Modeling insect growth regulators for pest management.

Insect growth regulators (IGRs) have been developed as effective control measures against harmful insect pests to disrupt their normal development. This study is to propose a mathematical model to evaluate the cost-effectiveness of IGRs for pest management. The key features of the model include the temperature-dependent growth of insects and realistic impulsive IGRs releasing strategies. The impulsive releases are carefully modeled by counting the number of implements during an insect's temperature-dependent development duration, which introduces a surviving probability determined by a product of terms corresponding to each release. Dynamical behavior of the model is illustrated through dynamical system analysis and a threshold-type result is established in terms of the net reproduction number. Further numerical simulations are performed to quantitatively evaluate the effectiveness of IGRs to control populations of harmful insect pests. It is interesting to observe that the time-changing environment plays an important role in determining an optimal pest control scheme with appropriate release frequencies and time instants.

More pests but less pesticide applications: Ambivalent effect of landscape complexity on conservation biological control.

In agricultural landscapes, the amount and organization of crops and semi-natural habitats (SNH) have the potential to promote a bundle of ecosystem services due to their influence on ecological community at multiple spatio-temporal scales. SNH are relatively undisturbed and are often source of complementary resources and refuges, therefore supporting more diverse and abundant natural pest enemies. However, the nexus of SNH proportion and organization with pest suppression is not trivial. It is thus crucial to understand how the behavior of pest and natural enemy species, the underlying landscape structure, and their interaction, may influence conservation biological control (CBC). Here, we develop a generative stochastic landscape model to simulate realistic agricultural landscape compositions and configurations of fields and linear elements. Generated landscapes are used as spatial support over which we simulate a spatially explicit predator-prey dynamic model. We find that increased SNH presence boosts predator populations by sustaining high predator density that regulates and keeps pest density below the pesticide application threshold. However, predator presence over all the landscape helps to stabilize the pest population by keeping it under this threshold, which tends to increase pest density at the landscape scale. In addition, the joint effect of SNH presence and predator dispersal ability among hedge and field interface results in a stronger pest regulation, which also limits pest growth. Considering properties of both fields and linear elements, such as local structure and geometric features, provides deeper insights for pest regulation; for example, hedge presence at crop field boundaries clearly strengthens CBC. Our results highlight that the integration of species behaviors and traits with landscape structure at multiple scales is necessary to provide useful insights for CBC.

Challenges of automation and scale: Bioinformatics and the evaluation of proteins to support genetically modified product safety assessments.

Bioinformatic analyses of protein sequences play an important role in the discovery and subsequent safety assessment of insect control proteins in Genetically Modified (GM) crops. Due to the rapid adoption of high-throughput sequencing methods over the last decade, the number of protein sequences in GenBank and other public databases has increased dramatically. Many of these protein sequences are the product of whole genome sequencing efforts, coupled with automated protein sequence prediction and annotation pipelines. Published genome sequencing studies provide a rich and expanding foundation of new source organisms and proteins for insect control or other desirable traits in GM products. However, data generated by automated pipelines can also confound regulatory safety assessments that employ bioinformatics. Largely this issue does not arise due to underlying sequence, but rather its annotation or associated metadata, and the downstream integration of that data into existing repositories. Observations made during bioinformatic safety assessments are described.

Using non-smooth models to determine thresholds for microbial pest management.

Releasing infectious pests could successfully control and eventually maintain the number of pests below a threshold level. To address this from a mathematical point of view, two non-smooth microbial pest-management models with threshold policy are proposed and investigated in the present paper. First, we establish an impulsive model with state-dependent control to describe the cultural control strategies, including releasing infectious pests and spraying chemical pesticide. We examine the existence and stability of an order-1 periodic solution, the existence of order-k periodic solutions and chaotic phenomena of this model by analyzing the properties of the Poincaré map. Secondly, we establish and analyze a Filippov model. By examining the sliding dynamics, we investigate the global stability of both the pseudo-equilibria and regular equilibria. The findings suggest that we can choose appropriate threshold levels and control intensity to maintain the number of pests at or below the economic threshold. The modelling and control outcomes presented here extend the results for the system with impulsive interventions at fixed moments.

