Exploiting Allee effects for managing biological invasions

Allee effects and population spread in patchy landscapes

Invasion of alien species is one of the major threats for natural community structures, potentially leading to high economic and environmental costs. In this work, we study through a reaction-diffusion model the dynamics of an invasion in a heterogeneous environment and in the presence of a strong Allee effect. We model space as an infinite landscape consisting of periodically alternating favourable and unfavourable patches. In addition, we consider that at the interface between patch types individuals may show preference for more favourable regions. Using homogenization techniques and a classical result for spread with Allee effect in homogeneous landscapes, we derive approximate expressions for the spread speed. When compared with numerical simulations, these expressions prove to be very accurate even beyond the expected small-scale heterogeneity limit of homogenization. We demonstrate how rates of spatial spread depend on demographic and movement parameters as well as on the landscape properties.

Exotic invaders gain foraging benefits by shoaling with native fish

Freshwater habitats are under increasing threat due to invasions of exotic fish. These invasions typically begin with the introduction of small numbers of individuals unfamiliar with the new habitat. One way in which the invaders might overcome this disadvantage is by associating with native taxa occupying a similar ecological niche. Here we used guppies (Poecilia reticulata) from a feral population in Mexico to test the prediction that exotic shoaling fish can associate with heterospecifics, and that they improve their foraging efficiency by doing so. Guppies have invaded the Mexican High Plateau and are implicated in the declines of many native topminnow (Goodeinae) species. We show that heterospecific associations between guppies and topminnows can deliver the same foraging benefits as conspecific shoals, and that variation in foraging gains is linked to differences in association tendency. These results uncover a mechanism enabling founding individuals to survive during the most vulnerable phase of an invasion and help explain why guppies have established viable populations in many parts of Mexico as well in every continent except Antarctica.

Allee effects in ants

1. Allee effects occur when the aggregation of individuals result in mutually beneficial intraspecific interactions whereby individual fitness, or per capita growth rate, increases with the number of individuals. Allee effects are common in social species due to their cooperative behaviours, such as breeding, feeding or defence. Allee effects have important implications for many aspects of basic and applied ecology. Over the past decades, the study of Allee effects has influenced population dynamics, community ecology, endangered species management and invasion biology. 2. Despite the fact that cooperation is the basis of their social structure, Allee effects have received little attention among eusocial insects. Extreme cooperation is common, and reproductive specialization of individuals occurs due to division of labour. These life-history traits suggest that the potential contribution of each caste to reproduction and survival may be differential and nonadditive. 3. We studied Allee effects in the invasive Argentine ant (Linepithema humile). In this species, many queens and workers are present in colonies, which allowed us to explore the differential effects of castes on the presence of Allee effects. In the laboratory, we measured brood production and individual survival in experimental colonies that differed in the initial numbers of queens and workers.4. Our results highlight the differential effect of queens and workers on survival and productivity. We found three positive density-dependent relationships indicative of component Allee effects at the colony level: both workers and queens had a positive effect on the productivity of the other caste, and queens had a positive effect on worker survivorship. 5. Our experimental results suggest a potential positive feedback between worker and queen abundance, which may have contributed to the evolution of large colony sizes. Our study provides the first evidence of Allee effects in eusocial insects and highlights the need to consider castes separately in population dynamics. Division of labour and differential reproductive rates are factors that should be integrated into the study of Allee effects.

Weakening density dependence from climate change and agricultural intensification triggers pest outbreaks: a 37-year observation of cotton bollworms

