In the field of Plant Protection Products (PPP), the combination of multiple active ingredients is a common strategy to improve the efficacy against target species. However, these mixtures may expose non-target species to untested chemical combinations due to varied application and degradation pathways. Developing a method to predict the effects of such mixtures without extensive testing is crucial for enhancing risk assessment for non-target organisms. Toxicokinetic (TK) and toxicodynamic (TD) models currently provide predictive power for the toxicity of mixture over time, utilizing the concentration addition and independent action principles. However, their capacity to capture complex, non-linear interactions - such as synergistic and antagonistic effects - remains limited. To overcome these limitations, we introduce a new methodology that integrates TKTD models using Ordinary Differential Equations (ODE) with neural networks (NN), offering a robust framework for modeling complex substance interactions. The ODE component encodes fundamental biological principles that constrain the neural network to biologically plausible solutions. Bayesian inference further refines the model by addressing uncertainties in data, model parameters, and biological processes, while also allowing quantification of prediction uncertainty, highlighting gaps in experimental data that warrant further investigation. This hybrid model was evaluated across 99 acute toxicity studies that included various PPP mixtures, testing its ability to identify and forecast deviations from expected mixture behaviors. Our findings demonstrate that while simpler linear models provide a robust and parsimonious baseline for predicting additive mixture effects, the neural network component serves as a powerful tool for selectively identifying and forecasting significant non-linear deviations from these expectations. This dual approach clarifies the distinct roles of both simple and complex models, providing a more responsible framework to anticipate the combined effects of untested chemical mixtures and inform risk assessment practices.

UNLABELLED: Various mathematical models have been used to explore the dynamics of transposable elements (TEs) within their host genomes. However, numerous factors can influence their dynamics, and we know only little about the dynamics of TEs when they first began to invade populations. In addition, the influence of population structuring has only recently been investigated. Transposable Element Simulator Dynamics, a population genomics simulation environment, has therefore been developed to provide a simple tool for analyzing the dynamics of TEs in a community based on (i) various TE parameters, such as the transposition and excision rates, the recombination rate and the coefficient of selection against TE insertions; and (ii) population parameters, such as population size and migration rates. The simulations can be used to illustrate the dynamic fate of TEs in structured populations, can be extended by using more specific molecular or demographic models, and can be useful for teaching population genetics and genomics. AVAILABILITY: TESD is distributed under GPL from the Pôle Bioinformatique Lyonnais (PBIL) web server at http://pbil.univ-lyon1.fr/software/TESD