A 2D analysis of correlations between the parameters of the Gompertz-Makeham model (or law?) of relationships between aging, mortality, and longevity

Abstract

When mortality (μ), aging rate (γ) and age (t) are treated according to the Gompertz model μ(t) = μ₀e^γt (GM), any mean age corresponds to a manifold of paired reciprocally changing μ₀ and γ. Therefore, any noisiness of data used to derive GM parameters makes them negatively correlated. Besides this artifactual factor of the Strehler-Mildvan correlation (SMC), other factors emerge when the age-independent mortality C modifies survival according to the Gompertz-Makeham model μ(t) = C+μ₀e^γt (GMM), or body resources are partitioned between survival and protection from aging [the compensation effect of mortality (CEM)]. Theoretical curves in (γ, logμ₀) coordinates show how μ₀ decreases when γ increases upon a constant mean age. Within a species-specific range of γ, such "isoage" curves look as nearly parallel straight lines. The slopes of lines constructed by applying GM to survival curves modeled according to GMM upon changes in C are greater than the isoage slopes. When CEM is modeled, the slopes are still greater. Based on these observations, CEM is shown to contribute to SMC associated with sex differences in lifespan, with the effects of several life-extending drugs, and with recent trends in survival/mortality patterns in high-life-expectancy countries; whereas changes in C underlie differences between even high-life-expectancy countries, not only between high- and low-life-expectancy countries. Such interpretations make sense only if GM is not merely a statistical model, but rather reflects biological realities. Therefore, GM is discussed as derivable by applying certain constraints to a natural law termed the generalized Gompertz-Makeham law.

Keywords: Aging; Gompertz–Makeham law; Lifespan; Mortality; Parametric analysis; Strehler–Mildvan correlation; Survival.