Simplified models to analyse time- and dose-dependent responses of populations to toxicants

The basis of ecotoxicology lies currently in the dose–response of organisms to toxicants, as typically described by probit and logistic models. While recognising its merits, standard endpoints ignore the process of toxicity with time, and consequently our ability to predict direct toxic effects in environmental risk assessments is seriously curtailed. Although the response of toxicants with time has been studied before, its application in ecotoxicology remains underutilised. One reason is that no convincing mechanism has been proposed to explain the hyperbolic curves of such responses, whereas a variety of models have been used to describe them. The explanation of both time- and dose-dependent responses is found ultimately in the natural variability of receptor sites among individuals of populations exposed to a toxicant inhibitor with time. The process can be explained by the kinetics of inhibition, and is appropriately described by a simple mathematical expression like the Michaelis–Menten equation, though other asymptotic models (e.g. logistic model) can also be used. The advantage of the hyperbolic model is that median effect values (e.g. LC₅₀ for dose- and ET₅₀ for time-dependent responses) enable calculation of toxicity effects at any concentration level and/or time of exposure, thus making it especially attractive for risk assessment.