The Deviant Dynamics of Death in Heterogeneous Populations

Abstract

FOREWORDLow fertility levels in IIASA countries are creating aging populations whose demands for health care and income maintenance (social security) will increase to unprecedented levels, thereby calling forth policies that will seek to promote increased family care and worklife flexibility. The Population Program is examining current patterns of population aging and changing lifestyles in llASA countries, projecting the needs for health and income support that such patterns are likely to generate during the next several decades, and considering alternative family and employment policies that might reduce the social costs of meeting these needs.The program is seeking to develop a better understanding of how low fertility and mortality combine to create aging populations, with high demands for health and income maintenance, and reduced family support systems that can provide that maintenance. The research will produce analyses of current demographic patterns in llASA countries together with an assessment of their probable future societal consequences and impacts on the aging. It will consider the position of the elderly within changing family structures, review national policies that seek to promote an enlarged role for family care, and examine the costs and benefits of alternative systems for promoting worklife flexibility by transferring income between different periods of life.In this report, James Vaupel (USA) and Anatoli Yashin (USSR) examine the impacts of heterogeneity on populations whose members are gradually making some major transition. Their focus is on human mortality, but the mathematics they develop is relevant to studies of, for example, migration, morbidity, marriage, criminal recidivism, drug addiction, and the reliability of equipment. The authors show that the observed dynamics of the surviving population -the population that has not yet made the transition -will systematically deviate from the dynamics of the behavior of any of the individuals that make up the aggregate population. Furthermore, they develop methods for uncovering the underlying dynamics of individual behavior, given observations of population behavior. These methods will be useful in explaining and predicting demographic patterns. In addition, because the impact of a policy intervention can sometimes only be correctly predicted if the varying responses of different kinds of individuals are taken into account, the methods should prove to be of value to policy analysts.

Exogenous determinants of early-life conditions, and mortality later in life

“…At the same time, one may argue that selection on survival until age 36 may lead to biased estimates of the effects of early life conditions (see e.g. Vaupel & Yashin, 1985, for details). But any selection most likely produces a selection of childhood survivors with favorable characteristics among those born in a bad year.…”

Variable fitness effects of Wolbachia infection in Drosophila melanogaster

“…Four mortality models were considered (Vaupel and Yashin, 1985). The Gompertz (G) model describes an exponential increase in mortality rate with age and is given by…”

Inequality in individual mortality and economic conditions earlier in life

“…Unobserved heterogeneity poses an additional problem if the current individual hazard rate is allowed to depend on the value of an explanatory variable at a point of time in the past but after the beginning of the spell; in our case the cyclical indicator during early childhood years (see e.g. Vaupel and Yashin, 1985). Basically, bad childhood years may give rise to selection of childhood survivors with favorable characteristics.…”