|SREL Reprint #1135|
Sigmoid Growth and the
Assessment of Hormesis: A Case for
Lehr Brisbin, Jr., Kenneth W. McLeod and Gary C. White
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: (1)
size: a measure of the asymptote approached by the growth process, (2) rate:
a measure of the approximate amount of time required to complete growth,
and (3) 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.
SREL Reprint #1135
Brisbin, I.L., Jr., K.W. McLeod, and G.C. White. 1987.
Sigmoid growth and the assessment of hormesis: A case for
caution. Health Physics 52:553-559.