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.     

Estimating Allee Dynamics before They Can Be Observed: Polar Bears as a Case Study

Allee effects are an important component in the population dynamics of numerous species. Accounting for these Allee effects in population viability analyses generally requires estimates of low-density population growth rates, but such data are unavailable for most species and particularly difficult to obtain for large mammals. Here, we present a mechanistic modeling framework that allows estimating the expected low-density growth rates under a mate-finding Allee effect before the Allee effect occurs or can be observed. The approach relies on representing the mechanisms causing the Allee effect in a process-based model, which can be parameterized and validated from data on the mechanisms rather than data on population growth. We illustrate the approach using polar bears (Ursus maritimus), and estimate their expected low-density growth by linking a mating dynamics model to a matrix projection model. The Allee threshold, defined as the population density below which growth becomes negative, is shown to depend on age-structure, sex ratio, and the life history parameters determining reproduction and survival. The Allee threshold is thus both density- and frequency-dependent. Sensitivity analyses of the Allee threshold show that different combinations of the parameters determining reproduction and survival can lead to differing Allee thresholds, even if these differing combinations imply the same stable-stage population growth rate. The approach further shows how mate-limitation can induce long transient dynamics, even in populations that eventually grow to carrying capacity. Applying the models to the overharvested low-density polar bear population of Viscount Melville Sound, Canada, shows that a mate-finding Allee effect is a plausible mechanism for slow recovery of this population. Our approach is generalizable to any mating system and life cycle, and could aid proactive management and conservation strategies, for example, by providing a priori estimates of minimum conservation targets for rare species or minimum eradication targets for pests and invasive species.     

Competition,facilitation and the Allee effect

Individuals of different species may interact in many different ways, such as competition, mutualism, or predation, to name but a few. Recent theory and experiments reveal that whether an interaction is beneficial or detrimental to the dynamics of a population often depends on species densities and other environmental factors. Here, we explore how, for suitable densities, facilitation may arise between two competing species with an Allee effect. We consider two different mechanisms for the Allee effect: 1) plant species with obligate insect pollination, and 2) generalist predation. In the first case, a second plant species, competing for nutrients, may have a facilitative effect by attracting more pollinators. In the second case, another potentially competing species may serve to satiate the same generalist predator and thereby have a facilitative effect. We explore three aspects of facilitation in each of the two systems. The focal species may benefit from the presence of a ‘competitor’ if it experiences 1) the removal of the Allee threshold, 2) a lowering of the Allee threshold, or 3) an increase in carrying capacity. We find that the latter two effects occur in both study systems whereas the first only occurs for the generalist predation system but not for the plant‐pollination system. We give precise conditions on when such a facilitative effect can be expected. We also demonstrate several unexpected outcomes of these two‐species interactions with multiple steady states, such as obligate co‐occurence; we draw parallels to the dynamics of species known as ‘ecosystem engineers’, and we discuss implications for conservation and management.     

How predator functional responses and Allee effects in prey affect the paradox of enrichment and population collapses

In Rosenzweig-MacArthur models of predator-prey dynamics, Allee effects in prey usually destabilize interior equilibria and can suppress or enhance limit cycles typical of the paradox of enrichment. We re-evaluate these conclusions through a complete classification of a wide range of Allee effects in prey and predator's functional response shapes. We show that abrupt and deterministic system collapses not preceded by fluctuating predator-prey dynamics occur for sufficiently steep type III functional responses and strong Allee effects (with unstable lower equilibrium in prey dynamics). This phenomenon arises as type III functional responses greatly reduce cyclic dynamics and strong Allee effects promote deterministic collapses. These collapses occur with decreasing predator mortality and/or increasing susceptibility of the prey to fall below the threshold Allee density (e.g. due to increased carrying capacity or the Allee threshold itself). On the other hand, weak Allee effects (without unstable equilibrium in prey dynamics) enlarge the range of carrying capacities for which the cycles occur if predators exhibit decelerating functional responses. We discuss the results in the light of conservation strategies, eradication of alien species, and successful introduction of biocontrol agents.     

