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.     

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.     

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

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

Deconstructing the eradication of new world screwworm in North America: retrospective analysis and climate warming effects

Before its eradication from North America, the subtropical‐tropical new world screwworm fly Cochliomyia hominivorax (Coquerel) invaded southwestern temperate areas of the U.S.A., where it caused myiasis in wildlife and livestock. Outbreaks of the fly occurred during years when adult migrants were carried northward on North American monsoon winds from the northern areas of Mexico and south Texas. We deconstruct, retrospectively, the biology and the effect of weather on the eradication of the fly in North America. Screwworm was found to be an ideal candidate for eradication using the sterile insect technique (SIT) because females mate only once, whereas males are polygynous, and, although it has a high reproductive potential, field population growth rates are low in tropical areas. In northern areas, eradication was enhanced by cool‐cold weather, whereas eradication in tropical Mexico and Central America is explained by the SIT. Despite low average efficacy of SIT releases (approximately 1.7%), the added pressure of massive SIT releases reduced intrinsically low fly populations, leading to mate‐limited extinction. Non‐autochthonous cases of myiasis occur in North America and, if the fly reestablishes, climate warming by 2045–2055 will expand the area of favourability and increase the frequency and severity of outbreaks.     

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.     

Predator-driven component Allee effects in a wild ungulate

Negative density dependence is an important driver of population dynamics of large vertebrates. Allee effects (positive density dependence), however, can affect small populations. Allee effects can be generated by predation and recent research has revealed potentially important indirect effects of predation on population dynamics. For wild populations, however, quantification of both Allee effects and indirect effects of predation remains scarce. We monitored for 27 years a bighorn sheep (Ovis canadensis) population that declined dramatically as episodes of cougar (Puma concolor) predation depressed survival. Predation led to a positive relationship between lamb survival and population size below a threshold, and to an overall positive relationship between yearling and adult ewe survival and population size. During years of high predation, lambs also suffer mortality through reduced growth, contributing a third of the total impact of predation on lamb survival. There was no positive association between population growth and population size, probably because growth was affected by several factors other than predation, including disease. Our results support the contention that predator-driven component Allee effects may exacerbate the effects of other environmental drivers and increase the risk of extinction of small populations.     

Modelling Allee effects in a transgenic mosquito population during range expansion

ABSTRACT

Mosquitoes are vectors for many diseases that cause significant mortality and morbidity. As mosquito populations expand their range, they may undergo mate-finding Allee effects such that their ability to successfully reproduce becomes difficult at low population density. With new technology, creating target specific gene modification may be a viable method for mosquito population control. We develop a mathematical model to investigate the effects of releasing transgenic mosquitoes into newly established, low-density mosquito populations. Our model consists of two life stages (aquatic and adults), which are divided into three genetically distinct groups: heterogeneous and homogeneous transgenic that cause female infertility and a homogeneous wild type. We perform analytical and numerical analyses on the equilibria to determine the level of saturation needed to eliminate mosquitoes in a given area. This model demonstrates the potential for a gene drive system to reduce the spread of invading mosquito populations.     

The stability of predator-prey systems subject to the Allee effects

In recent years, many theoreticians and experimentalists have concentrated on the processes that affect the stability of predator-prey systems. But few papers have addressed the Allee effect with focus on the their stability. In this paper, we select two classical models describing predator-prey systems and introduce the Allee effects into the dynamics of both the predator and prey populations in these models, respectively. By combining mathematical analysis with numerical simulation, we have shown that the Allee effect may be a destabilizing force in predator-prey systems: the equilibrium point of the system could be changed from stable to unstable or otherwise, the system, even when it is stable, will take much longer time to reach the stable state. We also conclude that the equilibrium of the prey population will be enlarged due to the Allee effect of the predator, but the Allee effects of the prey may decrease the equilibrium value of the predator, or that of both the predator and prey. It should also be pointed out that the impact of the Allee effects of predator and prey due to different mechanisms on different predator-prey systems could also vary.     

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.     

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.     

