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

Abstract

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. LC(50) for dose- and ET(50) 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.

From simple toxicological models to prediction of toxic effects in time

“…Table 5 shows the LC 50 s reported for the two neonicotinoids tested on these species of aquatic organisms. The corresponding predicted values were estimated using the hyperbolic model of Sánchez-Bayo and Goka (2007). A regression line on their transformed logarithms indicates a very good fit between the two sets of data (r 2 = 0.97), which can also be seen graphically in Fig.…”

“…4 Validation of the relationship between concentration and time to 50% mortality described in this paper. Predicted LC 50 values were obtained from their corresponding times to mortality using the hyperbolic model (Sánchez-Bayo and Goka 2007) predictions for the time series. Now, let's also imagine that the same toxicant was found in certain environmental waters at different concentrations (C 4 ) from the ones tested, so the hyperbolic model would be unable to predict the effects of C 4 .…”

“…The results show the cumulative effect of the toxicant over time, which follow first order kinetics. Mortality of the cladocerans at each of the five concentrations tested was recorded at several intervals during the entire experimental period, and the corresponding ET 50 s were calculated based on the published raw data, and were also reported in our previous paper (Sánchez-Bayo and Goka 2007).…”

“…The data was pooled from three different bioassays, which involved four replicates for each of the concentrations tested in accordance with standard guidelines for cladocerans (OECD 1993). The conditions of the assays are described in Sánchez-Bayo and Goka (2006), and the original data set and calculated ET 50 s were reported in Sánchez- Bayo and Goka (2007). The same experimental conditions were used with toxicity tests of D. magna cultures exposed to gradient concentrations of imidacloprid, but in this case post-exposures from 4 to 10 days were used.…”

Ecological risk assessment of PCBs and other organic contaminant residues in Laguna de Terminos, Mexico

“…Chronic exposure to very low concentrations of residues may still cause subtle sub-lethal toxic effects. However, modelling attempts to predict these effects are still in development (Sanchez-Bayo and Goka 2007). At the present time, it seems that the load of residues in water and sediments of Laguna de Terminos are well under concentration values at which serious acute toxic effects and even chronic effects would be observed in the aquatic fauna and, thus, on a one-by-one basis seem sufficiently low to not put ecosystem integrity and functioning at risk.…”