A two-component model of host-parasitoid interactions: determination of the size of inundative releases of parasitoids in biological pest control

Risk Analysis Frameworks Used in Biological Control and Introduction of a Novel Bayesian Network Tool

Classical biological control, the introduction of natural enemies to new environments to control unwanted pests or weeds, is, despite numerous successful examples, associated with rising concerns about unwanted environmental impacts such as population decline of nontarget species. Recognition of these biosafety risks is globally increasing, and prerelease assessments of biological control agents (BCAs) have become more rigorous in many countries. We review the current approaches to risk assessment for BCAs as used in Australasia, Europe, and North America. Traditionally, these assessments focus on providing assurance about the specificity of a proposed BCA, generally via a list of suitable versus nonsuitable hosts determined through laboratory specificity tests (i.e., by determining the BCA's physiological host range). The outcome of interactions of proposed agents in the natural environment can differ from laboratory-based predictions. Potential nontarget host testing may be incomplete, additional ecological barriers under field conditions may limit encounters between BCA and nontargets or reduce attack levels, and BCAs could disperse to habitats beyond those used by the target species and adversely affect nontarget species. We advocate for the adoption of more comprehensive, ecologically-based, probabilistic risk assessment approaches to BCA introductions. An example is provided using a Bayesian network that can integrate information on probabilities and uncertainties of a BCA to spread and establish in new habitats, interact with nontarget species in these habitats, and eventually negatively impact the populations of these nontarget species. Our new model, Biocontrol Adverse Impact Probability Assessment, aims to be incorporated into a structured decision-making framework to support national regulatory authorities.

Considerations for Insect Learning in Integrated Pest Management

The past 100 yr have seen dramatic philosophical shifts in our approach to controlling or managing pest species. The introduction of integrated pest management in the 1970s resulted in the incorporation of biological and behavioral approaches to preserve ecosystems and reduce reliance on synthetic chemical pesticides. Increased understanding of the local ecosystem, including its structure and the biology of its species, can improve efficacy of integrated pest management strategies. Pest management strategies incorporating insect learning paradigms to control insect pests or to use insects to control other pests can mediate risk to nontarget insects, including pollinators. Although our understanding of insect learning is in its early stages, efforts to integrate insect learning into pest management strategies have been promising. Due to considerable differences in cognitive abilities among insect species, a case-by-case assessment is needed for each potential application of insect learning within a pest management strategy.

A Host-Parasitoid Model for Aspidiotus rigidus (Hemiptera: Diaspididae) and Comperiella calauanica (Hymenoptera: Encyrtidae)

The outbreak of the coconut scale insect Aspidiotus rigidus Reyne (Hemiptera: Encyrtidae) posed a serious threat to the coconut industry in the Philippines. In this article, we modeled the interaction between A. rigidus and its parasitoid Comperiella calauanica Barrion, Almarinez, Amalin (Hymenoptera: Encyrtidae) using a system of ordinary differential equations based on a Holling type III functional response. The equilibrium points were determined, and their local stability was examined. Numerical simulations showed that C. calauanica may control the population density of A. rigidus below the economic injury level.

Best Timing to Determine Field Parasitism by Released Diachasmimorpha longicaudata (Hymenoptera: Braconidae) Against Anastrepha (Diptera: Tephritidae) Pest Populations

Our objective was to determine the timing of the highest parasitic activity by released Diachasmimorpha longicaudata (Ashmead) (Hymenoptera: Braconidae) in areas with fruits of sour orange and hog plums infested by Anastrepha ludens (Loew) and Anastrepha obliqua (McQuart) (Diptera: Tephritidae), under shaded and sunny conditions. Percent parasitism along fruit sampling period was related to host availability, which was influenced by the fruit size rather than environmental conditions. The highest parasitism in sour orange was obtained just the first day after release, but in hog plums this was observed during the first 3 days without significant differences between them. The levels of fruit infestation and parasitism were higher in shaded trees in sour orange as in hog plums. The high availability of larvae and the small size of hog plums were decisive for obtaining high levels of parasitism and keeping parasitoids near the release points. By contrast, the size and thick rind of sour orange provided to the larvae a physical refuge that was associated with lower parasitism, causing that parasitoids spread out in search of hosts more accessible. In sour orange, parasitism was exclusively by D. longicaudata, while in hog plums, we additionally found the coexistence of four native parasitoid species. This information suggests that in sour orange, the sampling should be performed 1 day after release, while in hog plums, the samplings can be extended to within the first 3 days. Such sampling can serve to better estimate the effect of D. longicaudata releases against Anastrepha pest populations in different fruit types.

