Toxicity models of pulsed copper exposure to Pimephales promelas and Daphnia magna

Semiempirical models are useful for interpreting the response of aquatic organisms to toxicants as a function of exposure concentration and duration. Most applications predict cumulative mortality at the end of the test for constant exposure concentrations. Summary measures, such as the median lethal concentration, are then estimated as a function of concentration. Real-world exposures are not constant. Effects may depend on pulse timing, and cumulative analysis based only on integrated exposure concentration is not sufficient to interpret results. We undertook a series of pulsed-exposure experiments using standard toxicological protocols and interpreted the results (mortality, biomass, and reproduction) using a dynamic generalization of a Mancini/Breck-type model that includes two compartments, one for internal concentration as a function of exposure and one for site-of-action concentration or accumulated damage as a function of the internal dose. At exposure concentrations near the effects level, the model explained approximately 50% of the variability in the observed time history of survival, 43% of the change in biomass, and 83% of the variability in net reproduction. Unexplained variability may result from differences in organism susceptibility, amplified by the effects of small sample sizes in standard tests. The results suggest that response is sensitive to prior conditions and that constant-exposure experiments can underestimate the risk from intermittent exposures to the same concentration. For pulsed exposures, neither the average nor the maximum concentration alone is an adequate index of risk, which depends on both the magnitude, duration, and timing of exposure pulses. Better understanding about the impacts of pulsed exposures will require use of experimental protocols with significantly greater numbers of replicates.