A generalized risk assessment index for forecasting insect population under the effect of temperature.

Life history traits have been studied under various environmental factors, but the ability to combine them into a simple function to assess pest response to climate is still lacking complete understanding. This study proposed a risk index derived by combining development, mortality, and fertility rates from a stage-structured dynamic mathematical model. The first part presents the theoretical framework behind the risk index. The second part of the study is concerned with the application of the index in two case studies of major economic pest: the brown planthopper (Nilaparvata lugens) and the spotted wing drosophila (Drosophila suzukii), pests of rice crops and soft fruits, respectively. The mathematical calculations provided a single function composed of the main thermal biodemographic rates. This function has a threshold value that determines the possibility of population increase as a function of temperature. The tests carried out on the two pest species showed the capability of the index to describe the range of favourable conditions. With this approach, we were able to identify areas where pests are tolerant to climatic conditions and to project them on a geospatial risk map. The theoretical background developed here provided a tool for understanding the biogeography of Nilaparvata lugens and Drosophila suzukii. It is flexible enough to deal with mathematically simple (N. lugens) and complex (D. Suzukii) case studies of crop insect pests. It produces biologically sound indices that behave like thermal performance curves. These theoretical results also provide a reasonable basis for addressing the challenge of pest management in the context of seasonal weather variations and climate change. This may help to improve monitoring and design management strategies to limit the spread of pests in invaded areas, as some non-invaded areas may be suitable for the species to develop.

Understanding biological control with entomopathogenic fungi-Insights from a stochastic pest-pathogen model.

In this study, an individual-based model is proposed to investigate the effect of demographic stochasticity on biological control using entomopathogenic fungi. The model is formulated as a continuous time Markov process, which is then decomposed into a deterministic dynamics using stochastic corrections and system size expansion. The stability and bifurcation analysis shows that the system dynamic is strongly affected by the contagion rate and the basic reproduction number. However, sensitivity analysis of the extinction probability shows that the persistence of a biological control agent depends to the proportion of spores collected from insect cadavers as well as their ability to be reactivated and infect insects. When considering the migration of each species within a set of patches, the dispersion relation shows a Hopf-damped Turing mode for a threshold contagion rate. A large size population led to a spatial and temporal resonant stochasticity and also induces an amplification effect on power spectrum density.

Theoretical analysis of spatial nonhomogeneous patterns of entomopathogenic fungi growth on insect pest.

This paper presents the study of the dynamics of intrahost (insect pests)-pathogen [entomopathogenic fungi (EPF)] interactions. The interaction between the resources from the insect pest and the mycelia of EPF is represented by the Holling and Powell type II functional responses. Because the EPF's growth is related to the instability of the steady state solution of our system, particular attention is given to the stability analysis of this steady state. Initially, the stability of the steady state is investigated without taking into account diffusion and by considering the behavior of the system around its equilibrium states. In addition, considering small perturbation of the stable singular point due to nonlinear diffusion, the conditions for Turing instability occurrence are deduced. It is observed that the absence of the regeneration feature of insect resources prevents the occurrence of such phenomena. The long time evolution of our system enables us to observe both spot and stripe patterns. Moreover, when the diffusion of mycelia is slightly modulated by a weak periodic perturbation, the Floquet theory and numerical simulations allow us to derive the conditions in which diffusion driven instabilities can occur. The relevance of the obtained results is further discussed in the perspective of biological insect pest control.

Using coupling imperfection to control amplitude death.

Previous studies of nonlinear oscillator networks have shown that amplitude death (AD) occurs after tuning oscillator parameters and coupling properties. Here, we identify regimes where the opposite occurs and show that a local defect (or impurity) in network connectivity leads to AD suppression in situations where identically coupled oscillators cannot. The critical impurity strength value leading to oscillation restoration is an explicit function of network size and system parameters. In contrast to homogeneous coupling, network size plays a crucial role in reducing this critical value. This behavior can be traced back to the steady-state destabilization through a Hopf's bifurcation, which occurs for impurity strengths below this threshold. This effect is illustrated across different mean-field coupled networks and is supported by simulations and theoretical analysis. Since local inhomogeneities are ubiquitous and often unavoidable, such imperfections can be an unexpected source of oscillation control.