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.     

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).     

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。     

Modeling the Effect of Prey Refuge on a Ratio-Dependent Predator–Prey System with the Allee Effect

The extinction of species is a major threat to the biodiversity. The species exhibiting a strong Allee effect are vulnerable to extinction due to predation. The refuge used by species having a strong Allee effect may affect their predation and hence extinction risk. A mathematical study of such behavioral phenomenon may aid in management of many endangered species. However, a little attention has been paid in this direction. In this paper, we have studied the impact of a constant prey refuge on the dynamics of a ratio-dependent predator–prey system with strong Allee effect in prey growth. The stability analysis of the model has been carried out, and a comprehensive bifurcation analysis is presented. It is found that if prey refuge is less than the Allee threshold, the incorporation of prey refuge increases the threshold values of the predation rate and conversion efficiency at which unconditional extinction occurs. Moreover, if the prey refuge is greater than the Allee threshold, situation of unconditional extinction may not occur. It is found that at a critical value of prey refuge, which is greater than the Allee threshold but less than the carrying capacity of prey population, system undergoes cusp bifurcation and the rich spectrum of dynamics exhibited by the system disappears if the prey refuge is increased further.     

With Allee effects,life for the social carnivore is complicated

Anthropogenic modification of the landscape, resultant habitat loss, and decades of persecution have resulted in severe decline and fragmentation of large carnivore populations worldwide. Infectious disease is also identified as a primary threat to many carnivores. In wildlife species, population demography and group persistence are strongly influenced by group or population size. This is referred to as the Allee effect, in which a population or group is at an increased risk of extinction when the number or density of individuals falls below some threshold due to ecological and/or genetic factors. However, in social mammalian species, the relationship between the number of individuals and the risk of extinction is complicated because aggregation may enhance pathogen exposure and transmission. Although theoretical studies of the interaction between infectious disease transmission and Allee effects reveal important implications for carnivore management and population extinction risk, information about the interaction has yet to be synthesized. In this paper, we assess life history strategies of medium to large carnivore species (≥2.4 kg) and their influence on population dynamics, with a special focus on infectious disease. While declining population trends are observed in 73 % of all carnivores (both social and solitary species), infectious disease is identified as a significant cause of population decline in 45 % of social carnivores and 3 % of solitary carnivores. Furthermore, where carnivores suffer a combination of rapid population decline and infectious disease, Allee effects may be more likely to impact social as compared to solitary carnivore populations. These potentially additive interactions may strongly influence disease transmission dynamics and population persistence potential. Understanding the mechanisms that can result in Allee effects in endangered carnivore populations and the manner in which infectious disease interfaces at this nexus may define the outcome of developed conservation strategies.     

Habitat selection reduces extinction of populations subject to Allee effects

Theoretical studies indicate that a single population under an Allee effect will decline to extinction if reduced below a particular threshold, but the existence of multiple local populations connected by random dispersal improves persistence of the global population. An additional process that can facilitate persistence is the existence of habitat selection by dispersers. Using analytic and simulation models of population change, I found that when habitat patches exhibiting Allee effects are connected by dispersing individuals, habitat selection by these dispersers increases the likelihood that patches persist at high densities, relative to results expected by random settlement. Populations exhibiting habitat selection also attain equilibrium more quickly than randomly dispersing populations. These effects are particularly important when Allee effects are large and more than two patches exist. Integrating habitat selection into population dynamics may help address why some studies have failed to find extinction thresholds in populations, despite well-known Allee effects in many species.     

