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.     

Long-distance dispersal of the gypsy moth (Lepidoptera: Lymantriidae) facilitated its initial invasion of Wisconsin

Gypsy moth (Lymantria dispar L.) spread is dominated by stratified dispersal, and, although spread rates are variable in space and time, the gypsy moth has invaded Wisconsin at a consistently higher rate than in other regions. Allee effects, which act on low-density populations ahead of the moving population that contribute to gypsy moth spread, have also been observed to be consistently weaker in Wisconsin. Because a major cause of an Allee effect in the gypsy moth is mate-finding failure at low densities, supplementing low-density populations with immigrants that arrive through dispersal may facilitate establishment and consequent spread. We used local indicator of spatial autocorrelation methods to examine space-time gypsy moth monitoring data from 1996 to 2006 and identify isolated, low-density colonies that arrived through dispersal. We measured the distance of these colonies from the moving population front to show that long-distance dispersal was markedly present in earlier years when Wisconsin was still mainly uninfested. Recently, however, immigrants arriving through long-distance dispersal may no longer be detected because instead of invading uninfested areas, they are now supplementing high-density colonies. In contrast, we observed no temporal pattern in the distance between low-density colonies and the population front in West Virginia and Virginia. We submit that long-distance dispersal, perhaps facilitated through meteorological mechanisms, played an important role in the spread dynamics of the initial Wisconsin gypsy moth invasion, but it currently plays a lesser role because the portion of Wisconsin most susceptible to long-distance immigrants from alternate sources is now heavily infested.     

Persistence of invading gypsy moth populations in the United States

Exotic invasive species are a mounting threat to native biodiversity, and their effects are gaining more public attention as each new species is detected. Equally important are the dynamics of exotic invasives that are previously well established. While the literature reports many examples of the ability of a newly arrived exotic invader to persist prior to detection and population growth, we focused on the persistence dynamics of an established invader, the European gypsy moth (Lymantria dispar) in the United States. The spread of gypsy moth is largely thought to be the result of the growth and coalescence of isolated colonies in a transition zone ahead of the generally infested area. One important question is thus the ability of these isolated colonies to persist when subject to Allee effects and inimical stochastic events. We analyzed the US gypsy moth survey data and identified isolated colonies of gypsy moth using the local indicator of spatial autocorrelation. We then determined region-specific probabilities of colony persistence given the population abundance in the previous year and its relationship to a suite of ecological factors. We observed that colonies in Wisconsin, US, were significantly more likely to persist in the following year than in other geographic regions of the transition zone, and in all regions, the abundance of preferred host tree species and land use category did not appear to influence persistence. We propose that differences in region-specific rates of persistence may be attributed to Allee effects that are differentially expressed in space, and that the inclusion of geographically varying Allee effects into colony-invasion models may provide an improved paradigm for addressing the establishment and spread of gypsy moth and other invasive exotic species.     

Natural enemies and environmental factors affecting the population dynamics of the gypsy moth

The population densities of the gypsy moth (Lymantria dispar; Lepidoptera: Lymantriidae) may reach outbreak levels that pose considerable economic and environmental impacts to forests in Europe, Asia, Africa and North America. Compared with the situation in its native European range feeding damage by gypsy moth is often found to be more severe in North America and other parts of the world. Thus, the release from natural enemies can be interpreted as an important cause for high feeding damages. Natural enemies, especially parasitoids, can cause delayed density‐dependent mortality, which may be responsible for population cycles. In North America where only few parasitoids have been introduced and the parasitism rates are considerably lower than in Europe, generalist predators play a larger role than in Europe. Many other factors seem to influence the population dynamics of the gypsy moth such as the host plants and weather. Nevertheless, much of the variability in population densities of the gypsy moth may be attributed to interacting effects of weather conditions and attack by natural enemies. In spite of the considerable number of studies on the ecology and population dynamics of the gypsy moth and the impact of their natural enemies, more quantitative information is required to predict the population dynamics of this pest species and to control its economic and ecologic impact.     

