A spread in the longevity of similar individuals is a feature of any collection of demographic data. Are these variations simply random, a matter of luck and happenstance, or do they reflect underlying genetic or environment differences that are presently only poorly understood, absent in the data recorded for each individual? In other words, how much of natural variation in human longevity has been explained by the research community, and its causes identified, at least to a first approximation? Are there significant differences between individuals yet to be understood? It is possible to use statistical techniques to identify the relative contributions of distinct classes of influence on these variations in longevity, and here, researchers replicate past findings by showing that hidden differences between individuals likely account for little of the observed variation in human longevity. This suggests that there are probably no very large surprises ahead of us when it comes to understanding influences on aging in our species.
Individual variance, especially in fitness components, plays a key role in demography, ecology, and evolutionary biology. From an evolutionary perspective, variance in fitness components is potential material on which natural selection can operate. Longevity (age at death) is a fitness component that varies widely among individuals. This variance arises as a result of two different underlying causes: individual stochasticity and heterogeneity.
Individual stochasticity is variance due to random outcomes of probabilistic demographic processes (living or dying, reproducing or not, making or not making a life cycle transition). Even in a completely homogeneous population, in which every individual experienced exactly the same (age-specific) mortality rates, variance due to individual stochasticity would exist. Any calculation of the variance in longevity from an ordinary life table implicitly assumes that every individual is subject to the (age-specific) mortality rates in that life table, and hence that the variance is only due to individual stochasticity.
Variance in longevity can also result from unobserved, or latent, heterogeneity in the properties of individuals. For example, individuals of the same age may differ in their mortality rates due to genetic, environmental, or maternal effects. Such differences are often referred to as heterogeneity in individual frailty. Because more frail individuals are more at risk than others, heterogeneity in frailty leads to changes in cohort composition with age, due to within-cohort selection. As a cohort ages, the representation of less frail individuals increases, and the average mortality rate in an old cohort will be lower than one would expect based on extrapolation of mortality rates at younger ages. This selection effect has been suggested as an explanation for the mortality plateaus often observed at very old ages.
The effects of unobserved heterogeneity in survival analysis can be estimated using frailty models. In frailty models, a baseline mortality schedule is modified by a term representing individual frailty. The variance in longevity in a frailty model is a result of both stochasticity and heterogeneity. Little is known about the relative contribution of each to the total variance in longevity, and how those contributions may depend on species, sex, environmental conditions, etc. Other researchers have presented an ad hoc approach to this problem: the relative contributions of heterogeneity and stochasticity were estimated by reducing the initial variance in frailty to zero and attributing the remaining longevity variance to stochasticity. In an analysis of Swedish females, the fraction of variance due to heterogeneity was estimated to be only 0.071. Applying the same approach to a model for women from Turin resulted in an even lower estimate of 0.012.
Here, we present a more rigorous model. The variance due to individual stochasticity can be calculated from a Markov chain description of the life cycle. The variance due to heterogeneity can be calculated from a multistate model that incorporates the heterogeneity. We show how to use this approach to decompose the variance in longevity into contributions from stochasticity and heterogeneous frailty for male and female cohorts from Sweden (1751-1899), France (1816-1903), and Italy (1872-1899), and also for a selection of period data for the same countries. The results were consistent between countries and sexes: most of this variance in remaining longevity is due to stochasticity. Only a small fraction is attributable to heterogeneity. This fraction increases with starting age, because stochasticity-induced variance decreases faster with age than does heterogeneity-induced variance. However, even conditioning on survival to a starting age of 70 years, the average fraction due to heterogeneity is less than 0.10 (for cohort mortality) or 0.15 (for period mortality). Although data quality is, for obvious reasons, better for later cohorts and periods than for earlier ones, we found no clear temporal patterns in the fraction of variance due to heterogeneity.