Brisbin I L, McLeod K W, White G C
Health Phys. 1987 May;52(5):553-9. doi: 10.1097/00004032-198705000-00005.
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.
近期在S形曲线分析方法上的进展，提供了一些灵敏的方法，用于检测和评估暴露于各种应激源的生物体生长反应中的兴奋效应。基于重新参数化的理查兹过程误差模型，这些方法能够对S形生长曲线的三个主要特性进行量化和独立评估：大小：衡量生长过程所趋近的渐近线的指标；速率：衡量完成生长所需的大致时间量的指标；形状：表示生长过程在生长期的时间限制内趋近渐近线所采取的特定路径或轨迹的量。当将这些分析应用于柏树幼苗以及长期暴露于各种低水平应激源的两种水禽的生长数据时，结果显示，与渐近大小或生长速率相比，曲线形状对压力的反应更有可能发生变化。观察到的变化类型表明，生长大小、速率和曲线形状可能会独立反应，在某些情况下，反应方向相反。因此，虽然生长的一个方面可能以暗示兴奋效应的方式发生变化（例如，更大的渐近线或更快的生长速率），但同一生长函数的其他方面可能以暗示应激反应的方式发生变化。因此，旨在揭示生长兴奋效应的研究，在选择特定的数学模型以及考虑生长反应的哪个方面时，都应该具体明确。
