Post-Darwinian longevity

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Life lived and left: Carey’s equality

In a stationary population, age composition and the distribution of remaining lifespans are identical. This equivalence can be used to estimate age structure if information is available on time to death.age composition, age estimation, remaining lifespan

Dr. Väinö Kannisto

This reflexion is published in memory of Väinö Kannisto, who died unexpectedly on 16 February 2002.

Total daily change with age equals average lifetime change

In a stationary population, the change with age in some characteristic at a point in time, summed over all the individuals in the population, equals the change in this characteristic, from the start to the end of the lifetime of each individual, averaged over all lifetimes of the individuals in the cohort.e dagger, Gompertz mortality, life expectancy, measures of senescence, population dynamics, stationary population

Lifesaving, lifetimes and lifetables

Mortality change roils period rates. In the short term, conventional calculations of age-specific probabilities of death and life expectancy in the period immediately after the change depend on how many lives have been saved. In the long term, the probabilities and period life expectancy also depend on how long these lives have been saved. When mortality is changing, calculations of period life expectancy do not, except in special circumstances, measure the life expectancy of a cohort of newborns that hypothetically live all their lives under the new mortality regime.life expectancy, life tables

Life Expectancy at Current Rates vs. Current Conditions

Life expectancy is overestimated if mortality is declining and underestimated if mortality is increasing. This is the fundamental claim made by Bongaarts and Feeney (2002) in their article "How Long Do We Live?", where they base their claim on arguments about "tempo effects on mortality". This Reflexion explains why this claim is true in most heterogeneous populations. It suggests that demographers should be careful about distinguishing between life expectancy under current conditions, which is difficult and problematic to assess, and life expectancy at current rates, which can be estimated using standard methods. Finally, it speculates that there may be a deep connection between tempo and heterogeneity.frailty, heterogeneity, life expectancy, tempo effects

Association of late childbearing with healthy longevity among the oldest-old in China

Statistical analysis of a large and unique longitudinal data set demonstrates that late childbearing after age 35 or 40 is significantly associated with survival and healthy survival among very old Chinese women and men. The association is stronger in oldest-old women than men. The estimates are adjusted for a variety of confounding factors of demographic characteristics, family support, social connections, health practices, and health conditions. Further analysis based on an extension of the Fixed Attribute Dynamics method shows that late childbearing is positively associated with long-term survival and healthy survival from ages 80-85 to 90-95 and 100-105. This association exists among oldest-old women and men, but, again, the effects are substantially stronger in women than men. We discuss four possible factors which may explain why late childbearing affects healthy longevity at advanced ages: (1) social factors; (2) biological changes caused by late pregnancy and delivery; (3) genetic and other biological characteristics; and (4) selection.

Senescence vs. sustenance: evolutionary-demographic models of aging

Humans, and many other species, suffer senescence: mortality increases and fertility declines with adult age. Some species, however, enjoy sustenance: mortality and fertility remain constant. Here we develop simple but general evolutionary-demographic models to explain the conditions that favor senescence vs. sustenance. The models illustrate how mathematical demography can deepen understanding of the evolution of aging.

The relative tail of longevity and the mean remaining lifetime

Vaupel (1998) posed the provocative question, “When it comes to death, how do people and flies differ from Toyotas?†He suggested that as the force of natural selection diminishes with age, structural reliability concepts can be profitably used in mortality analysis. Vaupel (2003) went a step further, using simulations to investigate the impact of redundancy, repair capacity, and heterogeneity on the relative length of post-reproductive life spans, called relative tails of longevity. His 2003 paper showed that structural redundancy and the possibility of repair decrease the relative tail of longevity, whereas greater heterogeneity increases it. Here, we consider the problem in much greater generality and prove these results analytically. Structures with repairable and non-repairable components are considered. Heterogeneity is described by a frailty-type model and different definitions of the tail of longevity are discussed.frailty, heterogeneity, life expectancy, life span, mortality, mortality rate, tail of longevity