Understanding drivers of population fluctuation, especially for agricultural pests, is central to the provision of agro-ecosystem services. Here, we examine the role of endogenous density dependence and exogenous factors of climate and human activity in regulating the 37-year population dynamics of an important agricultural insect pest, the cotton bollworm (Helicoverpa armigera), in North China from 1975 to 2011. Quantitative time-series analysis provided strong evidence explaining long-term population dynamics of the cotton bollworm and its driving factors. Rising temperature and declining rainfall exacerbated the effect of agricultural intensification on continuously weakening the negative density dependence in regulating the population dynamics of cotton bollworms. Consequently, ongoing climate change and agricultural intensification unleashed the tightly regulated pest population and triggered the regional outbreak of H. armigera in 1992. Although the negative density dependence can effectively regulate the population change rate to fluctuate around zero at stable equilibrium levels before and after outbreak in the 1992, the population equilibrium jumped to a higher density level with apparently larger amplitudes after the outbreak. The results highlight the possibility for exogenous factors to induce pest outbreaks and alter the population regulating mechanism of negative density dependence and, thus, the stable equilibrium of the pest population, often to a higher level, posing considerable risks to the provision of agro-ecosystem services and regional food security. Efficient and timely measures of pest management in the era of Anthropocene should target the strengthening and revival of weakening density dependence caused by climate change and human activities.

Pest persistence and eradication conditions in a deterministic model for sterile insect release

The release of sterile insects is an environment friendly pest control method used in integrated pest management programmes. Difference or differential equations based on Knipling's model often provide satisfactory qualitative descriptions of pest populations subject to sterile release at relatively high densities with large mating encounter rates, but fail otherwise. In this paper, I derive and explore numerically deterministic population models that include sterile release together with scarce mating encounters in the particular case of species with long lifespan and multiple matings. The differential equations account separately the effects of mating failure due to sterile male release and the frequency of mating encounters. When insects spatial spread is incorporated through diffusion terms, computations reveal the possibility of steady pest persistence in finite size patches. In the presence of density dependence regulation, it is observed that sterile release might contribute to induce sudden suppression of the pest population.

Mate finding, Allee effects and selection for sex-biased dispersal

Although dispersal requires context-dependent decision-making in three distinct stages (emigration, transit, immigration), these decisions are commonly ignored in simple models of dispersal. For sexually reproducing organisms, mate availability is an important factor in dispersal decisions. Difficulty finding mates can lead to an Allee effect where population growth decreases at low densities. Surprisingly, theoretical studies on mate finding and on sex-biased dispersal produce opposing predictions: in the former, one sex is predicted to move less if the other sex evolves to search more, whereas in the latter, mate-finding difficulties can select for less sex bias in dispersal when mate finding occurs after dispersal. Here, we develop a pair of models to examine the joint evolution of dispersal and settlement behaviour. Our first model resolves the apparent contradiction from the mate search and dispersal literatures. Our second model demonstrates that the relationship between mating system and sex-biased dispersal is more complex than a simple contrast between resource defence monogamy and female defence polygyny. Our results highlight that a key factor is the timing of mating relative to dispersal (before, during, or after). We also show that although movement has the potential to alleviate a mate-finding Allee effect, in some cases, it can actually exacerbate the effect.

Invasion rate of deer ked depends on spatiotemporal variation in host density

Invasive parasites are of great global concern. Understanding the factors influencing the spread of invading pest species is a first step in developing effective countermeasures. Growing empirical evidence suggests that spread rates are essentially influenced by spatiotemporal dynamics of host-parasite interactions, yet approaches modelling spread rate have typically assumed static environmental conditions. We analysed invasion history of the deer ked (Lipoptena cervi) in Finland with a diffusion-reaction model, which assumed either the movement rate, the population growth rate, or both rates may depend on spatial and temporal distribution of moose (Alces alces), the main host of deer ked. We fitted the model to the data in a Bayesian framework, and used the Bayesian information criterion to show that accounting for the variation in local moose density improved the model's ability to describe the pattern of the invasion. The highest ranked model predicted higher movement rate and growth rate of deer ked with increasing moose density. Our results suggest that the historic increase in host density has facilitated the spread of the deer ked. Our approach illustrates how information about the ecology of an invasive species can be extracted from the spatial pattern of spread even with rather limited data.