A spatially explicit model for an Allee effect: why wolves recolonize so slowly in Greater Yellowstone

A reduced probability of finding mates at low densities is a frequently hypothesized mechanism for a component Allee effect. At low densities dispersers are less likely to find mates and establish new breeding units. However, many mathematical models for an Allee effect do not make a distinction between breeding group establishment and subsequent population growth. Our objective is to derive a spatially explicit mathematical model, where dispersers have a reduced probability of finding mates at low densities, and parameterize the model for wolf recolonization in the Greater Yellowstone Ecosystem (GYE). In this model, only the probability of establishing new breeding units is influenced by the reduced probability of finding mates at low densities. We analytically and numerically solve the model to determine the effect of a decreased probability in finding mates at low densities on population spread rate and density. Our results suggest that a reduced probability of finding mates at low densities may slow recolonization rate.     

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.     

Bottom-up derivation of discrete-time population models with the Allee effect

This paper presents a framework in which various single-species discrete-time population models exhibiting the Allee effect are derived from first principles. Here, the Allee effect means a reduction in individual fitness at low population sizes. The derivation is based on the distribution of female and male individuals among discrete resource sites, in addition to competitive and cooperative interaction among individuals. These derivations show how the derived population models depend on the type and the intensity of competition, and the degree of clustering of individuals. Along with these models exhibiting the Allee effect, this paper also presents first-principles derivation of population models without the Allee effect which include a parameter relating to the intensity of competition.     

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.     

Pushed beyond the brink: Allee effects,environmental stochasticity,and extinction

To understand the interplay between environmental stochasticity and Allee effects, we analyse persistence, asymptotic extinction, and conditional persistence for stochastic difference equations. Our analysis reveals that persistence requires that the geometric mean of fitness at low densities is greater than one. When this geometric mean is less than one, asymptotic extinction occurs with high probability for low initial population densities. Additionally, if the population only experiences positive density-dependent feedbacks, conditional persistence occurs provided the geometric mean of fitness at high population densities is greater than one. However, if the population experiences both positive and negative density-dependent feedbacks, conditional persistence only occurs if environmental fluctuations are sufficiently small. We illustrate counter-intuitively that environmental fluctuations can increase the probability of persistence when populations are initially at low densities, and can cause asymptotic extinction of populations experiencing intermediate predation rates despite conditional persistence occurring at higher predation rates.     

Periodic dynamics in a two-stage Allee effect model are driven by tension between stage equilibria

Single species difference population models can show complex dynamics such as periodicity and chaos under certain circumstances, but usually only when rates of intrinsic population growth or other life history parameter are unrealistically high. Single species models with Allee effects (positive density dependence at low density) have also been shown to exhibit complex dynamics when combined with over-compensatory density dependence or a narrow fertility window. Here we present a simple two-stage model with Allee effects which shows large amplitude periodic fluctuations for some initial conditions, without these requirements. Periodicity arises out of a tension between the critical equilibrium of each stage, i.e. when the initial population vector is such that the adult stage is above the critical value, while the juvenile stage is below the critical value. Within this area of parameter space, the range of initial conditions giving rise to periodic dynamics is driven mainly by adult mortality rates. Periodic dynamics become more important as adult mortality increases up to a certain point, after which periodic dynamics are replaced by extinction. This model has more realistic life history parameter values than most 'chaotic' models. Conditions for periodic dynamics might arise in some marine species which are exploited (high adult mortality) leading to recruitment limitation (low juvenile density) and might be an additional source of extinction risk.     

Backward bifurcations and strong Allee effects in matrix models for the dynamics of structured populations

In nonlinear matrix models, strong Allee effects typically arise when the fundamental bifurcation of positive equilibria from the extinction equilibrium at r=1 (or R₀=1) is backward. This occurs when positive feedback (component Allee) effects are dominant at low densities and negative feedback effects are dominant at high densities. This scenario allows population survival when r (or equivalently R₀) is less than 1, provided population densities are sufficiently high. For r>1 (or equivalently R₀>1) the extinction equilibrium is unstable and a strong Allee effect cannot occur. We give criteria sufficient for a strong Allee effect to occur in a general nonlinear matrix model. A juvenile–adult example model illustrates the criteria as well as some other possible phenomena concerning strong Allee effects (such as positive cycles instead of equilibria).     

