Pushed to the edge: Spatial sorting can slow down invasions

Our ability to understand population spread dynamics is complicated by rapid evolution, which renders simple ecological models insufficient. If dispersal ability evolves, more highly dispersive individuals may arrive at the population edge than less dispersive individuals (spatial sorting), accelerating spread. If individuals at the low-density population edge benefit (escape competition), high dispersers have a selective advantage (spatial selection). These two processes are often described as forming a positive feedback loop; they reinforce each other, leading to faster spread. Although spatial sorting is close to universal, this form of spatial selection is not: low densities can be detrimental for organisms with Allee effects. Here, we present two conceptual models to explore the feedback loops that form between spatial sorting and spatial selection. We show that the presence of an Allee effect can reverse the positive feedback loop between spatial sorting and spatial selection, creating a negative feedback loop that slows population spread.     

Stochastic and spatial dynamics of nematode parasites in farmed ruminants

Host-parasite systems provide powerful opportunities for the study of spatial and stochastic effects in ecology; this has been particularly so for directly transmitted microparasites. Here, we construct a fully stochastic model of the population dynamics of a macroparasite system: trichostrongylid gastrointestinal nematode parasites of farmed ruminants. The model subsumes two implicit spatial effects: the host population size (the spatial extent of the interaction between hosts) and spatial heterogeneity ('clumping') in the infection process. This enables us to investigate the roles of several different processes in generating aggregated parasite distributions. The necessity for female worms to find a mate in order to reproduce leads to an Allee effect, which interacts nonlinearly with the stochastic population dynamics and leads to the counter-intuitive result that, when rare, epidemics can be more likely and more severe in small host populations. Clumping in the infection process reduces the strength of this Allee effect, but can hamper the spread of an epidemic by making infection events too rare. Heterogeneity in the hosts' response to infection has to be included in the model to generate aggregation at the level observed empirically.     

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.     

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.     

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.     

Allee effects, aggregation, and invasion success

Understanding the factors that influence successful colonization can help inform ecological theory and aid in the management of invasive species. When founder populations are small, individual fitness may be negatively impacted by component Allee effects through positive density dependence (e.g., mate limitation). Reproductive and survival mechanisms that suffer due to a shortage of conspecifics may scale up to be manifest in a decreased per-capita population growth rate (i.e., a demographic Allee effect). Mean-field population level models are limited in representing how component Allee effects scale up to demographic Allee effects when heterogeneous spatial structure influences conspecific availability. Thus, such models may not adequately characterize the probability of establishment. In order to better assess how individual level processes influence population establishment and spread, we developed a spatially explicit individual-based stochastic simulation of a small founder population. We found that increased aggregation can affect individual fitness and subsequently impact population growth; however, relatively slow dispersal—in addition to initial spatial structure—is required for establishment, ultimately creating a tradeoff between probability of initial establishment and rate of subsequent spread. Since this result is sensitive to the scaling up of component Allee effects, details of individual dispersal and interaction kernels are key factors influencing population level processes. Overall, we demonstrate the importance of considering both spatial structure and individual level traits in assessing the consequences of Allee effects in biological invasions.     

Integrodifference equations in patchy landscapes

We analyze integrodifference equations (IDEs) in patchy landscapes. Movement is described by a dispersal kernel that arises from a random walk model with patch dependent diffusion, settling, and mortality rates, and it incorporates individual behavior at an interface between two patch types. Growth follows a simple Beverton–Holt growth or linear decay. We obtain explicit formulae for the critical domain-size problem, and we illustrate how different individual behavior at the boundary between two patch types affects this quantity. We also study persistence conditions on an infinite, periodic, patchy landscape. We observe that if the population can persist on the landscape, the spatial profile of the invasion evolves into a discontinuous traveling periodic wave that moves with constant speed. Assuming linear determinacy, we calculate the dispersion relation and illustrate how movement behavior affects invasion speed. Numerical simulations justify our approach by showing a close correspondence between the spread rate obtained from the dispersion relation and from numerical simulations.     