From integrated pest management to integrated pest eradication: technologies and future needs

BACKGROUND

With growing globalization and trade, insect incursions are increasing worldwide. A proportion of incursions involve pests of major economic crops (e.g.Mediterranean fruit fly), conservation value (e.g. tramp ants) or health significance(e.g.mosquitoes), and maybe the targets of eradication programmes. Historically, such responses have included the use of broad spectrum insecticides. However, with increasing public awareness of the negative aspects of pesticides, new environmentally friendly and effective techniques are needed. Here, we review and evaluate a range of selective to broad-spectrum tactical options for suppression which either have, or show potential for, integration within arthropod eradication programmes.

RESULTS

Most of the available technologies have their roots in pest management, but higher efficacy is required. Further refinement may be needed for use in eradication. Integration of several tactics is usually needed, as compatible tools can be used simultaneously to target different parts of the pest life cycle. However, not all technologies are fully compatible; for example, the simultaneous use of mass trapping and the sterile insect technique (SIT) may be suboptimal, although sequential application may still be effective.

CONCLUSIONS

Broad-spectrum insecticides are generally incompatible with some biologically based technologies such as the SIT, but may be used to reduce the population so that density-dependent tactics can be used. Several novel technologies with fewer nontarget impacts have been proposed in recent years, and need to be properly evaluated for their applicability to insecteradication. Overall, there are still major gaps in surveillance and selective eradication technologies for most insects.

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.

Linking vital rates to invasiveness of a perennial herb

Invaders generally show better individual performance than non-invaders and, therefore, vital rates (survival, growth, fecundity) could potentially be used to predict species invasiveness outside their native range. Comparative studies have usually correlated vital rates with the invasiveness status of species, while few studies have investigated them in relation to population growth rate. Here, I examined the influence of five vital rates (plant establishment, survival, growth, flowering probability, seed production) and their variability (across geographic regions, habitat types, population sizes and population densities) on population growth rate (λ) using data from 37 populations of an invasive, iteroparous herb (Lupinus polyphyllus) in a part of its invaded range in Finland. Variation in vital rates was often related to habitat type and population density. The performance of the populations varied from declining to rapidly increasing independently of habitat type, population size or population density, but differed between regions. The population growth rate increased linearly with plant establishment, and with the survival and growth of vegetative individuals, while the survival of flowering individuals and annual seed production were not related to λ. The vital rates responsible for rapid population growth varied among populations. These findings highlight the importance of both regional and local conditions to plant population dynamics, demonstrating that individual vital rates do not necessarily correlate with λ. Therefore, to understand the role of individual vital rates in a species ability to invade, it is necessary to quantify their effect on population growth rate.

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.

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.

Modeling the relationship between propagule pressure and invasion risk to inform policy and management

Predicting population establishment based on initial population size is a theoretically and empirically challenging problem whose resolution informs a multitude of applications. Indeed, it is a central problem in the management of introduced, endangered, harvested, and pathogenic organisms. We focus here on introduced species. We synthesize the current state of modeling in this predictive enterprise and outline future directions in the application of these models to developing regulations intended to prevent the establishment of invaders. Descriptive and mechanistic models of single-population introductions are fairly well developed and have provided insight into invasion risk in laboratory and field conditions. However, many invasions stem from large-scale and repeated releases of a multitude of species from relatively indiscriminate invasion vectors associated with international trade and travel. Vector-scale models of invasion risk are less well developed and are characterized largely by the use of untested proxy variables for propagule pressure. We illustrate the problems associated with proxy variables and introduce a more mechanistic theoretical formulation characterizing vector-scale invasion pressure in terms of propagule pressure (number of introduced individuals) and colonization pressure (number of introduced species). We outline key questions to be addressed in applying both single-population and vector-scale models to the development of threshold-based invasion regulations. We illustrate these ecological and applied questions using examples from terrestrial, aquatic, and marine systems. We develop in detail examples from ballast-water transport that, as one of the best-characterized global invasion vectors and one that is subject to emerging international threshold-based biosecurity regulations, provides a rich case study.

