Quantifying the shape of aging

Abstract

In Biodemography, aging is typically measured and compared based on aging rates. We argue that this approach may be misleading, because it confounds the time aspect with the mere change aspect of aging. To disentangle these aspects, here we utilize a time-standardized framework and, instead of aging rates, suggest the shape of aging as a novel and valuable alternative concept for comparative aging research. The concept of shape captures the direction and degree of change in the force of mortality over age, which—on a demographic level—reflects aging. We 1) provide a list of shape properties that are desirable from a theoretical perspective, 2) suggest several demographically meaningful and non-parametric candidate measures to quantify shape, and 3) evaluate performance of these measures based on the list of properties as well as based on an illustrative analysis of a simple dataset. The shape measures suggested here aim to provide a general means to classify aging patterns independent of any particular mortality model and independent of any species-specific time-scale. Thereby they support systematic comparative aging research across different species or between populations of the same species under different conditions and constitute an extension of the toolbox available to comparative research in Biodemography.

Fig 1. Comparison of rankings as provided by the different shape measures.

For the ten populations used in [19] (HG stands for hunter-gatherers, ChimpW for wild chimpanzees, ChimpC for captive chimpanzees), the ranking of shape values (from lowest to highest value) is similar for all of the shape measures S ₁–S ₇.

Fig 2. The effect of pace standardization on age-specific hazard can reverse conclusions.

Gompertz mortality μ(x) = ae ^0.1x with a = 0.00001 (black line) and a = 0.001 (red line). Left: unstandardized perspective. Right: standardized perspective. The intensity of the colors is proportional to the value of the respective survival function. If the strength of aging is measured by how steeply age-specific hazard increases over life, the unstandardized perspective implies that the population with a = 10⁻³ experiences stronger aging than the population with a = 10⁻⁵; however, if the difference in life span is accounted for, i.e., if the hazard curves are standardized, the conclusion is reversed.

Fig 3. Species in pace-shape space.

Pace values (as measured by life expectancy e ₀) on the x-axis versus shape values (as measured by S ₇) on the y-axis for ten populations taken from [19] (HG stands for hunter-gatherers, ChimpW for wild chimpanzees, ChimpC for captive chimpanzees).