Invasion dynamics of epidemic with the Allee effect

Investigating the likely success of epidemic invasion is important in the epidemic management and control. In the present study, the invasion of epidemic is initially introduced to a predator-prey system, both species of which are considered to be subject to the Allee effect. Mathematically, the invasion dynamics is described by three nonlinear diffusion-reaction equations and the spatial implicit and explicit models are designed. By means of extensive numerical simulations, the results of spatial implicit model show that the Allee effect has an opposite impact on the invasion criteria and local dynamics when that on the different species. As the intensity of the Allee effect increases, the domain of epidemic invasion reduces and the system dynamics is changed from the stable state to the limit cycle and finally becomes the chaotic state when the susceptible prey with the Allee effect, but the domain expands and the system dynamics is changed from limit cycle to a table point when the predator is subject to the Allee effect. Results from the spatial explicit model show that the strong intensity of the Allee effect can lead to the catastrophic global extinction of all species in the case of that on the susceptible prey. While the predator with the Allee effect, the increased intensity of which makes spatial species reach a stable state. Furthermore, numerical simulations reveal a certain relationship between the invasion speed and spatial patterns.     

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.     

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.     

Allee效应对具有生境恢复的集合种群的影响

Allee效应与种群的灭绝密切相关,其研究对生态保护和管理至关重要。Allee效应对物种续存是潜在的干扰因素,濒危物种更容易受其影响,可能会增加生存于生境破碎化斑块的濒危物种的死亡风险,因此研究Allee效应对种群的动态和续存的影响是必要的。从包含由生物有机体对环境的修复产生的Allee效应的集合种群模型出发,引入由其他机制形成的Allee效应,建立了常微分动力系统模型和基于网格模型的元胞自动机模型。通过理论分析和计算机模拟表明:(1)强Allee效应不利于具有生境恢复的集合种群的续存;(2)生境恢复有利于种群续存;(3)局部扩散影响了集合种群的空间结构、动态行为和稳定性,生境斑块之间的局部作用将会减缓或消除集合种群的Allee效应,有利于集合种群的续存。     

A graph-based approach to investigating the influence of the landscape on population spread processes

Modelling of landscape connectivity is a key point in the study of the movement of populations within a given landscape. For studies focused on the preservation of biodiversity, graph-based methods provide an interesting framework to investigate the landscape influence on population spread processes. Such an approach is described here, based on the mapping of landscape categories in habitat patches, including a diachronic data set describing the population spread within the habitat patches. A minimum planar graph was built by computing spatial distances between all pairs of neighbouring patches. From this structure, two types of analysis are proposed: one focused on the links of the graph and consists in correlating spatial distances and gap indicators computed from the diachronic data. The other was based on the correlations between population data and connectivity metrics at the patch level. As an example, this approach was applied to the spread of the fossorial water vole on the Jura plateau (France), with annual population data covering eleven years from 1989 to 2000. Link analysis allowed to find an optimal set of resistance values used in the least-cost distances computations, and thus to build a relevant graph. From this graph, patch analysis displayed a cyclic correlation between a metric based on potential dispersal flux and the population density, outlining the strong role of landscape connectivity in the population spread. The present study clearly shows that landscape modelling and graph-based approach can produce parameters which are consistent with field observations and thus pave the way to simulating the effect of landscape modification on population dynamics.     

Sperm storage reduces the strength of the mate‐finding Allee effect

Mate searching is a key component of sexual reproduction that can have important implications for population viability, especially for the mate‐finding Allee effect. Interannual sperm storage by females may be an adaptation that potentially attenuates mate limitation, but the demographic consequences of this functional trait have not been studied. Our goal is to assess the effect of female sperm storage durability on the strength of the mate‐finding Allee effect and the viability of populations subject to low population density and habitat alteration. We used an individual‐based simulation model that incorporates realistic representations of the demographic and spatial processes of our model species, the spur‐thighed tortoise (Testudo graeca). This allowed for a detailed assessment of reproductive rates, population growth rates, and extinction probabilities. We also studied the relationship between the number of reproductive males and the reproductive rates for scenarios combining different levels of sperm storage durability, initial population density, and landscape alteration. Our results showed that simulated populations parameterized with the field‐observed demographic rates collapsed for short sperm storage durability, but were viable for a durability of one year or longer. In contrast, the simulated populations with a low initial density were only viable in human‐altered landscapes for sperm storage durability of 4 years. We find that sperm storage is an effective mechanism that can reduce the strength of the mate‐finding Allee effect and contribute to the persistence of low‐density populations. Our study highlights the key role of sperm storage in the dynamics of species with limited movement ability to facilitate reproduction in patchy landscapes or during population expansion. This study represents the first quantification of the effect of sperm storage durability on population dynamics in different landscapes and population scenarios.     