Evidence of a component Allee effect driven by predispersal seed predation in a plant (Pedicularis rex, Orobanchaceae)

A small or sparse population may suffer a reduction in fitness owing to Allee effects. Here, we explored effects of plant density on pollination, reproduction and predation in the alpine herb Pedicularis rex over two years. We did not detect a significant difference in the pollination rate or fecundity (fruit set and the initial seed set) before predation between sparse and dense patches in either year, indicating no pollination-driven Allee effect. However, dense patches experienced significantly fewer attacks by predispersal seed predators in both years, resulting in a significantly decreased realized fecundity (final seed set), suggesting a component Allee effect driven by predispersal seed predation. Predation-driven Allee effects have been predicted by many models and demonstrated for a range of animals, but there is scant evidence for such effects in plants. Our study provides strong evidence of a component Allee effect driven by predation in a plant species.

Efficient mitigation of founder effects during the establishment of a leading-edge oak population

Numerous plant species are shifting their range polewards in response to ongoing climate change. Range shifts typically involve the repeated establishment and growth of leading-edge populations well ahead of the main species range. How these populations recover from founder events and associated diversity loss remains poorly understood. To help fill this gap, we exhaustively investigated a newly established population of holm oak (Quercus ilex) growing more than 30 km ahead of the nearest larger stands. Pedigree reconstructions showed that plants belong to two non-overlapping generations and that the whole population originates from only two founder trees. The four first-generation trees that have reached maturity showed disparate mating patterns despite being full-sibs. Long-distance pollen immigration was notable despite the strong isolation of the stand: 6 per cent gene flow events in acorns collected on the trees (n = 255), and as much as 27 per cent among their established offspring (n = 33). Our results show that isolated leading-edge populations of wind-pollinated forest trees can rapidly restore their genetic diversity through the interacting effects of efficient long-distance pollen flow and purging of inbred individuals during recruitment. They imply that range expansions of these species are primarily constrained by initial propagule arrival rather than by subsequent gene flow.

Will plant movements keep up with climate change?

In the face of anthropogenic climate change, species must acclimate, adapt, move, or die. Although some species are moving already, their ability to keep up with the faster changes expected in the future is unclear. 'Migration lag' is a particular concern with plants, because it could threaten both biodiversity and carbon storage. Plant movements are not realistically represented in models currently used to predict future vegetation and carbon-cycle feedbacks, so there is an urgent need to understand how much of a problem failure to track climate change is likely to be. Therefore, in this review, we compare how fast plants need to move with how fast they can move; that is, the velocity of climate change with the velocity of plant movement.

Range expansion promotes cooperation in an experimental microbial metapopulation

Natural populations throughout the tree of life undergo range expansions in response to changes in the environment. Recent theoretical work suggests that range expansions can have a strong effect on evolution, even leading to the fixation of deleterious alleles that would normally be outcompeted in the absence of migration. However, little is known about how range expansions might influence alleles under frequency- or density-dependent selection. Moreover, there is very little experimental evidence to complement existing theory, since expanding populations are difficult to study in the natural environment. In this study, we have used a yeast experimental system to explore the effect of range expansions on the maintenance of cooperative behaviors, which commonly display frequency- and density-dependent selection and are widespread in nature. We found that range expansions favor the maintenance of cooperation in two ways: (i) through the enrichment of cooperators at the front of the expanding population and (ii) by allowing cooperators to "outrun" an invading wave of defectors. In this system, cooperation is enhanced through the coupling of population ecology and evolutionary dynamics in expanding populations, thus providing experimental evidence for a unique mechanism through which cooperative behaviors could be maintained in nature.