A test for Allee effects in the self‐incompatible wasp‐pollinated milkweed Gomphocarpus physocarpus

It has been suggested that plants that are good colonizers will generally have either an ability to self‐fertilize or a generalist pollination system. This prediction is based on the idea that these reproductive traits should confer resistance to Allee effects in founder populations and was tested using Gomphocarpus physocarpus (Asclepiadoideae: Apocynaceae), a species native to South Africa that is invasive in other parts of the world. We found no significant relationships between the size of G. physocarpus populations and various measures of pollination success (pollen deposition, pollen removal and pollen transfer efficiency) and fruit set. A breeding system experiment showed that plants in a South African population are genetically self‐incompatible and thus obligate outcrossers. Outcrossing is further enhanced by mechanical reconfiguration of removed pollinaria before the pollinia can be deposited. Self‐pollination is reduced when such reconfiguration exceeds the average duration of pollinator visits to a plant. Observations suggest that a wide variety of wasp species in the genera Belonogaster and Polistes (Vespidae) are the primary pollinators. We conclude that efficient pollination of plants in small founding populations, resulting from their generalist wasp‐pollination system, contributes in part to the colonizing success of G. physocarpus. The presence of similar wasps in other parts of the world has evidently facilitated the expansion of the range of this milkweed.     

The effects of reproduction on courtship, fertility and longevity within and between alternative male mating tactics of the horned beetle, Onthophagus binodis

Life history theory provides a powerful tool to study an organism's biology within an evolutionary framework. The notion that males face a longevity cost of competing for and displaying to females lies at the core of sexual selection theory. Likewise, recent game theory models of the evolution of ejaculation strategies assume that males face a trade-off between expenditure on the ejaculate and expenditure on gaining additional matings. Males of the dung beetle Onthophagus binodis adopt alternative reproductive tactics in which major males fight for and help provision females, and minor males sneak copulations with females that are guarded by major males. Minor males are always subject to sperm competition, and consistent with theoretical expectation, minor males have a greater expenditure on their ejaculate than major males. We used this model system to seek evidence that mating comes at a cost for future fertility and/or male expenditure on courtship and attractiveness, and to establish whether these traits vary between alternative mating tactics. We monitored the lifespan of males exposed to females and nonmating populations, and sampled males throughout their lives to assess their fertility and courtship behaviour. We found a significant longevity cost of reproduction, but no fertility cost. On average, males from mating populations had a lower courtship rate than those from nonmating populations. This small effect, although statistically nonsignificant, was associated with significant increases in the time males required to achieve mating. Minor males had lower courtship rates than major males, and took longer to achieve mating. Although we did not measure ejaculate expenditure in this study, the correlation between lower courtship rate and longer mating speed of minor males documented here with their greater expenditure on the ejaculate found in previous studies, is consistent with game theory models of ejaculate expenditure which assume that males trade expenditure on gaining matings for expenditure on gaining fertilizations.     

Pollination processes and the Allee effect in highly fragmented populations: consequences for the mating system in urban environments

The urban environment was used to study the plant reproductive system in small fragmented populations as well as the potential adaptations of plants to urban conditions. We examined the effect of density on the pollination process and on reproduction in urban populations of the allogamous species Crepis sancta. The habitat is composed of small uncultivated square patches (c. 2 m2) regularly spaced along the pavement in streets of the city of Montpellier, France. Pollinator behaviour (the presence of pollinators, the number of flowers visited and the duration of each visit) and seed set as a function of the number of plants in patches and selfing rates, determined using progeny array analysis, were studied. The propensity for the urban populations to produce seeds by self-fertilization in insect-proof glasshouse was also analysed. We found strong evidence of reduced pollinator activities at low densities, resulting in reduced pollination and a reduction in seed set from 80 to 20% of ovules fertilized (the Allee effect). Progeny array analysis revealed a slight increase (marginally significant) in selfing rates in urban populations compared with large populations. In spite of lower pollinator activity, urban populations did not show a greater ability to self-fertilize compared with rural populations from the nearby countryside.