Host-Parasitoid Dynamics and the Success of Biological Control When Parasitoids Are Prone to Allee Effects

In sexual organisms, low population density can result in mating failures and subsequently yields a low population growth rate and high chance of extinction. For species that are in tight interaction, as in host-parasitoid systems, population dynamics are primarily constrained by demographic interdependences, so that mating failures may have much more intricate consequences. Our main objective is to study the demographic consequences of parasitoid mating failures at low density and its consequences on the success of biological control. For this, we developed a deterministic host-parasitoid model with a mate-finding Allee effect, allowing to tackle interactions between the Allee effect and key determinants of host-parasitoid demography such as the distribution of parasitoid attacks and host competition. Our study shows that parasitoid mating failures at low density result in an extinction threshold and increase the domain of parasitoid deterministic extinction. When proned to mate finding difficulties, parasitoids with cyclic dynamics or low searching efficiency go extinct; parasitoids with high searching efficiency may either persist or go extinct, depending on host intraspecific competition. We show that parasitoids suitable as biocontrol agents for their ability to reduce host populations are particularly likely to suffer from mate-finding Allee effects. This study highlights novel perspectives for understanding of the dynamics observed in natural host-parasitoid systems and improving the success of parasitoid introductions.     

Modelling mate-finding Allee effects and populations dynamics,with applications in pest control

In this paper, we review how mate-finding Allee effects enter population dynamical models that consider both sexes, highlight possible limitations of the more widely used “one-sex” models, and outline the links between the different model classes. We further explore interactions between the mate-finding Allee effect and other mechanisms relevant to pest-control strategies: release of natural enemies, sterile male release, and culling. Many of these strategies impose an additional component Allee effect on the population, and we discuss which of them might be efficient in the control of pest species that also suffer from the failure to locate mates. We focus primarily on eradication thresholds; our simple models show that most of the strategies yield similar results, and depending on the costs, one strategy or a combination of several can lead to the most efficient control.     

Incorporating Allee effects into reintroduction strategies

Allee effects, the reduction of vital rates at low population densities, can occur through several mechanisms, all of which potentially apply to reintroduced populations. Reintroduced populations are initially at low densities, hence Allee effects can potentially lead to reintroduction failure despite habitat quality being sufficient to allow long-term persistence if the population survived the establishment phase. The probability of such failures can potentially be reduced by releasing large numbers of organisms, by reducing post-release dispersal or mortality through management, or by directly managing the Allee effects, e.g., by implementing predator control or food supplementation until population size increases. However, such measures incur costs, as large releases have a greater impact on source populations, and management actions require financial and other resources. It is therefore essential to compare the costs and benefits of attempting to reduce Allee effects in reintroduction programs. Here we advocate the use of structured decision-making frameworks whereby alternative strategies are nominated, probability distributions of outcomes obtained under different strategies, and utilities assigned to different outcomes. We illustrate the potential application of such decision frameworks using projections from a stochastic population model including Allee effects. As there will seldom be estimates of Allee effects available from the species or system involved, it will be necessary to predict these effects based on the biology of the species and data from other systems. In doing so, it is important to identify mechanisms for proposed Allee effects, and to avoid misleading inferences from correlations subject to confounds. In particular, naive interpretations of correlations between numbers released and reintroduction success may exaggerate the benefits of releasing large numbers.     

Dynamics of an age-structured population with Allee effects and harvesting

We propose a discrete-time, age-structured population model to study the impact of Allee effects and harvesting. It is assumed that survival probabilities from one age class to the next are constants and fertility rate is a function of weighted total population size. Global extinction is certain if the maximal growth rate of the population is less than one. The model can have multiple attractors and the asymptotic dynamics of the population depend on its initial distribution if the maximal growth rate is larger than one. An Allee threshold depending on the components of the unstable interior equilibrium is derived when only the last age class can reproduce. The population becomes extinct if its initial population distribution is below the threshold. Harvesting on any particular age class can decrease the magnitude of the possible stable interior equilibrium and increase the magnitude of the unstable interior equilibrium simultaneously.     

