided. These two strategies may have different consequences in a world where many populations are being artificially reduced to low density: in the first case, population growth rate can be maintained, while in the second case, the mechanism to avoid Allee effects has been destroyed. It is therefore in these latter populations that we predict the greatest evidence for mate-finding Allee effects and associated demographic consequences. This idea is supported by the existing empirical evidence for demographic Allee effects. Given a strong effect that mate-finding appears to have on individual fitness, we support the continuing quest to find connections between component mate-finding Allee effects (individual reproductive fitness) and the demographic consequences. There are many reasons why such studies are difficult, but it is important, particularly given the increasing number of populations and species of conservation concern, that the ecological community understands more about how widespread demographic Allee effects really are, and why.     

Invasive spread in meta-food-webs depends on landscape structure,fertilization and species characteristics

Land use change and biological invasions collectively threaten biodiversity. Yet, few studies have addressed how altering the landscape structure and nutrient supply can promote biological invasions and particularly invasive spread (the spread of an invader from the place of introduction), or asked whether and how these factors interact with biotic interactions and invader properties. We here bridge this knowledge gap by providing a holistic network-based approach. Our approach combines a trophic network model with a spatial network model allowing us to test which combinations of abiotic and biotic factors can facilitate invasions and in particular invasive spread in food webs. We numerically simulated 6300 single-species invasions in clustered and random landscapes at different levels of nutrient supply. In total, our simulation experiment yielded 69% successful invasions – 71% in clustered landscapes and 66% in random landscapes, with the proportion of successful invasions increasing with nutrient supply. However, invasive spread was generally higher in random than in clustered landscapes. The latter can facilitate invasive spread within a habitat cluster, but prevent invasive spread between clusters. Low nutrient levels generally prevented the establishment of invasive species and their subsequent spread. However, successful invaders could have more severe impacts as they contribute more to total biomass density and species richness under such conditions. Good dispersal abilities drive the broad-scale spread of invasive species in fragmented landscapes. Our approach makes an important contribution towards a better understanding of what combination of landscape and invader properties can facilitate or prevent invasive spread in natural ecosystems. This should allow ecologists to more effectively predict and manage biological invasions.     

Bioeconomic synergy between tactics for insect eradication in the presence of Allee effects

Preventing the establishment of invading pest species can be beneficial with respect to averting future environmental and economic impacts and also in preventing the accumulation of control costs. Allee effects play an important role in the dynamics of newly established, low-density populations by driving small populations into self-extinction, making Allee effects critical in influencing outcomes of eradication efforts. We consider interactions between management tactics in the presence of Allee effects to determine cost-effective and time-efficient combinations to achieve eradication by developing a model that considers pesticide application, predator augmentation and mating disruption as control tactics, using the gypsy moth as a case study. Our findings indicate that given a range of constant expenditure levels, applying moderate levels of pesticides in conjunction with mating disruption increases the Allee threshold which simultaneously substantially decreases the time to eradication relative to either tactic alone. In contrast, increasing predation in conjunction with other tactics requires larger economic expenditures to achieve similar outcomes for the use of pesticide application or mating disruption alone. These results demonstrate the beneficial synergy that may arise from nonlinearities associated with the simultaneous application of multiple eradication tactics and offer new prospects for preventing the establishment of damaging non-native species.     

Establishing a beachhead: a stochastic population model with an Allee effect applied to species invasion

We formulated a spatially explicit stochastic population model with an Allee effect in order to explore how invasive species may become established. In our model, we varied the degree of migration between local populations and used an Allee effect with variable birth and death rates. Because of the stochastic component, population sizes below the Allee effect threshold may still have a positive probability for successful invasion. The larger the network of populations, the greater the probability of an invasion occurring when initial population sizes are close to or above the Allee threshold. Furthermore, if migration rates are low, one or more than one patch may be successfully invaded, while if migration rates are high all patches are invaded.     

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.     

Its all about connections: hubs and invasion in habitat networks

During the early stages of invasion, the interaction between the features of the invaded landscape, notably its spatial structure, and the internal dynamics of an introduced population has a crucial impact on establishment and spread. By approximating introduction areas as networks of patches linked by dispersal, we characterised their spatial structure with specific metrics and tested their impact on two essential steps of the invasion process: establishment and spread. By combining simulations with experimental introductions of Trichogramma chilonis (Hymenoptera: Trichogrammatidae) in artificial laboratory microcosms, we demonstrated that spread was hindered by clusters and accelerated by hubs but was also affected by small‐population mechanisms prevalent for invasions, such as Allee effects. Establishment was also affected by demographic mechanisms, in interaction with network metrics. These results highlight the importance of considering the demography of invaders as well as the structure of the invaded area to predict the outcome of invasions.     