The Allee effect, stochastic dynamics and the eradication of alien species

Previous treatments of the population biology of eradication have assumed that eradication can only be achieved via 100% removal of the alien population. However, this assumption appears to be incorrect because stochastic dynamics and the Allee effect typically contribute to the extinction of very low‐density populations. We explore a model that incorporates Allee dynamics and stochasticity to observe how these two processes contribute to the extinction of isolated populations following eradication treatments of varying strength (percentage mortality). As a case study, we used historical data on the dynamics of isolated gypsy moth, Lymantria dispar, populations to fit parameters to this model. The parameterized model was then used in simulations that evaluated the efficacy of various eradication strategies. The results indicated that eradication of isolated gypsy moth populations could be easily achieved following a treatment of >80% mortality as long as populations were relatively low (indicated by <100 males captured in pheromone traps).     

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。     

Mate‐finding failure as an important cause of Allee effects along the leading edge of an invading insect population

The movement of humans and goods has facilitated the arrival of non‐native insects, some of which successfully establish and cause negative consequences to the composition, services, and functioning of ecosystems. The gypsy moth, Lymantria dispar (L.) (Lepidoptera: Lymantriidae), is currently invading North American forests at variable rates, spreading by local and long‐distance movement in a process known as stratified dispersal. Newly arriving colonizers often occur considerably ahead of the population front, and a key question is the degree to which they successfully establish. Prior research has highlighted mate‐finding failures in sparse populations as a cause of an Allee effect (positive density dependence). We explored this mechanism by measuring the relationship between female mating success and background male moth densities along the gypsy moth western front in Northern Wisconsin (USA) over 2 years. The mating results were then compared with analogous previous studies in southern Wisconsin, and the southern front in West Virginia and Virginia (USA). Mate‐finding failures in low‐density populations were consistently observed to be density‐dependent across all years and locations. Mate‐finding failures in low‐density populations have important ramifications to invasive species management, particularly in predicting species invasiveness, preventing successful establishment by small founder populations, and concentrating eradication efforts where they are most likely to succeed.     

Dispersion in time and space affect mating success and Allee effects in invading gypsy moth populations

1. Understanding why invading populations sometimes fail to establish is of considerable relevance to the development of strategies for managing biological invasions. 2. Newly arriving populations tend to be sparse and are often influenced by Allee effects. Mating failure is a typical cause of Allee effects in low-density insect populations, and dispersion of individuals in space and time can exacerbate mate-location failure in invading populations. 3. Here we evaluate the relative importance of dispersal and sexual asynchrony as contributors to Allee effects in invading populations by adopting as a case study the gypsy moth (Lymantria dispar L.), an important insect defoliator for which considerable demographic information is available. 4. We used release-recapture experiments to parameterize a model that describes probabilities that males locate females along various spatial and temporal offsets between male and female adult emergence. 5. Based on these experimental results, we developed a generalized model of mating success that demonstrates the existence of an Allee threshold, below which introduced gypsy moth populations are likely to go extinct without any management intervention.     

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.     

Exploiting Allee effects for managing biological invasions

Biological invasions are a global and increasing threat to the function and diversity of ecosystems. Allee effects (positive density dependence) have been shown to play an important role in the establishment and spread of non-native species. Although Allee effects can be considered a bane in conservation efforts, they can be a benefit in attempts to manage non-native species. Many biological invaders are subject to some form of an Allee effect, whether due to a need to locate mates, cooperatively feed or reproduce or avoid becoming a meal, yet attempts to highlight the specific exploitation of Allee effects in biological invasions are surprisingly unprecedented. In this review, we highlight current strategies that effectively exploit an Allee effect, and propose novel means by which Allee effects can be manipulated to the detriment of biological invaders. We also illustrate how the concept of Allee effects can be integral in risk assessments and in the prioritization of resources allocated to manage non-native species, as some species beset by strong Allee effects could be less successful as invaders. We describe how tactics that strengthen an existing Allee effect or create new ones could be used to manage biological invasions more effectively.     

Critical patch size generated by Allee effect in gypsy moth, Lymantria dispar (L.)

Allee effects are important dynamical mechanisms in small-density populations in which per capita population growth rate increases with density. When positive density dependence is sufficiently severe (a 'strong' Allee effect), a critical density arises below which populations do not persist. For spatially distributed populations subject to dispersal, theory predicts that the occupied area also exhibits a critical threshold for population persistence, but this result has not been confirmed in nature. We tested this prediction in patterns of population persistence across the invasion front of the European gypsy moth (Lymantria dispar) in the United States in data collected between 1996 and 2008. Our analysis consistently provided evidence for effects of both population area and density on persistence, as predicted by the general theory, and confirmed here using a mechanistic model developed for the gypsy moth system. We believe this study to be the first empirical documentation of critical patch size induced by an Allee effect.     