Modeling the Temperature- and Age-Dependent Survival, Development, and Oviposition Rates of Stable Flies (Stomoxys calcitrans) (Diptera: Muscidae)

Stable flies (Stomoxys calcitrans (L.)) can be a serious pest associated with cattle facilities. In Denmark, they occur most abundantly at organic farms, where they cannot be controlled by means of insecticides. On traditional farms, where chemical control is widely used, development of resistance is of increasing concern. Therefore, interest in biological control or other alternative methods has been growing during the recent years. In order to understand the complex relationships between a pest and its natural enemies in a variable environment, it is necessary to know how temperature affects the dynamics of the involved species. In this paper, we apply data derived from several existing sources to investigate the influence of temperature on development and survival of eggs, larvae, pupae, and adult stable flies, as well as on the fecundity of adult females. We demonstrate that the same modeling framework (called SANDY), previously applied to lifetable data of the pteromalid pupal parasitoid (Spalangia cameroni Perkins), a biological control agent used against stable flies, can also be used to model S. calcitrans. However, the predicted temperature responses depend on the data sources used to parameterize the model, which is reflected by differences in estimated population growth rates obtained from American and non-American studies. Elasticity analysis shows that growth rates are more sensitive to changes in viability, in particular of adult flies, than in fecundity, which may have implications for the management of stable fly populations.

A FOOD CHAIN SYSTEM WITH HOLLING IV FUNCTIONAL RESPONSES AND IMPULSIVE EFFECT

In the paper, according to biological and chemical control strategy for pest control, our main purpose is to construct a three trophic level food chain system with Holling IV functional responses and periodic constant impulsive effect concerning integrated pest management (IPM), and investigate the dynamic behaviors of this system. By using the Floquet theory and comparison theorem of impulsive differential equation and analytic method, we prove that there exists a globally asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value. Further, condition for permanence of the system is established. Finally, numerical simulation shows that there exists a stable positive periodic solution with a maximum value no larger than a given level.

GLOBAL ATTRACTIVITY OF A STAGE-STRUCTURE VARIABLE COEFFICIENTS PREDATOR-PREY SYSTEM WITH TIME DELAY AND IMPULSIVE PERTURBATIONS ON PREDATORS

In this work, we consider a delayed stage-structured variable coefficients predator-prey system with impulsive perturbations on predators. By using the discrete dynamical system determined by stroboscopic map and the standard comparison theorem, we obtain the sufficient conditions which guarantee the global attractivity of prey-extinction periodic solution of the investigated system. We also prove that all solutions of the system are uniformly ultimately bounded. Our results provide reliable tactic basis for the practical pest management.

Discrete-time host-parasitoid models with pest control

We propose a simple discrete-time host-parasitoid model to investigate the impact of external input of parasitoids upon the host-parasitoid interactions. It is proved that the input of the external parasitoids can eventually eliminate the host population if it is above a threshold and it also decreases the host population level in the unique interior equilibrium. It can simplify the host-parasitoid dynamics when the host population practices contest competition. We then consider a corresponding optimal control problem over a finite time period. We also derive an optimal control model using a chemical as a control for the hosts. Applying the forward-backward sweep method, we solve the optimal control problems numerically and compare the optimal host populations with the host populations when no control is applied. Our study concludes that applying a chemical to eliminate the hosts directly may be a more effective control strategy than using the parasitoids to indirectly suppress the hosts.

