Does Makeham make sense?

Abstract

Numerical modeling was used to explore the behavior of ideal cohorts obeying the Gompertz-Makeham (GM) law of mortality (-dn/dt 1/n(t) = C + lambda egammat) supplemented with the Strehler-Mildvan (SM) correlation (ln lambda = A - Bgamma) and to show how changes in the age-independent parameter C will produce an apparent SM correlation if C is ignored in mortality data treatment as in the case of the so-called longitudinal gompertzian analysis of historical changes in human mortality patterns. The essential difference between the Makeham term C and Gompertz term lambda e(gammat) has been suggested to be not that the latter is age-dependent whereas the former is not, but that C comprises the contributions of inherently irresistible stresses to mortality, whereas lambda e(gammat) comprises the contributions of resistible stresses and shows how changes in the resistance to them are translated into changes in mortality. This assumption was used to show by modeling how the transition of stresses from irresistible to resistible may result in decreased late survivorship as the cost of increased early survivorship, in line with the antagonistic pleiotropy theory of aging. On the whole, the modeling suggests that the GM equation is not only a mathematical tool for treatment of mortality data but that it also has a fundamental biological significance, and its Makeham term C should not be ignored in any analysis of mortality data.