Effect of impulsive controls in a model system for age-structured population over a patchy environment.

In this paper, a very general model of impulsive delay differential equations in n-patches is rigorously derived to describe the impulsive control of population of a single species over n-patches. The model allows an age structure consisting of immatures and matures, and also considers mobility and culling of both matures and immatures. Conditions are obtained for extinction and persistence of the model system under three special scenarios: (1) without impulsive control; (2) with impulsive culling of the immatures only; and (3) with impulsive culling of the matures only, respectively. In the case of persistence, the persistence level is also estimated for the systems in the case of identical n patches, by relating the issue to the dynamics of multi-dimensional maps. Two illustrative examples and their numerical simulations are given to show the effectiveness of the results. Based on the theoretical results, some strategies of impulsive culling are provided to eradicate the population of a pest species.

Ensuring successful introduction of Wolbachia in natural populations of Aedes aegypti by means of feedback control.

The control of the spread of dengue fever by introduction of the intracellular parasitic bacterium Wolbachia in populations of the vector Aedes aegypti, is presently one of the most promising tools for eliminating dengue, in the absence of an efficient vaccine. The success of this operation requires locally careful planning to determine the adequate number of individuals carrying the Wolbachia parasite that need to be introduced into the natural population. The introduced mosquitoes are expected to eventually replace the Wolbachia-free population and guarantee permanent protection against the transmission of dengue to human. In this study, we propose and analyze a model describing the fundamental aspects of the competition between mosquitoes carrying Wolbachia and mosquitoes free of the parasite. We then use feedback control techniques to devise an introduction protocol that is proved to guarantee that the population converges to a stable equilibrium where the totality of mosquitoes carry Wolbachia.

Hindrances to bistable front propagation: application to Wolbachia invasion.

We study the biological situation when an invading population propagates and replaces an existing population with different characteristics. For instance, this may occur in the presence of a vertically transmitted infection causing a cytoplasmic effect similar to the Allee effect (e.g. Wolbachia in Aedes mosquitoes): the invading dynamics we model is bistable. We aim at quantifying the propagules (what does it take for an invasion to start?) and the invasive power (how far can an invading front go, and what can stop it?). We rigorously show that a heterogeneous environment inducing a strong enough population gradient can stop an invading front, which will converge in this case to a stable front. We characterize the critical population jump, and also prove the existence of unstable fronts above the stable (blocking) fronts. Being above the maximal unstable front enables an invading front to clear the obstacle and propagate further. We are particularly interested in the case of artificial Wolbachia infection, used as a tool to fight arboviruses.

Wolbachia spreading dynamics in mosquitoes with imperfect maternal transmission.

Mosquitoes are primary vectors of life-threatening diseases such as dengue, malaria, and Zika. A new control method involves releasing mosquitoes carrying bacterium Wolbachia into the natural areas to infect wild mosquitoes and block disease transmission. In this work, we use differential equations to describe Wolbachia spreading dynamics, focusing on the poorly understood effect of imperfect maternal transmission. We establish two useful identities and employ them to prove that the system exhibits monomorphic, bistable, and polymorphic dynamics, and give sufficient and necessary conditions for each case. The results suggest that the largest maternal transmission leakage rate supporting Wolbachia spreading does not necessarily increase with the fitness of infected mosquitoes. The bistable dynamics is defined by the existence of two stable equilibria, whose basins of attraction are divided by the separatrix of a saddle point. By exploring the analytical property of the separatrix with some sharp estimates, we find that Wolbachia in a completely infected population could be wiped out ultimately if the initial population size is small. Surprisingly, when the infection shortens the lifespan of infected females that would impede Wolbachia spreading, such a reversion phenomenon does not occur.

Optimal control approach for establishing wMelPop Wolbachia infection among wild Aedes aegypti populations.

