Sigmoid growth and the assessment of hormesis: a case for caution

Recent advances in procedures for the analysis of sigmoid curves have provided some sensitive methods of detecting and evaluating hormesis in the growth responses of organisms exposed to a variety of stressors. Based on a reparameterized Richards process error model, these procedures allow the quantification and independent evaluation of the three major properties of a sigmoid growth curve: size: a measure of the asymptote approached by the growth process, rate: a measure of the approximate amount of time required to complete growth, and shape: a quantity which indicates the specific path or trajectory taken by the growth process to approach the asymptote within the time constraints of the growing period. When applied to growth data for cypress tree seedlings and two species of waterfowl exposed chronically to low levels of a variety of stressors, these analyses revealed that curve shape was more likely to change in response to stress than were either asymptotic size or growth rate. The types of changes observed suggested that growth size, rate and curve shape may respond independently and in some cases, in opposite directions. Thus, while one aspect of growth may change in a fashion suggestive of hormesis (e.g. larger asymptote or faster growth rate), other aspects of the same growth function may be changing in a way suggestive of a stress response. Thus, studies designed to reveal growth hormesis should be specific with respect to which particular mathematical model is chosen, as well as with respect to which aspect of the growth response is being considered.