A model for predicting the phenology of Philaenus spumarius.

The design and implementation of Philaenus spumarius control strategies can take advantage of properly calibrated models describing and predicting the phenology of vector populations in agroecosystems. We developed a temperature-driven physiological-based model based on the system of Kolmogorov partial differential equations to predict the phenological dynamics of P. spumarius. The model considers the initial physiological age distribution of eggs, the diapause termination process, and the development rate functions of post-diapausing eggs and nymphal stages, estimated from data collected in laboratory experiments and field surveys in Italy. The temperature threshold and cumulative degree days for egg diapause termination were estimated as 6.5 °C and 120 DD, respectively. Preimaginal development rate functions exhibited lower thresholds ranging between 2.1 and 5.0 °C, optimal temperatures between 26.6 and 28.3 °C, and upper threshold between 33.0 and 35 °C. The model correctly simulates the emergence of the 3rd, 4th, and 5th nymphal instars, key stages to target monitoring actions and control measures against P. spumarius. Precision in simulating the phenology of the 1st and 2nd nymphal stages was less satisfactory. The model is a useful rational decision tool to support scheduling monitoring and control actions against the late and most important nymphal stages of P. spumarius.

Conservation of Forces and Total Work at the Interface Using the Internodes Method.

The Internodes method is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into disjoint subdomains. In this paper we are interested in measuring how much the Internodes method is conservative across the interface. If hp-fem discretizations are employed, we prove that both the total force and total work generated by the numerical solution at the interface of the decomposition vanish in an optimal way when the mesh size tends to zero, i.e., like O ( h p ) , where p is the local polynomial degree and h the mesh-size. This is the same as the error decay in the H 1-broken norm. We observe that the conservation properties of a method are intrinsic to the method itself because they depend on the way the interface conditions are enforced rather then on the problem we are called to approximate. For this reason, in this paper, we focus on second-order elliptic PDEs, although we use the terminology (of forces and works) proper of linear elasticity. Two and three dimensional numerical experiments corroborate the theoretical findings, also by comparing Internodes with Mortar and WACA methods.

A nonlinear model for stage-structured population dynamics with nonlocal density-dependent regulation: An application to the fall armyworm moth.

The assessment and the management of the risks linked to insect pests can be supported by the use of physiologically-based demographic models. These models are useful in population ecology to simulate the dynamics of stage-structured populations, by means of functions (e.g., development, mortality and fecundity rate functions) realistically representing the nonlinear individuals physiological responses to environmental forcing variables. Since density-dependent responses are important regulating factors in population dynamics, we propose a nonlinear physiologically-based Kolmogorov model describing the dynamics of a stage-structured population in which a time-dependent mortality rate is coupled with a nonlocal density-dependent term. We prove existence and uniqueness of the solution for this resulting highly nonlinear partial differential equation. Then, the equation is discretized by finite volumes in space and semi-implicit backward Euler scheme in time. The model is applied for simulating the population dynamics of the fall armyworm moth (Spodoptera frugiperda), a highly invasive pest threatening agriculture worldwide.