Wolbachia-based biocontrol has recently emerged as a potential method for prevention and control of dengue and other vector-borne diseases. Major vector species, such as Aedes aegypti females, when deliberately infected with Wolbachia become less capable of getting viral infections and transmitting the virus to human hosts. In this paper, we propose an explicit sex-structured population model that describes an interaction of uninfected (wild) male and female mosquitoes and those deliberately infected with wMelPop strain of Wolbachia in the same locality. This particular strain of Wolbachia is regarded as the best blocker of dengue and other arboviral infections. However, wMelPop strain of Wolbachia also causes the loss of individual fitness in Aedes aegypti mosquitoes. Our model allows for natural introduction of the decision (or control) variable, and we apply the optimal control approach to simulate wMelPop Wolbachia infestation of wild Aedes aegypti populations. The control action consists in continuous periodic releases of mosquitoes previously infected with wMelPop strain of Wolbachia in laboratory conditions. The ultimate purpose of control is to find a tradeoff between reaching the population replacement in minimum time and with minimum cost of the control effort. This approach also allows us to estimate the number of Wolbachia-carrying mosquitoes to be released in day-by-day control action. The proposed method of biological control is safe to human health, does not contaminate the environment, does not make harm to non-target species, and preserves their interaction with mosquitoes in the ecosystem.

Alternative stable states explain unpredictable biological control of Salvinia molesta in Kakadu.

Suppression of the invasive plant Salvinia molesta by the salvinia weevil is an iconic example of successful biological control. However, in the billabongs (oxbow lakes) of Kakadu National Park, Australia, control is fitful and incomplete. By fitting a process-based nonlinear model to thirteen-year data sets from four billabongs, here we show that incomplete control can be explained by alternative stable states--one state in which salvinia is suppressed and the other in which salvinia escapes weevil control. The shifts between states are associated with annual flooding events. In some years, high water flow reduces weevil populations, allowing the shift from a controlled to an uncontrolled state; in other years, benign conditions for weevils promote the return shift to the controlled state. In most described ecological examples, transitions between alternative stable states are relatively rare, facilitated by slow-moving environmental changes, such as accumulated nutrient loading or climate change. The billabongs of Kakadu give a different manifestation of alternative stable states that generate complex and seemingly unpredictable dynamics. Because shifts between alternative stable states are stochastic, they present a potential management strategy to maximize effective biological control: when the domain of attraction to the state of salvinia control is approached, augmentation of the weevil population or reduction of the salvinia biomass may allow the lower state to trap the system.

Optimal Culling and Biocontrol in a Predator-Prey Model.

Invasive species cause enormous problems in ecosystems around the world. Motivated by introduced feral cats that prey on bird populations and threaten to drive them extinct on remote oceanic islands, we formulate and analyze optimal control problems. Their novelty is that they involve both scalar and time-dependent controls. They represent different forms of control, namely the initial release of infected predators on the one hand and culling as well as trapping, infecting, and returning predators on the other hand. Combinations of different control methods have been proposed to complement their respective strengths in reducing predator numbers and thus protecting endangered prey. Here, we formulate and analyze an eco-epidemiological model, provide analytical results on the optimal control problem, and use a forward-backward sweep method for numerical simulations. By taking into account different ecological scenarios, initial conditions, and control durations, our model allows to gain insight how the different methods interact and in which cases they could be effective.

The Effect of Farmers' Decisions on Pest Control with Bt Crops: A Billion Dollar Game of Strategy.

A farmer's decision on whether to control a pest is usually based on the perceived threat of the pest locally and the guidance of commercial advisors. Therefore, farmers in a region are often influenced by similar circumstances, and this can create a coordinated response for pest control that is effective at a landscape scale. This coordinated response is not intentional, but is an emergent property of the system. We propose a framework for understanding the intrinsic feedback mechanisms between the actions of humans and the dynamics of pest populations and demonstrate this framework using the European corn borer, a serious pest in maize crops. We link a model of the European corn borer and a parasite in a landscape with a model that simulates the decisions of individual farmers on what type of maize to grow. Farmers chose whether to grow Bt-maize, which is toxic to the corn borer, or conventional maize for which the seed is cheaper. The problem is akin to the snow-drift problem in game theory; that is to say, if enough farmers choose to grow Bt maize then because the pest is suppressed an individual may benefit from growing conventional maize. We show that the communication network between farmers' and their perceptions of profit and loss affects landscape scale patterns in pest dynamics. We found that although adoption of Bt maize often brings increased financial returns, these rewards oscillate in response to the prevalence of pests.

