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.     

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.     

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.     

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).     

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.     

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.     

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.     

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.     

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.     

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.     

Elevational gradient in the cyclicity of a forest-defoliating insect

Observed changes in the cyclicity of herbivore populations along latitudinal gradients and the hypothesis that shifts in the importance of generalist versus specialist predators explain such gradients has long been a matter of intense interest. In contrast, elevational gradients in population cyclicity are largely unexplored. We quantified the cyclicity of gypsy moth populations along an elevational gradient by applying wavelet analysis to spatially referenced 31-year records (1975–2005) of defoliation. Based on geographically weighted regression and nonlinear regression, we found either a hump-shaped or plateauing relationship between elevation and the cyclicity of gypsy moth populations and a positive relationship between cyclicity and the density of the gypsy moth’s preferred host-tree species. The potential effects of elevational gradients in the density of generalist predators and preferred host-tree species on the cyclicity of gypsy moth populations were evaluated with mechanistic simulation models. The models suggested that an elevational gradient in the densities of preferred host tree species could partially explain elevational patterns of gypsy moth cyclicity. Results from a model assuming a type-III functional response of generalist predators to changes in gypsy moth density were inconsistent with the observed elevational gradient in gypsy moth cyclicity. However, a model with a more realistic type-II functional response gave results roughly consistent with the empirical findings. In contrast to classical studies on the effects of generalist predators on prey population cycles, our model with a type-II functional response predicts a unimodal relationship between generalist-predator density and the cyclicity of gypsy moth populations.     

Migration and Allee effects in the six-spot burnet moth Zygaena filipendulae

Abstract 1. Migration into local populations may increase the likelihood of persistence but emigration may decrease the persistence of small and isolated populations. The dispersal behaviour of a day-flying moth Zygaena filipendulae was examined to determine whether emigration is correlated positively or negatively with population size and host plant density.
2. A mark–release–recapture study showed that most moths moved small distances (< 40 m on average) and only 6% of movements were > 100 m.
3. Twenty-five individuals moved between populations, a measured exchange rate of 8%. Moths were more likely to move between patches that were close together and they moved to relatively large patches.
4. The fraction of residents increased with increasing population size in the patch and increasing host plant cover. Relatively high proportions of individuals left small patches with small moth populations.
5. Moths released in grassland lacking Lotus corniculatus (the host plant) tended to leave the area and biased their movement towards host plant areas, whereas those released within an area containing L. corniculatus tended to stay in that area.
6. Biased movement away from small populations and areas of low host plant density (normally with low population density) was found. This migration-mediated Allee effect is likely to decrease patch occupancy in metapopulations, the opposite of the rescue effect. The effects on metapopulation persistence are not known.     

Allee effects and resilience in stochastic populations

Allee effects, or positive functional relationships between a population’s density (or size) and its per unit abundance growth rate, are now considered to be a widespread if not common influence on the growth of ecological populations. Here we analyze how stochasticity and Allee effects combine to impact population persistence. We compare the deterministic and stochastic properties of four models: a logistic model (without Allee effects), and three versions of the original model of Allee effects proposed by Vito Volterra representing a weak Allee effect, a strong Allee effect, and a strong Allee effect with immigration. We employ the diffusion process approach for modeling single-species populations, and we focus on the properties of stationary distributions and of the mean first passage times. We show that stochasticity amplifies the risks arising from Allee effects, mainly by prolonging the amount of time a population spends at low abundance levels. Even weak Allee effects become consequential when the ubiquitous stochastic forces affecting natural populations are accounted for in population models. Although current concepts of ecological resilience are bound up in the properties of deterministic basins of attraction, a complete understanding of alternative stable states in ecological systems must include stochasticity.     

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.     

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.     