Evolutionary game dynamics with impulsive effects

The jumps in population size due to the occurrence of an unfavorable physical environment (e.g. the effects of periodic climate disaster on the population size), or due to the intrinsic physiological and reproductive mechanisms of the population (e.g. the seasonal reproduction of most animal populations), can be called impulsive perturbations. A two-phenotype evolutionary game dynamics with impulsive effects is investigated. The main goal is to show how the evolutionary game dynamics is affected by the impulsive perturbations. The results show that the impulsive perturbations not only result in periodic behavior, but also it is possible that an ESS strategy based on the traditional concept of evolutionary stability can be replaced successfully by a non-ESS strategy.

Multiple attractors of host-parasitoid models with integrated pest management strategies: eradication, persistence and outbreak

Host-parasitoid models including integrated pest management (IPM) interventions with impulsive effects at both fixed and unfixed times were analyzed with regard to host-eradication, host-parasitoid persistence and host-outbreak solutions. The host-eradication periodic solution with fixed moments is globally stable if the host's intrinsic growth rate is less than the summation of the mean host-killing rate and the mean parasitization rate during the impulsive period. Solutions for all three categories can coexist, with switch-like transitions among their attractors showing that varying dosages and frequencies of insecticide applications and the numbers of parasitoids released are crucial. Periodic solutions also exist for models with unfixed moments for which the maximum amplitude of the host is less than the economic threshold. The dosages and frequencies of IPM interventions for these solutions are much reduced in comparison with the pest-eradication periodic solution. Our results, which are robust to inclusion of stochastic effects and with a wide range of parameter values, confirm that IPM is more effective than any single control tactic.

Pest management through continuous and impulsive control strategies

In this paper, we propose two mathematical models concerning continuous and, respectively, impulsive pest control strategies. In the case in which a continuous control is used, it is shown that the model admits a globally asymptotically stable positive equilibrium under appropriate conditions which involve parameter estimations. As a result, the global asymptotic stability of the unique positive equilibrium is used to establish a procedure to maintain the pests at an acceptably low level in the long term. In the case in which an impulsive control is used, it is observed that there exists a globally asymptotically stable susceptible pest-eradication periodic solution on condition that the amount of infective pests released periodically is larger than some critical value. When the amount of infective pests released is less than this critical value, the system is shown to be permanent, which implies that the trivial susceptible pest-eradication solution loses its stability. Further, the existence of a nontrivial periodic solution is also studied by means of numerical simulation. Finally, the efficiency of continuous and impulsive control policies is compared.

Extinction and permanence of one-prey multi-predators of Holling type II function response system with impulsive biological control

In this paper, one investigates the dynamic behaviors of one-prey multi-predator model with Holling type II functional response by introducing impulsive biological control strategy (periodic releasing natural enemies at different fixed time). By using Floquet theorem and small amplitude perturbation method, it is proved that there exists an asymptotically stable pest-eradication periodic solution when the impulsive period is less than some critical value and permanence condition is established via the method of comparison involving multiple Liapunov functions. It is shown that multi-predator impulsive control strategy is more effective than the classical and single one.

State-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences

A state-dependent impulsive model is proposed for integrated pest management (IPM). IPM involves combining biological, mechanical, and chemical tactics to reduce pest numbers to tolerable levels after a pest population has reached its economic threshold (ET). The complete expression of an orbitally asymptotically stable periodic solution to the model with a maximum value no larger than the given ET is presented, the existence of which implies that pests can be controlled at or below their ET levels. We also prove that there is no periodic solution with order larger than or equal to three, except for one special case, by using the properties of the LambertW function and Poincare map. Moreover, we show that the existence of an order two periodic solution implies the existence of an order one periodic solution. Various positive invariant sets and attractors of this impulsive semi-dynamical system are described and discussed. In particular, several horseshoe-like attractors, whose interiors can simultaneously contain stable order 1 periodic solutions and order 2 periodic solutions, are found and the interior structure of the horseshoe-like attractors is discussed. Finally, the largest invariant set and the sufficient conditions which guarantee the global orbital and asymptotic stability of the order 1 periodic solution in the meaningful domain for the system are given using the Lyapunov function. Our results show that, in theory, a pest can be controlled such that its population size is no larger than its ET by applying effects impulsively once, twice, or at most, a finite number of times, or according to a periodic regime. Moreover, our theoretical work suggests how IPM strategies could be used to alter the levels of the ET in the farmers' favour.