Abstract
The aim of this work is to propose methods to test mechanism of synergy of toxic agents in bees. A synergy between prochloraz, an imidazole fungicide, and deltamethrin, a pyrethroid insecticide, was demonstrated experimentally. The hypothesis is that prochloraz modifies the penetration or the metabolism of deltamethrin. This hypothesis is tested using a pharmacokinetic box model. A previous experimental work showed that bee instantaneous mortalities were higher, from the time t1 to the time t2 after spraying, in groups sprayed with deltamethrin at dose D0 in the presence of prochloraz (Δ+P) than in those sprayed with deltamethrin alone at a dose α time as high (αΔ). We postulate that accrued mortality is proportional to the cumulated internal deltamethrin (ID2). ID2 of treatment (Δ+P) had to be greater than ID2 of treatment (αΔ) during the period from t1 to t2 so that the hypothesis would be consistent with the experimental data. The limit, for which the hypothesis is conceivable, is the ID2(αΔ) = ID2(Δ+P) curve. We study, in particular, the asymptotic behaviour of the limit curve when different parameters of the kinetic model tend to 0 or ∞. These limits allow to verify quickly and easily whether a mechanism is conceivable or not As the limits are calculated with algebraic values, the test can be used for other synergies.
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