Gypsy moth invasion in North America: A simulation study of the spatial pattern and the rate of spread

Gypsy moth is regarded as one of the top most harmful invasive species. Its invasion in the northeastern US has led to widespread forest defoliation, wildlife disruption and even a change in biogeochemical conditions over the area of 10⁶ km². Spread of gypsy moth has a few distinct features such as a patchy spatial distribution of the gypsy moth population, which is largely uncorrelated to the environmental heterogeneity, and a high variability (almost over an order of magnitude) in the spread rates. These features are usually explained by human-assisted dispersal, e.g. when masses of gypsy moth eggs are inadvertently transported by cars and vehicles. This theory, however, somewhat disagrees with the existence of the strong Allee effect that tends to wipe out small new colonies. In this paper, we suggest an alternative explanation that the patchy structure can result from the interplay between two natural factors such as wind dispersal and viral infection. In order to check this hypothesis, we describe the gypsy moth spread with a diffusive SI model and study its properties by means of extensive computer simulations. Interestingly, in a certain parameter range our model shows formation of spatial patterns that are qualitatively similar to those observed in the field. To find out the relevant parameter range, we make a careful review of available literature sources. For biologically meaningful parameter values, we then show that the rates of gypsy moth spread predicted by our model are in good agreement with the lower band of the rates observed in nature.     

The presence of heterospecific males causes an Allee effect

The Allee effect is a positive causal relationship between any component of fitness and population density or size. Allee effects strongly affect the persistence of small or sparse populations. Predicting Allee effects remains a challenge, possibly because not all causal mechanisms are known. We hypothesized that reproductive interference (an interspecific reproductive interaction that reduces the fitness of the species involved) can generate an Allee effect. If the density of the interfering species is constant, an increase in the population of the species receiving interference may dilute the per capita effect of reproductive interference and may generate an Allee effect. To test this hypothesis, we examined the effect of heterospecific males on the relationship between per capita fecundity and conspecific density in Callosobruchus chinensis and C. maculatus. Of the two species, only C. maculatus females suffer reproductive interference from heterospecific males. Only C. maculatus, the species susceptible to reproductive interference, demonstrated an Allee effect, and only when heterospecific males were present. In contrast, C. chinensis, the species not susceptible to reproductive interference, demonstrated no Allee effect regardless of the presence of heterospecific males. Our results show that reproductive interference in fact generated an Allee effect, suggesting the potential importance of interspecific sexual interactions especially in small or sparse populations, even in the absence of a shared resource. It may be possible to predict Allee effects produced by this mechanism a priori by testing reproductive interference between closely related species.     

Variation in developmental time affects mating success and Allee effects

A fundamental question in biological conservation and invasion biology is why do some populations go extinct? Allee effects, notably those caused by mate location failure, are potentially key factors leading to the extinction of sparse populations. Several previous studies have focused on the inability of males and females to locate each other in space when populations are at low densities but here we investigate the effects of differences in the timing of male and female maturation on mating success. We develop a generalized model to clarify the role of protandry (the appearance of males before female emergence) and variability in adult maturation times. We show that temporal asynchrony can substantially reduce the probability of successful mating. We then apply this generalized model to estimate mating success in invading populations of the gypsy moth in North America in relation to local climate and its associated seasonality. Considerable geographic heterogeneity was observed in simulated mating success and this variability was not correlated with previous evaluations of bioclimatic requirements and habitat suitability. Furthermore, we found that the generalized model of temporal asynchrony provided reliable predictions and that detailed modeling of gypsy moth development was not necessary.     

The evidence for Allee effects

Allee effects are an important dynamic phenomenon believed to be manifested in several population processes, notably extinction and invasion. Though widely cited in these contexts, the evidence for their strength and prevalence has not been critically evaluated. We review results from 91 studies on Allee effects in natural animal populations. We focus on empirical signatures that are used or might be used to detect Allee effects, the types of data in which Allee effects are evident, the empirical support for the occurrence of critical densities in natural populations, and differences among taxa both in the presence of Allee effects and primary causal mechanisms. We find that conclusive examples are known from Mollusca, Arthropoda, and Chordata, including three classes of vertebrates, and are most commonly documented to result from mate limitation in invertebrates and from predator–prey interactions in vertebrates. More than half of studies failed to distinguish component and demographic Allee effects in data, although the distinction is crucial to most of the population-level dynamic implications associated with Allee effects (e.g., the existence of an unstable critical density associated with strong Allee effects). Thus, although we find conclusive evidence for Allee effects due to a variety of mechanisms in natural populations of 59 animal species, we also find that existing data addressing the strength and commonness of Allee effects across species and populations is limited; evidence for a critical density for most populations is lacking. We suggest that current studies, mainly observational in nature, should be supplemented by population-scale experiments and approaches connecting component and demographic effects. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

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.