Invariances in relations between aging, exposure to external hazards, and mortality reflected in life table aging rate (LAR) patterns examined through the lens of generalized Gompertz-Makeham law.

According to the Gompertz law, the age-dependent change in the logarithm of mortality (life-table aging rate, LAR) is equal to the population-averaged age-independent biological aging rate (γ), and LAR would be constant if aging were the only cause of mortality increase. However, LAR is influenced by population exposures to the external hazards. If they were constant, according to the Gompertz-Makeham law (GML), LAR would be below γ at lower ages and asymptotically and monotonically approach γ with increasing age. Actually, LAR trajectories derived from data on mortality in different countries and historical periods feature systematic undulations. In the present investigation, mortality-vs.-age trajectories were modeled based on a generalized GML (gGML). Unlike the canonical GML terms, which are population-specific constants, the respective terms of the gGML are represented with some population-specific functions of age. Invariant in gGML are the modes of translation of these functions into the dependency of mortality on age: linear for population exposure to the irresistible external hazards or exponential for population-averaged ability to withstand the resistible external and internal hazards. Modeling suggests that, at earlier ages, LAR undulations are attributable to changes in population exposures to the former hazards. However, only their unrealistically high levels can produce the transient increase in LAR at about 65 to 90 years. This pervasive undulation of LAR-vs.-age trajectory is rather caused by an increment in γ. Reasons to regard gGML as a genuine natural law, which defines relations between mortality, aging and environment, are discussed.