Benefits and harm caused by the introduced generalist tachinid, <Emphasis Type="Italic">Compsilura concinnata</Emphasis>, in North America

We review North American research on Compsilura concinnata (Meigen), a highly generalist tachinid parasitoid that was introduced in 1906 to control two invasive forest insects: gypsy moth and browntail moth. The impact on gypsy moth in natural populations in North America has long thought to be minor, a view confirmed by recent work in Canada and Wisconsin, USA. However, research with experimentally created populations of gypsy moth suggests that it may be more important than previously realized. Studies on browntail moth in both naturally occurring and experimental populations suggest that C. concinnata is probably the main reason browntail moth disappeared from most of its former range in North America. Research on giant silk moths suggests that C. concinnata has become the major source of mortality among several species and may be responsible for the notable decline in their densities that has occurred over the last century. C. concinnata has been touted as a premier example of the generalist natural enemy that should be avoided in classical biological control introductions, yet in the case of browntail moth its effect has been extremely beneficial.     

Density-dependent resistance of the gypsy moth <Emphasis Type="Italic">Lymantria dispar</Emphasis> to its nucleopolyhedrovirus,and the consequences for population dynamics

The processes controlling disease resistance can strongly influence the population dynamics of insect outbreaks. Evidence that disease resistance is density-dependent is accumulating, but the exact form of this relationship is highly variable from species to species. It has been hypothesized that insects experiencing high population densities might allocate more energy to disease resistance than those at lower densities, because they are more likely to encounter density-dependent pathogens. In contrast, the increased stress of high-density conditions might leave insects more vulnerable to disease. Both scenarios have been reported for various outbreak Lepidoptera in the literature. We tested the relationship between larval density and disease resistance with the gypsy moth (Lymantria dispar) and one of its most important density-dependent mortality factors, the nucleopolyhedrovirus (NPV) LdMNPV, in a series of bioassays. Larvae were reared in groups at different densities, fed the virus individually, and then reared individually to evaluate response to infection. In this system, resistance to the virus decreased with increasing larval density. Similarly, time to death was faster at high densities than at lower densities. Implications of density–resistance relationships for insect–pathogen population dynamics were explored in a mathematical model. In general, an inverse relationship between rearing density and disease resistance has a stabilizing effect on population dynamics.     

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.     

Allee effects under climate change

Understanding how climate change affects population dynamics is crucial for assessing future of biodiversity. Here I ask how can Allee effects, occurring when mean individual fitness is reduced in rare populations, respond to increasing temperature. Despite the role Allee effects play in ecology of invasive, threatened and harvested populations, impacts of climate change on Allee effects are practically unknown. Analysis of two population models reveals that whereas the Allee effect driven by predation generally weakens as temperature increases, the Allee effect due to need of finding mates is predicted to become stronger when warming occurs. For the former model, the metabolic theory suggests that with increasing temperature prey growth rate should increase faster than predator attack rate. Increasing temperature thus weakens the Allee effect. In the latter, gypsy moth population model, mating rate increases with warming due to enhanced female?male encounter rate and temperature‐induced modifications in female and male adult emergence distributions. However, male and female mortality rates increase, too and the net effect is strengthening of the Allee effect. These results have repercussions also for pest control, indicating that augmentation of biocontrol agents may perhaps be not as effective as using pesticides or disrupting mating.     

Potential interactions between invasive woody shrubs and the gypsy moth (Lymantria dispar), an invasive insect herbivore

As the range of the invasive and highly polyphagous gypsy moth (Lymantria dispar) expands, it increasingly overlaps with forest areas that have been subject to invasion by non-native shrubs. We explored the potential for interactions between these co-occurring invasions through a gypsy moth feeding trial using the following three highly invasive, exotic shrubs: honeysuckle (Lonicera maackii), privet (Ligustrum sinense) and burning bush (Euonymus alatus). We compared these with two native shrubs: spicebush (Lindera benzoin) and pawpaw (Asimina triloba). We fed gypsy moth caterpillars foliage exclusively from one of the five shrubs and measured their relative consumptive rate (RCR), relative growth rate (RGR), and development time (DT). The RCR of gypsy moth was strongly influenced by the species of foliage (F = 31.9; P < 0.0001) with little or no consumption of honeysuckle and privet. Caterpillar RGR was influenced by the shrub species (F = 66.2; P < 0.0001), and those caterpillars fed spicebush, honeysuckle or privet lost weight over the course of the assay. Caterpillar DT was also significantly (F = 11.79, P < 0.0001) influenced by the shrub species and those fed honeysuckle, privet and spicebush died prior to molting. Overall, our data suggest that honeysuckle, privet, and spicebush could benefit (indirectly) from the invasion of gypsy moth, while burning bush and pawpaw could be negatively impacted due to direct effects (herbivory). Similarly, invading gypsy moth populations could be sustained on a shrub layer of burning bush and pawpaw in the event of canopy defoliation. Further field and laboratory analysis is needed to clarify herbivore resistance of invasive shrubs, and to investigate the potential interactions among co-occurring insect and plant invasions.     

