Adaptive iterative design (AID): a novel approach for evaluating the interactive effects of multiple stressors on aquatic organisms.

The study of stressor interactions by eco-toxicologists using nonlinear response variables is limited by required amounts of a priori knowledge, complexity of experimental designs, the use of linear models, and the lack of use of optimal designs of nonlinear models to characterize complex interactions. Therefore, we developed AID, an adaptive-iterative design for eco-toxicologist to more accurately and efficiently examine complex multiple stressor interactions. AID incorporates the power of the general linear model and A-optimal criteria with an iterative process that: 1) minimizes the required amount of a priori knowledge, 2) simplifies the experimental design, and 3) quantifies both individual and interactive effects. Once a stable model is determined, the best fit model is identified and the direction and magnitude of stressors, individually and all combinations (including complex interactions) are quantified. To validate AID, we selected five commonly co-occurring components of polluted aquatic systems, three metal stressors (Cd, Zn, As) and two water chemistry parameters (pH, hardness) to be tested using standard acute toxicity tests in which Daphnia mortality is the (nonlinear) response variable. We found after the initial data input of experimental data, although literature values (e.g. EC-values) may also be used, and after only two iterations of AID, our dose response model was stable. The model ln(Cd)*ln(Zn) was determined the best predictor of Daphnia mortality response to the combined effects of Cd, Zn, As, pH, and hardness. This model was then used to accurately identify and quantify the strength of both greater- (e.g. As*Cd) and less-than additive interactions (e.g. Cd*Zn). Interestingly, our study found only binary interactions significant, not higher order interactions. We conclude that AID is more efficient and effective at assessing multiple stressor interactions than current methods. Other applications, including life-history endpoints commonly used by regulators, could benefit from AID's efficiency in assessing water quality criteria.