On an integro-differential model for pest control in a heterogeneous environment.

Insect pests pose a major threat to a balanced ecology as it can threaten local species as well as spread human diseases; thus, making the study of pest control extremely important. In practice, the sterile insect release method (SIRM), where a sterile population is introduced into the wild population with the aim of significantly reducing the growth of the population, has been a popular technique used to control pest invasions. In this work we introduce an integro-differential equation to model the propagation of pests in a heterogeneous environment, where this environment is divided into three regions. In one region SIRM is not used making this environment conducive to propagation of the insects. A second region is the eradication zone where there is an intense release of sterile insects, leading to decay of the population in this region. In the final region we explore two scenarios. In the first case, there is a small release of sterile insects and we prove that if the eradication zone is sufficiently large the pests will not invade. In the second case, when SIRM is not used at all in this region we show that invasions always occur regardless of the size of the eradication zone. Finally, we consider the limiting equation of the integro-differential equation and prove that in this case there is a critical length of the eradication zone which separates propagation from obstruction. Moreover, we provide some upper and lower bound for the critical length.

Is more better? Higher sterilization of infected hosts need not result in reduced pest population size.

We analyze the effect of sterilization in the infected hosts in several epidemiological models involving infectious diseases that can be transmitted both vertically and horizontally. Sterilizing pathogens can be used as pest control agents by intentionally inoculating the target population, with the goal of reducing or eliminating it completely. Contrary to previous models that did not include vertical transmission we found that the population size at the endemic equilibrium may actually increase with higher levels of sterility. This effect is proved to exist for low to high efficiencies of vertical transmission. On the other hand, if the disease is sexually transmitted and the host reproduction and disease transmission are both consistently mediated by mating, we do not observe such a counter-intuitive effect and the population size in the stable endemic equilibrium is decreasing with higher levels of sterility. We suggest that models of the pest control techniques involving the release of sterilizing pathogens have to carefully consider the routes such pathogens use for transmission.

[The ecology of ticks, tick-borne diseases and biological tick control in Baden-Württemberg]. / Ökologie von Zecken als Überträger von Krankheitserregern in Baden-Württemberg und biologische Zeckenbekämpfung.

Ticks and tick-borne diseases are of great significance for the health of humans and animals. However, the factors influencing their distribution and dynamics are inadequately known. In a project financed by the Baden-Württemberg Ministry of the Environment, Climate and Energy Industry, as part of the program BWPLUS, interdisciplinary specialists work together to determine the influence of weather, (micro)climate, habitat, land use, human activities, and the population dynamics of host animals on the distribution and abundance of ticks and the diseases that they transmit in Baden-Württemberg. The project comprises four modules: the large-scale distribution of ticks in Baden-Württemberg (module 1), detailed studies of host-tick-pathogen interaction in relation to the microclimate (module 2), and the spatial occurrence of important tick-borne pathogens (module 3). The fourth module involves the comprehensive analysis and synthesis of all data in order to determine the relative importance of the factors studied and to develop a risk model. Recently, intensive investigations into tick control have been undertaken using various entomopathogenic fungi and nematodes as well as a parasitoid wasp. Our aim was to determine whether these natural enemies could be used to effectively reduce the number of free-living ticks.

Impact of biodiversity on tick-borne diseases.