Eight questions about invasions and ecosystem functioning

I pose eight questions central to understanding how biological invasions affect ecosystems, assess progress towards answering those questions and suggest ways in which progress might be made. The questions concern the frequency with which invasions affect ecosystems; the circumstances under which ecosystem change is most likely; the functions that are most often affected by invaders; the relationships between changes to ecosystems, communities, and populations; the long-term responses of ecosystems to invasions; interactions between biological invasions and other anthropogenic activities and the difficulty of managing undesirable impacts of non-native species. Some questions have been answered satisfactorily, others require more data and thought, and others might benefit from being reformulated or abandoned. Actions that might speed progress include careful development of trait-based approaches; strategic collection and publication of new data, including more frequent publication of negative results; replacement of expert opinion with hard data where needed; careful consideration of whether questions really need to be answered, especially in cases where answers are being provided for managers and policy-makers; explicit attention to and testing of the domains of theories; integrating invasions better into an ecosystem context; and remembering that our predictive ability is limited and will remain so for the foreseeable future.     

Allee effects, mating systems and the extinction risk in populations with two sexes

The Allee effect is one of the population consequences of sexual reproduction that has received increased attention in recent years. Due to its impact on small population dynamics, it is commonly accepted that Allee effects should render populations more extinction prone. In particular, monogamous species are considered more susceptible to the Allee effect and hence, more extinction prone, than polygamous species. Although this hypothesis has received theoretical support, there is little empirical evidence. In this study, we investigate (1) how variation in tertiary sex ratio affects the presence and intensity of the Allee effect induced by mating system, as well as (2) how this effect contributes to extinction risk. In contrast with previous predictions, we show that all mating systems are likely to experience a strong Allee effect when the operational sex ratio (OSR) is balanced. This strong Allee effect does not imply being exceptionally extinction prone because it is associated with an OSR that result in a relatively small extinction risk. As a consequence, the impact of Allee effects on overall extinction risk is buffered. Moreover, the OSR of natural populations appears to be often male biased, thus making it unlikely that they will suffer from an Allee effect induced by mating system.     

局域种群的Allee效应和集合种群的同步性

从包含Allee效应的局域种群出发,建立了耦合映像格子模型,即集合种群模型.通过分析和计算机模拟表明:(1)当局域种群受到Allee效应强度较大时,集合种群同步灭绝;(2)而当Allee效应强度相对较弱时,通过稳定局域种群动态(减少混沌)使得集合种群发生同步波动,而这种同步波动能够增加集合种群的灭绝风险;(3)斑块间的连接程度对集合种群同步波动的发生有很大的影响,适当的破碎化有利于集合种群的续存.全局迁移和Allee效应结合起来增加了集合种群同步波动的可能,从而增加集合种群的灭绝风险.这些结果对理解同步性的机理、利用同步机理来制定物种保护策略和害虫防治都有重要的意义.     

Population Genetic Consequences of the Allee Effect and the Role of Offspring-Number Variation

A strong demographic Allee effect in which the expected population growth rate is negative below a certain critical population size can cause high extinction probabilities in small introduced populations. But many species are repeatedly introduced to the same location and eventually one population may overcome the Allee effect by chance. With the help of stochastic models, we investigate how much genetic diversity such successful populations harbor on average and how this depends on offspring-number variation, an important source of stochastic variability in population size. We find that with increasing variability, the Allee effect increasingly promotes genetic diversity in successful populations. Successful Allee-effect populations with highly variable population dynamics escape rapidly from the region of small population sizes and do not linger around the critical population size. Therefore, they are exposed to relatively little genetic drift. It is also conceivable, however, that an Allee effect itself leads to an increase in offspring-number variation. In this case, successful populations with an Allee effect can exhibit less genetic diversity despite growing faster at small population sizes. Unlike in many classical population genetics models, the role of offspring-number variation for the population genetic consequences of the Allee effect cannot be accounted for by an effective-population-size correction. Thus, our results highlight the importance of detailed biological knowledge, in this case on the probability distribution of family sizes, when predicting the evolutionary potential of newly founded populations or when using genetic data to reconstruct their demographic history.     

捕食者具有厌食性反应且食饵具有Allee效应的捕食系统

在Dubis动力系统的基础上,建立了具有Allee效应的捕食系统模型。对系统的稳定性进行了分析,受Allee效应的影响,食饵种群可能因为种群大小处于临界点以下而趋于灭绝。通过对系统进行模拟,结果表明:不受Allee效应的影响,系统的演化属于一种理想化的情形系统到达P(平衡)点的时间较不受Allee效应影响时系统到达P点的时间短,不利于生物的进化,而在Allee效应的影响下,系统的演化将达到一个平衡状态。由此,说明Allee效应为濒临灭绝物种的管理提供了重要的理论依据,对管理部门的决策有参考指导作用。     