Bifurcations and chaos in a predator-prey system with the Allee effect

It is known from many theoretical studies that ecological chaos may have numerous significant impacts on the population and community dynamics. Therefore, identification of the factors potentially enhancing or suppressing chaos is a challenging problem. In this paper, we show that chaos can be enhanced by the Allee effect. More specifically, we show by means of computer simulations that in a time-continuous predator-prey system with the Allee effect the temporal population oscillations can become chaotic even when the spatial distribution of the species remains regular. By contrast, in a similar system without the Allee effect, regular species distribution corresponds to periodic/quasi-periodic oscillations. We investigate the routes to chaos and show that in the spatially regular predator-prey system with the Allee effect, chaos appears as a result of series of period-doubling bifurcations. We also show that this system exhibits period-locking behaviour: a small variation of parameters can lead to alternating regular and chaotic dynamics.     

Population cycles produce periodic range boundary pulses

Classical theories of biological invasions predict constant rates of spread that can be estimated from measurable life history parameters, but such outcomes depend strongly on assumptions that are often unmet in nature. Subsequent advances have demonstrated how relaxing assumptions of these foundational models results in other spread patterns seen in nature, including invasions that accelerate through time, or that alternate among periods of expansion, retraction, and stasis of range boundaries. In this paper, we examine how periodic population fluctuations affect temporal patterns of range expansion by coupling empirical data on the gypsy moth invasion in North America with insights from a model incorporating population cycles, Allee effects, and stratified diffusion. In an analysis of field data, we found that gypsy moth spread exhibits pulses with a period of 6 yr, which field data and model simulations suggest is the result of a 6‐yr population cycle in established populations near the invasion front. Model simulations show that the development of periodic behavior in range expansion depends primarily on the period length of population cycles. The period length of invasion pulses corresponded to the population cycle length, and the regularity of invasion pulses tended to decline with increases in population cycle length. A key insight of this research is that dynamics of established populations, behind the invasion front, can have strong effects on spread. Our findings suggest that coordination between separate management programs targeting low‐density spreading and established outbreaking populations, respectively, could increase the efficacy of efforts to mitigate gypsy moth impacts. Given the variety of species experiencing population fluctuations, Allee effects, and stratified diffusion, insights from this study are potentially important to understanding how the range boundaries of many species change.     

Density dependence in group dynamics of a highly social mongoose, Suricata suricatta

1.?For social species, the link between individual behaviour and population dynamics is mediated by group-level demography. 2.?Populations of obligate cooperative breeders are structured into social groups, which may be subject to inverse density dependence (Allee effects) that result from a dependence on conspecific helpers, but evidence for population-wide Allee effects is rare. 3.?We use field data from a long-term study of cooperative meerkats (Suricata suricatta; Schreber, 1776) - a species for which local Allee effects are not reflected in population-level dynamics - to empirically model interannual group dynamics. 4.?Using phenomenological population models, modified to incorporate environmental conditions and potential Allee effects, we first investigate overall patterns of group dynamics and find support only for conventional density dependence that increases after years of low rainfall. 5.?To explain the observed patterns, we examine specific demographic rates and assess their contributions to overall group dynamics. Although per-capita meerkat mortality is subject to a component Allee effect, it contributes relatively little to observed variation in group dynamics, and other (conventionally density dependent) demographic rates - especially emigration - govern group dynamics. 6.?Our findings highlight the need to consider demographic processes and density dependence in subpopulations before drawing conclusions about how behaviour affects population processes in socially complex systems.     