It is a well-known fact that high biodiversity is related to the health and proper functioning of environment. Recently, the attempts to search the relations between biodiversity and human health are also undertaken. A number of studies demonstrate that people living in undegraded environment are less exposed to the diseases of affluence. However, they are at a higher risk of contracting zoonoses. It is believed that the higher the number of animals, the higher is the number of ticks. Consequently, there is a serious risk of borreliosis and other tick-borne diseases. Such assumption, however, may be erroneous. A number of studies suggest a decreasing prevalence of tick-borne disease pathogens in high-biodiversity areas. In this paper, a promising hypothesis explaining this relation is discussed.

Modelling the use of Wolbachia to control dengue fever transmission.

Experiments and field trials have shown that the intracellular bacterium Wolbachia may be introduced into populations of the mosquito Aedes aegypti, the primary vector for dengue fever. In the absence of Wolbachia, a mosquito acquiring the dengue virus from an infected human enters an exposed (infected but not infectious) period before becoming infectious itself. A Wolbachia-infected mosquito that acquires dengue (i) may have a reduced lifespan, so that it is less likely to survive the exposed period and become infectious, and (ii) may have a reduced ability to transmit dengue, even if it has survived the exposed period. Wolbachia introduction has therefore been suggested as a potential dengue control measure. We set up a mathematical model for the system to investigate this suggestion and to evaluate the desirable properties of the Wolbachia strain to be introduced. We show that Wolbachia has excellent potential for dengue control in areas where R 0 is not too large. However, if R 0 is large, Wolbachia strains that reduce but do not eliminate dengue transmission have little effect on endemic steady states or epidemic sizes. Unless control measures to reduce R 0 by reducing mosquito populations are also put in place, it may be worth the extra effort in such cases to introduce Wolbachia strains that eliminate dengue transmission completely.

Adaptive release of natural enemies in a pest-natural enemy system with pesticide resistance.

Integrated pest management options such as combining chemical and biological control are optimal for combating pesticide resistance, but pose questions if a pest is to be controlled to extinction. These questions include (i) what is the relationship between the evolution of pesticide resistance and the number of natural enemies released? (ii) How does the cumulative number of natural enemies dying affect the number of natural enemies to be released? To address these questions, we developed two novel pest-natural enemy interaction models incorporating the evolution of pesticide resistance. We investigated the number of natural enemies to be released when threshold conditions for the extinction of the pest population in two different control tactics are reached. Our results show that the number of natural enemies to be released to ensure pest eradication in the presence of increasing pesticide resistance can be determined analytically and depends on the cumulative number of dead natural enemies before the next scheduled release time.

Combined use of two biocontrol agents with different biocontrol mechanisms most likely results in less than expected efficacy in controlling foliar pathogens under fluctuating conditions: a modeling study.

Effective use of biocontrol agents (BCAs) is a potentially important component of sustainable agriculture; recently, there has been a trend for combined use of several BCAs, with an expectation of synergistic interactions among them. A previous numerical study suggested that, under homogenous conditions in which two BCAs occupied the same host tissue as the pathogen, combined use of two BCAs with different biocontrol mechanisms resulted, in most cases, in efficacies similar to using the more efficacious one alone; this result is consistent with published experimental results. The present study investigates whether combined use of a mycoparasitic and a competitive BCA leads to greater efficacy than that expected when the model is modified to allow for fluctuating temperature regimes and the effects of temperature on the pathogen and BCAs. Within the range of parameter values considered, combined use of two BCAs is shown to be less effective than that expected under the assumption of Bliss independence, and to result in a level of efficacy similar to that achieved by the more efficacious component used alone, indicating antagonistic interactions between the two BCAs. Nevertheless, combined use of two BCAs resulted in a slightly longer delay in epidemic development than did individual use of BCAs. Stochastic variability in simulated hourly temperatures did not result in a high level of variability in efficacy among replicates; nevertheless, the among-replicate variability appeared to be greater for the combined use of BCAs than for individual BCAs used alone. In contrast, there were greater effects of varying BCA-temperature relationships and application time (reflected in the temperature profile) on efficacy, suggesting the importance of characterizing the relationship between BCA activity and environmental conditions in future research.