Improved empirical models describing hormesis

During the past two decades, the phenomenon of hormesis has gained increased recognition. To promote research in hormesis, a sound statistical quantification of important parameters, such as the level and significance of the increase in response and the range of concentration where it occurs, is strongly needed. Here, we present an improved statistical model to describe hormetic dose-response curves and test for the presence of hormesis. Using the delta method and freely available software, any percentage effect dose or concentration can be derived with its associated standard errors. Likewise, the maximal response can be extracted and the growth stimulation calculated. The new model was tested on macrophyte data from multiple-species experiments and on laboratory data of Lemna minor. For the 51 curves tested, significant hormesis was detected in 18 curves, and for another 17 curves, the hormesis model described that data better than the logistic model did. The increase in response ranged from 5 to 109%. The growth stimulation occurred at an average dose somewhere between zero and concentrations corresponding to approximately 20 to 25% of the median effective concentration (EC50). Testing the same data with the hormesis model proposed by Brain and Cousens in 1989, we found no significant hormesis. Consequently, the new model is shown to be far more robust than previous models, both in terms of variation in data and in terms of describing hormetic effects ranging from small effects of a 10% increase in response up to effects of an almost 100% increase in response.