Temperature-dependent Allee effects in a stage-structured model for <Emphasis Type="Italic">Bythotrephes</Emphasis> establishment

Whether the invasive freshwater cladoceran Bythotrephes longimanus can establish after introduction into a water body depends on several biotic and abiotic factors. Among these, water temperature is important because both development rates and mode of reproduction (parthenogenetic or sexual) in Bythotrephes are influenced by temperature. We built a stage-structured model for the population dynamics of Bythotrephes based on the temperature-dependency of events in its life cycle and used the density of resting eggs at the end of each year to track changes in population density. The model was parameterized using data from published laboratory experiments and data on the Bythotrephes population in Harp Lake, Canada, from 1994 to 2005. The parameterized model was then used to simulate the outcome of invasions with different initial resting egg densities under different temperature regimes. A strong Allee effect emerged from the model, i.e. there is a critical threshold density above which the population can establish and below which it goes extinct. We showed analytically that the existence of an Allee effect arises from the model structure and is therefore robust to the parameter values. An increase in temperature reduces the establishment threshold for introductions in the same year as well as for introductions in the previous years. We therefore hypothesize that climate warming might facilitate Bythotrephes invasions. Finally, we study how the establishment threshold is influenced by the timing of the introduction event and thus identify time periods during the year when lakes may be particularly susceptible to Bythotrephes invasions.     

Modelling the mating system of polar bears: a mechanistic approach to the Allee effect

Allee effects may render exploited animal populations extinction prone, but empirical data are often lacking to describe the circumstances leading to an Allee effect. Arbitrary assumptions regarding Allee effects could lead to erroneous management decisions so that predictive modelling approaches are needed that identify the circumstances leading to an Allee effect before such a scenario occurs. We present a predictive approach of Allee effects for polar bears where low population densities, an unpredictable habitat and harvest-depleted male populations result in infrequent mating encounters. We develop a mechanistic model for the polar bear mating system that predicts the proportion of fertilized females at the end of the mating season given population density and operational sex ratio. The model is parametrized using pairing data from Lancaster Sound, Canada, and describes the observed pairing dynamics well. Female mating success is shown to be a nonlinear function of the operational sex ratio, so that a sudden and rapid reproductive collapse could occur if males are severely depleted. The operational sex ratio where an Allee effect is expected is dependent on population density. We focus on the prediction of Allee effects in polar bears but our approach is also applicable to other species.     

Growth of newly established alien populations: comparison of North American gypsy moth colonies with invasion theory

A common characteristic observed in many biological invasions is the existence of a lag between the time of arrival by the alien population and the time when established populations are noticed. Considerable advances have been made in modeling the expansion of invading species, and there is often remarkable congruence between the behavior of these models with spread of actual populations. While these models have been used to characterize expansion of very newly founded colonies, there have been few attempts to compare the behavior predicted from theory with spread in actual newly founded populations, largely due to the difficulty of sampling sparse populations. Models predict that time lags in the radial expansion of newly invaded populations may be due to time requirements for the population to grow from founding to detectable levels. Models also indicate that these time lags can be predicted based upon population parameters such as the intrinsic rate of population growth and diffusion coefficient. In this paper, we compared the behavior of these models with historical data on gypsy moth, Lymantria dispar, establishment and spread to show similarities between model predictions and observed population spread, both of which exhibited temporal lags of expansion. However, actual populations exhibited certain behaviors that were not predicted, and this could be due, in part, to the existence of Allee effects and stochasticity. Further work that incorporates these effects is needed to more fully understand the growth of incipient colonies of invading species. Ultimately, this information can be of critical importance in the selection of effective strategies for their detection and eradication.     

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.