A conceptual framework for the spatial analysis of landscape genetic data

Understanding how landscape heterogeneity constrains gene flow and the spread of adaptive genetic variation is important for biological conservation given current global change. However, the integration of population genetics, landscape ecology and spatial statistics remains an interdisciplinary challenge at the levels of concepts and methods. We present a conceptual framework to relate the spatial distribution of genetic variation to the processes of gene flow and adaptation as regulated by spatial heterogeneity of the environment, while explicitly considering the spatial and temporal dynamics of landscapes, organisms and their genes. When selecting the appropriate analytical methods, it is necessary to consider the effects of multiple processes and the nature of population genetic data. Our framework relates key landscape genetics questions to four levels of analysis: (i) node-based methods, which model the spatial distribution of alleles at sampling locations (nodes) from local site characteristics; these methods are suitable for modeling adaptive genetic variation while accounting for the presence of spatial autocorrelation. (ii) Link-based methods, which model the probability of gene flow between two patches (link) and relate neutral molecular marker data to landscape heterogeneity; these methods are suitable for modeling neutral genetic variation but are subject to inferential problems, which may be alleviated by reducing links based on a network model of the population. (iii) Neighborhood-based methods, which model the connectivity of a focal patch with all other patches in its local neighborhood; these methods provide a link to metapopulation theory and landscape connectivity modeling and may allow the integration of node- and link-based information, but applications in landscape genetics are still limited. (iv) Boundary-based methods, which delineate genetically homogeneous populations and infer the location of genetic boundaries; these methods are suitable for testing for barrier effects of landscape features in a hypothesis-testing framework. We conclude that the power to detect the effect of landscape heterogeneity on the spatial distribution of genetic variation can be increased by explicit consideration of underlying assumptions and choice of an appropriate analytical approach depending on the research question.     

Variation in Allee effects: evidence,unknowns, and directions forward

Allee effects, positive effects of population size or density on per-capita fitness, are of broad interest in ecology and conservation due to their importance to the persistence of small populations and to range boundary dynamics. A number of recent studies have highlighted the importance of spatiotemporal variation in Allee effects and the resulting impacts on population dynamics. These advances challenge conventional understanding of Allee effects by reframing them as a dynamic factor affecting populations instead of a static condition. First, we synthesize evidence for variation in Allee effects and highlight potential mechanisms. Second, we emphasize the “Allee slope,” i.e., the magnitude of the positive effect of density on the per-capita growth rate, as a metric for demographic Allee effects. The more commonly used quantitative metric, the Allee threshold, provides only a partial picture of the underlying forces acting on population growth despite its implications for population extinction. Third, we identify remaining unknowns and strategies for addressing them. Outstanding questions about variation in Allee effects fall broadly under three categories: (1) characterizing patterns of natural variability; (2) understanding mechanisms of variation; and (3) implications for populations, including applications to conservation and management. Future insights are best achieved through robust interactions between theory and empiricism, especially through mechanistic models. Understanding spatiotemporal variation in the demographic processes contributing to the dynamics of small populations is a critical step in the advancement of population ecology.     

Density dependent dispersal decisions and the Allee effect

The decision to move between patches in the environment is among the most important life history choices an organism can make. I derive a new density dependent dispersal rule, and examine how dispersal decisions based on avoiding fitness loss associated with an Allee effect or competitive effects impact upon population dynamics in spatially structured populations with qualitatively different dynamics. I also investigate the effects of the number of patches in the system and a limit to the patch sampling time available to dispersers. Dispersing to avoid competitive pressures can destabilise otherwise stable population dynamics, and stabilise chaotic dynamics. Dispersing to avoid an Allee effect does not qualitatively change local population dynamics until eventually driving unstable populations to global extinction with a sufficiently high fitness threshold. A time limit for sampling can stabilise dynamics if dispersal is based on escaping the Allee effect, and rescue populations from global extinction. The results are sensitive to the number of patches available in the environment and suggest that dispersal to avoid an Allee effect will only arise under biologically plausible conditions, i.e. where there is a limit to the number of dispersal attempts that can be made between generations.     

滨海湿地植物种群Allee效应驱动机制研究进展

Allee效应是指生物个体适应度与种群规模或密度之间呈正向关联的现象,因与植物种群动态和种群灭绝密切相关而受到生态学家的普遍重视。阐释多重胁迫下滨海湿地植物种群响应机制,从保护生物多样性和维持生态系统稳定性层面发展系统性生态修复措施成为相关研究关注的重点。本研究分别从遗传过程、花粉扩散过程和生物互作关系不同层面,总结分析了植物种群Allee效应驱动机制的研究进展。一方面,植物因遗传过程中近交衰退、遗传变异丧失、有害突变累积等遗传结构改变造成繁殖失败而引发Allee效应;另一方面,植物花粉扩散过程和动植物互作关系影响下的花粉限制也通过影响植物种群繁殖力成为驱动Allee效应的关键因素。滨海湿地水盐梯度变异及格局破碎化影响下,植物种群遭受Allee效应的风险需引起关注,维持滨海湿地植物种群适宜分布格局和生物连通过程成为缓解Allee效应的重要手段。结合生理学与化学生态学研究手段和长时间尺度动态监测技术,有助于进一步阐释环境及生物等多重胁迫下Allee效应的非线性驱动机制。