Do social groups prevent Allee effect related extinctions?: The case of wild dogs

Background

Allee effects may arise as the number of individuals decreases, thereby reducing opportunities for cooperation and constraining individual fitness, which can lead to population decrease and extinction. Obligate cooperative breeders rely on a minimum group size to subsist and are thus expected to be particularly susceptible to Allee effects. Although Allee effects in some components of the fitness of cooperative breeders have been detected, empirical confirmation of population extinction due to Allee effects is lacking yet. Because previous studies of cooperation have focused on Allee effects affecting individual fitness (component Allee effect) and population dynamics (demographic Allee effect), we argue that a new conceptual level of Allee effect, the group Allee effect, is needed to understand the special case of cooperative breeders.

Results

We hypothesize that whilst individuals are vulnerable to Allee effects, the group could act as a buffer against population extinction if: (i) individual fitness and group fate depend on group size but not on population size and (ii) group size is independent of population size (that is, at any population size, populations comprise both large and small groups). We found that both conditions apply for the African wild dog, Lycaon pictus, and data on this species in Zimbabwe support our hypothesis.

Conclusions

The importance of groups in obligate cooperative breeders needs to be accounted for within the Allee effect framework, through a group Allee effect, because the group mediates the relationship between individual fitness and population performance. Whilst sociality is associated with a high probability of Allee effects, we suggest that cooperative individuals organized in relatively autonomous groups within populations might be behaving in ways that diminish extinction risks caused by Allee effects. This study opens new avenues to a better understanding of the role of the evolution of group-living on the probability of extinction faced by social species.

Quasi-one-dimensional waves in rodent populations in heterogeneous habitats: a consequence of elevational gradients on spatio-temporal dynamics

Wave propagation can be clearly discerned in data collected on mouse populations in the Cibola National Forest (New Mexico, USA) related to seasonal changes. During an exploration of the construction of a methodology for investigations of the spread of the Hantavirus epidemic in mice we have built a system of interacting reaction diffusion equations of the Fisher-Kolmogorov-Petrovskii-Piskunov type. Although that approach has met with clear success recently in explaining Hantavirus refugia and other spatiotemporal correlations, we have discovered that certain observed features of the wave propagation observed in the data we mention are impossible to explain unless modifications are made. However, we have found that it is possible to provide a tentative explanation/description of the observations on the basis of an assumed Allee effect proposed to exist in the dynamics. Such incorporation of the Allee effect has been found useful in several of our recent investigations both of population dynamics and pattern formation and appears to be natural to the observed system. We report on our investigation of the observations with our extended theory.

Know when to run, know when to hide: can behavioral differences explain the divergent invasion success of two sympatric lizards?

Invasive species represent a select subset of organisms that have successfully transitioned through each stage of the introduction process (transportation, establishment, and spread). Although there is a growing realization that behavior plays a critical role in invasion success, few studies have focused on the initial stages of introduction. We examined whether differences in the grouping tendencies and exploratory behavior of two sympatric lizard species could contribute to their divergent invasion success. While the nondirected activity of the two species did not differ, the invasive delicate skink (Lampropholis delicata) was found to be more exploratory than the congeneric noninvasive garden skink (L. guichenoti), which enabled it to more effectively locate novel environments and basking site resources. The delicate skink also exhibited a greater tendency to hide, which may act to enhance its probability of ensnarement in freight and cargo and decrease its likelihood of detection during transit. The grouping tendencies of the two species did not differ. Together, our results suggest that while the two species have an equivalent “opportunity” for unintentional human-assisted transportation, several pre-existing behavioral traits may enhance the success of the delicate skink in negotiating the initial stages of the introduction process, and subsequent post-establishment spread.

The biology of small, introduced populations, with special reference to biological control

Populations are introduced into novel environments in different contexts, one being the biological control of pests. Despite intense efforts, less than half introduced biological control agents establish. Among the possible approaches to improve biological control, one is to better understand the processes that underpin introductions and contribute to ecological and evolutionary success. In this perspective, we first review the demographic and genetic processes at play in small populations, be they stochastic or deterministic. We discuss the theoretical outcomes of these different processes with respect to individual fitness, population growth rate, and establishment probability. Predicted outcomes differ subtly in some cases, but enough so that the evaluating results of introductions have the potential to reveal which processes play important roles in introduced populations. Second, we attempt to link the theory we have discussed with empirical data from biological control introductions. A main result is that there are few available data, but we nonetheless report on an increasing number of well-designed, theory-driven, experimental approaches. Combining demography and genetics from both theoretical and empirical perspectives highlights novel and exciting avenues for research on the biology of small, introduced populations, and great potential for improving both our understanding and practice of biological control.

