The Pull of the Plateau and the Sway of the Mode: Formal Relationships to Estimate the Pace of Senescence

BACKGROUND How rapidly does the risk of death due to old age rise with age? It has been hypothesized that this pace of senescence is constant over age, time, and place for every human, today and in the past. Attempts to empirically test this superficially preposterous theory have not been successful—the theory has not yet been proven or disproven. OBJECTIVE Take advantage of theory about heterogeneous populations, and in particular the gamma-Gompertz model, and the knowledge that death rates approach a plateau to develop formal relationships that can be used to estimate the pace of senescence, i.e., the rate of mortality increase with age for individuals because of deterioration with age, and also to estimate how disparate the risk of senescent death is for individuals of the same age. RESULTS Proofs are given for new formal relationships that depend on the level of the mortality plateau, the modal age of death or both. These equations hinge on—and might be useful in testing—the hypothesis that senescent mortality can be described by a gamma-Gompertz model. CONTRIBUTION Discovering that there is (1) an invariant pace of senescence for individuals and (2) an invariant distribution of relative risk of senescent death across individuals—for all humans (and perhaps for some other species)—would be of fundamental physiological, evolutionary, and demographic significance. The formal relationships presented here may further empirical research to find such physiological invariants—or to disprove their existence.