Dynamics of an age-structured population with Allee effects and harvesting

We propose a discrete-time, age-structured population model to study the impact of Allee effects and harvesting. It is assumed that survival probabilities from one age class to the next are constants and fertility rate is a function of weighted total population size. Global extinction is certain if the maximal growth rate of the population is less than one. The model can have multiple attractors and the asymptotic dynamics of the population depend on its initial distribution if the maximal growth rate is larger than one. An Allee threshold depending on the components of the unstable interior equilibrium is derived when only the last age class can reproduce. The population becomes extinct if its initial population distribution is below the threshold. Harvesting on any particular age class can decrease the magnitude of the possible stable interior equilibrium and increase the magnitude of the unstable interior equilibrium simultaneously.     

Evolutionary dynamics and strong Allee effects

We describe the dynamics of an evolutionary model for a population subject to a strong Allee effect. The model assumes that the carrying capacity k(u), inherent growth rate r(u), and Allee threshold a(u) are functions of a mean phenotypic trait u subject to evolution. The model is a plane autonomous system that describes the coupled population and mean trait dynamics. We show bounded orbits equilibrate and that the Allee basin shrinks (and can even disappear) as a result of evolution. We also show that stable non-extinction equilibria occur at the local maxima of k(u) and that stable extinction equilibria occur at local minima of r(u). We give examples that illustrate these results and demonstrate other consequences of an Allee threshold in an evolutionary setting. These include the existence of multiple evolutionarily stable, non-extinction equilibria, and the possibility of evolving to a non-evolutionary stable strategy (ESS) trait from an initial trait near an ESS.     

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.     

Neglecting uncertainty behind Allee effect estimation may generate false predictions of population extinction risk

Estimation of extinction thresholds arising from Allee effects (Allee thresholds) and related probabilities of population extinction is notoriously difficult. One way is to analyze adequately parameterized population models. Traditionally, a point estimate is substituted for the Allee effect strength in such models. However, each point estimate entails an underlying uncertainty. We explore how accounting for this uncertainty affects the probability of population extinction, and show that this probability decreases sigmoidally with increasing population density, even in the absence of any stochasticity. Deviations from when only a point estimate of the Allee effect strength is used can be significant, unless stochasticity is added and the stochastic noise intensity is high. Significant deviations from when only a point estimate is used also occur when the Allee threshold and the environmental carrying capacity of the species are close enough one to another. We also show that the impact of the uncertainty in the Allee effect strength estimate increases as the Allee effect strength itself increases and decreases as the species recovery potential increases. This is not a good news, since we would like to preferentially and efficiently manage slowly recovering populations prone to strong Allee effects. Still, there is a way to come up with relatively good Allee threshold estimates. Besides an obvious option of collecting as many data as possible, the impact of the uncertainty can be mitigated by diversifying Allee effect experiments such that we put more emphasis on larger size groups. This is somewhat surprising, given that frequent complaints on the (im)possibility of detecting Allee effects concern difficulties in locating, observing and experimenting on rare populations. Our results extend current theory surrounding Allee effects and have broad ramifications for applied ecology.     

Allee-like effects in metapopulation dynamics

The existences of the Allee effect at the local population level and of the Allee-like effect at the metapopulation level are important for both ecology and conservation. Although there have been a great many papers on the Allee effect, they have mainly referred to only local populations and have not dealt with the relationship between the two. In this paper, we begin with local population dynamics and then construct a model including both local population and metapopulation dynamics. Then we simulate with computer at these two levels. The results indicate that the Allee-like effect in a metapopulation may emerge from the imposed Allee effect at the local population level. This threshold fraction of occupied patches below which the metapopulation goes extinct is seriously affected by the per capita migration rate, the survival rate during migration and the initial population size on the occupied patches. We also find that severe demographic stochasticity may compound the metapopulation extinction risk posed by the Allee effect. These conclusions are helpful for nature conservation, especially for the preservation of rare species.     

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。