A nonlinear stochastic model for the dynamics of a population with either a continuous size structure or a discontinuous stage structure is formulated in the Eulerian formalism. It takes into account dispersion effects due to stochastic variability of the development process of the individuals. The discrete equations of the numerical approximation are derived, and an analysis of the existence and stability of the equilibrium states is performed. An application to a copepod population is illustrated; numerical results of Eulerian and Lagrangian models are compared.
International standards propose several methods for measuring thermal conductivity; however, they often require expensive experimental layouts and marginally consider the uncertainty in the estimation procedure. In this article, we propose a temperature transient method and a Bayesian procedure to estimate the thermal conductivity of a homogeneous mass, and to reproduce the entire temperature profile evolution over time by means of latent temperature data. To validate the approach, experiments are conducted giving heating and cooling cycles to a polymethyl methacrylate (PMMA) specimen. Results show the applicability of the proposed approach and good estimations.
Control interventions in sustainable pest management schemes are set according to the phenology and the population abundance of the pests. This information can be obtained using suitable mathematical models that describe the population dynamics based on individual life history responses to environmental conditions and resource availability. These responses are described by development, fecundity and survival rate functions, which can be estimated from laboratory experiments. If experimental data are not available, data on field population dynamics can be used for their estimation. This is the case of the extrinsic mortality term that appears in the mortality rate function due to biotic factors. We propose a Bayesian approach to estimate the probability density functions of the parameters in the extrinsic mortality rate function, starting from data on population abundance. The method investigates the time variability in the mortality parameters by comparing simulated and observed trajectories. The grape berry moth, a pest of great importance in European vineyards, has been considered as a case study. Simulated data have been considered to evaluate the convergence of the algorithm, while field data have been used to obtain estimates of the mortality for the grape berry moth.
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