Density dependence: an ecological Tower of Babel

The concept of density dependence represents the effect of changing population size on demographic rates and captures the demographic role of social and trophic mechanisms (e.g. competition, cooperation, parasitism or predation). Ecologists have coined more than 60 terms to denote different statistical and semantic properties of this concept, resulting in a formidable lexicon of synonymies and polysemies. We have examined the vocabulary of density dependence used in the modern ecological literature from the foundational lexicon developed by Smith, Allee, Haldane, Neave and Varley. A few simple rules suffice to abate terminological inconsistency and to enhance the biological meaning of this important concept. Correct citation of original references by ecologists and research journals could ameliorate terminological standards in our discipline and avoid linguistic confusion of mathematically and theoretically complex patterns.

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.

Invasions in heterogeneous habitats in the presence of advection

We investigate invasions from a biological reservoir to an initially empty, heterogeneous habitat in the presence of advection. The habitat consists of a periodic alternation of favorable and unfavorable patches. In the latter the population dies at fixed rate. In the former it grows either with the logistic or with an Allee effect type dynamics, where the population has to overcome a threshold to grow. We study the conditions for successful invasions and the speed of the invasion process, which is numerically and analytically investigated in several limits. Generically advection enhances the downstream invasion speed but decreases the population size of the invading species, and can even inhibit the invasion process. Remarkably, however, the rate of population increase, which quantifies the invasion efficiency, is maximized by an optimal advection velocity. In models with Allee effect, differently from the logistic case, above a critical unfavorable patch size the population localizes in a favorable patch, being unable to invade the habitat. However, we show that advection, when intense enough, may activate the invasion process.

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.

Modelling the effect of temperature on the range expansion of species by reaction-diffusion equations

The spatial dynamics of range expansion is studied in dependence of temperature. The main elements population dynamics, competition and dispersal are combined in a coherent approach based on a system of coupled partial differential equations of the reaction-diffusion type. The nonlinear reaction terms comprise population dynamic models with temperature dependent reproduction rates subject to an Allee effect and mutual competition. The effect of temperature on travelling wave solutions is investigated for a one dimensional model version. One main result is the importance of the Allee effect for the crossing of regions with unsuitable habitats. The nonlinearities of the interaction terms give rise to a richness of spatio-temporal dynamic patterns. In two dimensions, the resulting non-linear initial boundary value problems are solved over geometries of heterogeneous landscapes. Geo referenced model parameters such as mean temperature and elevation are imported into the finite element tool COMSOL Multiphysics from a geographical information system. The model is applied to the range expansion of species at the scale of middle Europe.

Fatty-acid preference changes during development in Drosophila melanogaster

Fatty-acids (FAs) are required in the diet of many animals throughout their life. However, the mechanisms involved in the perception of and preferences for dietary saturated and unsaturated FAs (SFAs and UFAs, respectively) remain poorly explored, especially in insects. Using the model species Drosophila melanogaster, we measured the responses of wild-type larvae and adults to pure SFAs (14, 16, and 18 carbons) and UFAs (C18 with 1, 2, or 3 double-bonds). Individual and group behavioral tests revealed different preferences in larvae and adults. Larvae preferred UFAs whereas SFAs tended to induce both a strong aversion and a persistent aggregation behavior. Adults generally preferred SFAs, and laid more eggs and had a longer life span when ingesting these substances as compared to UFAs. Our data suggest that insects can discriminate long-chain dietary FAs. The developmental change in preference shown by this species might reflect functional variation in use of FAs or stage-specific nutritional requirements, and may be fundamental for insect use of these major dietary components.