利用元胞自动机研究一类捕食食饵模型中的斑块扩散现象

利用概率元胞自动机模型对空间隐式的、食饵具Allee效应的一类捕食食饵模型进行模拟,发现随着相关参数的变化,种群的空间扩散前沿由连续的扩散波逐渐转变为一种相互隔离的斑块向外扩散,这种斑块扩散现象与以往的扩散模式有所不同。研究结果表明：(1)在斑块扩散的情况下,相关参数的微小变化会导致种群灭绝或者形成连续的扩散波,即斑块扩散发生在种群趋于灭绝和连续扩散之间;(2)当种群的空间扩散方式为斑块扩散时,种群的扩散速度会变慢,与其他扩散方式下的速度有着明显的区别。该研究结果对生物入侵控制和外来物种监测有重要的启发和指导作用。     

General Allee effect in two-species population biology

The main objective of this work is to present a general framework for the notion of the strong Allee effect in population models, including competition, mutualistic, and predator–prey models. The study is restricted to the strong Allee effect caused by an inter-specific interaction. The main feature of the strong Allee effect is that the extinction equilibrium is an attractor. We show how a ‘phase space core’ of three or four equilibria is sufficient to describe the essential dynamics of the interaction between two species that are prone to the Allee effect. We will introduce the notion of semistability in planar systems. Finally, we show how the presence of semistable equilibria increases the number of possible Allee effect cores.     

Spatially implicit approaches to understand the manipulation of mating success for insect invasion management

Recent work indicates that Allee effects (the positive relationship between population size and per capita growth rate) are critical in determining the successful establishment of invading species. Allee effects may create population thresholds, and failure to establish is likely if invading populations fall below these thresholds. There are many mechanisms that may contribute to Allee effects, but mate-location failure is a common cause in sexually reproducing insects. Consequently, mate-location failure represents a type of “weak link” that may be enhanced in order to achieve eradication of insect populations during the early stages of invasion. In this paper, spatially implicit models that account for mating behavior of both sexes are used to explore the enhancement of mate-location failure in pest eradication programs. Distinct from the previous studies, the Allee effect emerges from a mechanistic representation of mate-location failure in our model. Three specific eradication strategies, sterile insect release, mass-trapping, and mating disruption, are incorporated into the model and tested for their ability to depress population growth during the early stages of invasions. We conducted simulations with the model parameterized to represent two types of insects: Coleopteran-like insects which are long-lived and capable of multiple matings, but have low daily reproductive rates, and Lepidopteran-like insects which are capable of mating only once per generation, have an ephemeral reproductive stage, and have high reproductive rates. Simulations indicated that: (1) many insect pests are more likely to be eradicated than had been previously predicted by classic models which do not account for mate-finding difficulties, (2) for Lepidopteran-like insects, mass-trapping has the greatest potential for eradication among the three methods when a large number of traps can be installed, although mating-disruption will be the most effective if we can anticipate confusion or trail-masking mechanisms of disruption, and (3) populations of Coleopteran-like insects may be most effectively eradicated using the sterile male release method. Though more detailed models should be tailored for individual species, we expect that the spatially implicit approaches outlined in this paper can be widely adapted to study the efficiency of various eradication approaches in sparse conditions. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Fatal disease and demographic Allee effect: population persistence and extinction

If a healthy stable host population at the disease-free equilibrium is subject to the Allee effect, can a small number of infected individuals with a fatal disease cause the host population to go extinct? That is, does the Allee effect matter at high densities? To answer this question, we use a susceptible–infected epidemic model to obtain model parameters that lead to host population persistence (with or without infected individuals) and to host extinction. We prove that the presence of an Allee effect in host demographics matters even at large population densities. We show that a small perturbation to the disease-free equilibrium can eventually lead to host population extinction. In addition, we prove that additional deaths due to a fatal infectious disease effectively increase the Allee threshold of the host population demographics.     

Combining tactics to exploit Allee effects for eradication of alien insect populations

Invasive species increasingly threaten ecosystems, food production, and human welfare worldwide. Hundreds of eradication programs have targeted a wide range of nonnative insect species to mitigate the economic and ecological impacts of biological invasions. Many such programs used multiple tactics to achieve this goal, but interactions between tactics have received little formal consideration, specifically as they interact with Allee dynamics. If a population can be driven below an Allee threshold, extinction becomes more probable because of factors such as the failure to find mates, satiate natural enemies, or successfully exploit food resources, as well as demographic and environmental stochasticity. A key implication of an Allee threshold is that the population can be eradicated without the need and expense of killing the last individuals. Some combinations of control tactics could interact with Allee dynamics to increase the probability of successful eradication. Combinations of tactics can be considered to have synergistic (greater efficiency in achieving extinction from the combination), additive (no improvement over single tactics alone), or antagonistic (reduced efficiency from the combination) effects on Allee dynamics. We highlight examples of combinations of tactics likely to act synergistically, additively, or antagonistically on pest populations. By exploiting the interacting effects of multiple tactics on Allee dynamics, the success and cost-effectiveness of eradication programs can be enhanced.