On the thermodynamical and biological interpretation of the Gompertzian mortality rate distribution

Abstract

"Thermodynamical" foundations of a Gompertzian representation of mortality rate distribution vs. age are reviewed. The two fundamental assumptions of the original model (as developed by Strehler and Mildvan) are: (1) challenges that threaten the lives of organisms of a given species have an exponential distribution in harmfulness; and (2) vitality ("energetic" reserve to be used to counteract the challenges and restore proper function of the organism) declines linearly with age. It is proposed that the external environment should not only be characterized by a "temperature", but also by a "pressure" (related to the average time between successive hits). While recent progress of health sciences have essentially lowered the "temperature" factor, future progress might also lower the "pressure" factor. The effect of this would be to provide only a slight extension of observed longevity in humans. Internal cause(s) of ageing that lead to death are not specified in the model (except that they should be compatible with the linear decline in vitality). It is shown that death cannot be attributed to a slowing down of the recovery machinery that restores the organism's state following a challenge or a disease. A mechanism of this kind would instead lead to a gamma- (rather than a Gompertzian) distribution of ages at death, at great ages. Whatever the modalities of the challenges (they are, of course, not necessarily of a literally energetic nature), the model is shown to assume that death is linked to single, large amplitude challenges, rather than to the conjunction of independent, small amplitude damages. The concept of programmed longevity is proposed and integrated into the model. In this new model, Gompertzian distributions are characterized by the two parameters alpha (slope) and L (longevity) rather than by the two traditional parameters alpha and R0 (mortality rate at birth). This new presentation is more parsimonious than the original one, in that only alpha (not L) is temperature dependent. Models with fixed longevity automatically display a negative correlation between ln R0 and alpha, as was noted by Strehler and Mildvan. There exists a definite lag of time (of 23-29 years) between longevity and the most probable age at death. Assuming that the human species has a maximum programmed longevity of 120 years, this implies that the progress of health sciences will allow the present survival curve to evolve, not towards a rectangular shape as previously believed, but rather to a given limiting curve such as is depicted.