HYPOTHESES ON LONGEVITY HORMESIS 19impact of caloric restriction on linear Gompertz plots of male laboratory
rats.28 Note that a is reduced in the calorically restricted animals, without a
change in In Q0. This alteration of the linear Gompertz function is distinctly
different from that observed with longevity hormesis. Yet, both caloric
restriction and longevity hormesis enhance mean and median survival times.
It is therefore recommended that investigators not only report mean and/or
median survival times, but also provide survival/mortality data (preferably
in the form of Gompertz plots).
In order to illustrate how longevity hormesis and caloric restriction affect
the survivalship functions of linear Gompertz models, Figures 1.6 and 1.7
were constructed. In both figures, the control curves are identical, although
scales on the abscissa differ. For the linear Gompertz model, the survival-
ship function is the following:41
S(x) = exp -[(h(x)G/a) (e- - 1)] (17)where S(x) is fractional survival at time x, h(x)G is the hazard function at
zero-time, and the other terms have already been defined. Although this
equation was not explicitly used to construct the control animal survivalship
Figure 1.5. Gompertz plots illustrating the effect of caloric restriction on the Gompertz
function of laboratory rats (male Fischer 344 strain). The study commenced
utilizing 26- to 30-day old weanling rats. Time on the abscissa began at 6
weeks of age. The group 1 population consisted of 40 male animals who were
fed ad libitum. The group 2 population consisted of 40 male animals who
were fed at about 60% the mean caloric intake of population 1 until 18
months of age, and then maintained at their 18 month caloric intake until
death. To adjust for vitamin and mineral intake, the diet of group 2 animals
contained 1.53-fold more minerals and 1.66-fold more vitamins. The linear
Gompertz function (Equation 3) was fit to all data simultaneously (using
different values of a for different feeding regimens), employing weighted
least-squares regression analysis. For calorically restricted animals, note the
reduction in a (slope), with no alteration in the vulnerability parameter
(intercept). The original data came from Yu et al.82 Reprinted from Neafsey et
al.,28 p. 360, by permission of Marcel Dekker, Inc.