On invariant property in population statistics

Concept of aging is developed to yield a relationship between life spans and the velocity of aging. The mathematical analysis shows that the mean extent of the advancement of aging throughout one’s life is conserved, or equivalently, the product of the mean life span, T, and the mean rate of aging, , is constant, . The result is in harmony with our experiences: it accounts for the unlimited replicability of tumor cells, and predicts the prolonged life spans of hibernating hamsters according to the equation, (T_χ=0 is a constant and χ denotes the total fraction of hibernation periods), in accordance with the Lyman and co-workers experiment. Comparing the present result and the empirical relationship between life spans of various mammals and basal metabolic rates, it is suggested that the mean rate of aging is intimately connected with the mean basal metabolic rate. With the help of this information, we inquire the reason of the difference in mean life spans between women and men, the result showing that the relative mean life span of women to men is T_women/T_men ≅ 1.08 for various nations, which is close to the corresponding relative value of the basal metabolic rate. The present analysis suggests, however, that this relationship between life spans and basal metabolic rates must be treated with caution.