Mathematical models for the comprehension of chemical contamination into the hive

Honey bees are very sensitive organisms, and their vulnerability toward chemical pollution is a priority environmental issue. In this chapter, the importance and the fundamental of a mathematical model able to predict the fate of chemicals in the hive are described. The “hive model” presented here is able to consider different contamination pathways: from inside the hive via pesticide treatments against bee pests or from outside by means of the eventual contamination present in nectar, pollen, resin, water, air, or vegetation. The input parameters of the model are the physical-chemical properties of the compound and the major characteristics of the hive ecosystem, from which it calculates contamination residues in bee products (honey, pollen, royal jelly, wax, and propolis) over time. The model can be applied to all nonionic chemicals with a measurable vapor pressure (volatile or semivolatile compounds). The model was validated with contamination data in bees, wax, and honey following tau-fluvalinate application in two experimental hives. The comparison between measured and modeled data over a period of 6 months was very good. Even if more experimental data should be provided for a better calibration of the model, it seems to correctly quantify the main contamination pathways from outside and within the hive.