How Change in Age-Specific Mortality Affects Life Expectancy

At current mortality rates, life expectancy is most responsive to change in mortality rates at older ages. Mathematical formulas that describe the linkage between change in age-specific mortality rates and change in life expectancy reveal why. These formulas also shed light on how past progress against mortality has been translated into increases in life expectancy--and on the impact that future progress is likely to have. Furthermore, the mathematics can be adapted to study the effect of mortality change in heterogeneous populations in which those who die at some age would, if saved, have a different life expectancy than those who live

Some General Relationships in Population Dynamics

Important recent research by Samuel Preston and Ansley Coale (1982) extends the Lotka system of stable population equations (Lotka 1939) to any population. Here we present an alternative general system and describe its duality with the Preston-Coale system: We derive these results by considering the calculus of change on the surface of population density defined over age and time. We show that analysis of this Lexis surface leads to all the known fundamental relationships of the dynamics of single-region human populations, as well as some interesting new relationships

Concentration Curves and Have-Statistics for Ecological Analysis of Diversity: Part II: Species and Other Diversity

The application of concentration curves and have-statistics to studies of dominance and evenness in reproductive success was discussed in Part I of this series of three papers. Concentration curves and have-statistics can also aid ecologists in studies of species diversity and community structure; a start in this direction was made by Patil and Taillie (1979) and Taillie (1979). Essentially, the method is the same as before except that now the "haves" are species rather than individuals and the "hads" are individuals, biomass, caloric intake, etc., rather than an individual's offspring. In addition, concentration curves and have-statistics can be applied to other ecological topics pertaining to variation and inequality, including the temporal or spatial distribution of some resource, such as food supply or rainfall. Various examples, from studies of diatoms, a community of herbaceous plants, a tropical forest, a model of niche preemption, and temporal variation in the breeding of tropical and temperate bird species illustrate this approach

Repeated Resuscitation: How Lifesaving alters Lifetables

How does saving lives affect the force of mortality and lifetable statistics? How can the progress being made in reducing the force of mortality be interpreted in terms of lifesaving? How many times can a person expect to have his or her life saved as a result of this progress? We develop a model to answer these questions and illustrate the results using U.S. mortality rates for 1900 and 1980 and as projected for 2050

Cancer Rates over Age, Time and Place: Insights from Stochastic Models of Heterogeneous Populations

Individuals at the same age in the same population differ along numerous risk factors that affect their chances of various causes of death. The frail and susceptible tend to die first. This differential selection may partially account for some of the puzzles in cancer epidemiology, including the lack of apparent progress in reducing cancer incidence and mortality rates over time

The Deviant Dynamics of Death in Heterogeneous Populations

The members of most populations gradually die off or drop out: people die, machines wear out, residents move out, etc. In many such "aging" populations, some members are more likely to "die" than others. Standard analytical methods largely ignore this heterogeneity; the methods assume that all members of a population at a given age face the same probability of death. This paper presents some mathematical methods for studying how the behavior over time of a heterogeneous population deviates from the behavior of the individuals that make up the population. The methods yield some startling results: individuals age faster than populations, eliminating a cause of death can decrease life expectancy, a population can suffer a higher death rate than another population even though its members have lower death rates, population death rates can be increasing even though its members' death rates are decreasing

Passage to Methuselah: Some Demographic Consequences of Continued Progress Against Mortality

Suppose progress continues to be made in reducing mortality rates at all ages. What impact would this progress have on the size and age composition of the U.S. population? The supposition that mortality rates will continue to fall is admittedly questionable. The view popularized by James F. Fries is that "the median natural human life span is set at a maximum of 85 years with a standard error of less than one year" (Fries and Crapo, 1981). Paul Demeny, in making long-term population forecasts for the World Bank, assumes that even by the year 2100 there will be no country with a life expectancy above 82.5 years. Demeny notes that in some countries life expectancy seems to be slowly decreasing. The possibility of a general decline in life expectancy cannot be ruled out. On the other hand, as Demeny points out, "the upper limit to life expectancy" of 82.5 years "may yield to technological changes in medicine and to changes in life styles, perhaps even within the next few decades" (Demeny, 1984). As documented by Crimmins (1981), remarkably rapid progress in reducing mortality rates was made in the United States from 1968 to 1977. This progress has continued and even accelerated from 1977 to 1983. At most ages, including older ages, mortality rates over the last decade have been declining at a rate of one or two percent per year. Hope that this progress might continue is butressed by recent advances in the biological, medical, and gerontological sciences. The life sciences appear to be poised at roughly the point the physical sciences were a century ago and breakthroughs comparable to electricity, automobiles, television, and computers may be forthcoming in the areas of genetic engineering, prevention and treatment of such diseases as atherosclerosis, cancer, and diabetes, and perhaps understanding and control of the process of aging itself (see, e.g. Walford (1983), Bulkley (1983), and Rosenfeld (1976)). In this note, we explore three possibilities: no change in mortality rates, continued progress at two percent per year at all ages, and a radical breakthrough that cuts mortality rates in half in the year 2000. Our focus is on the impact of such scenarios on the size and age composition of the U.S. population. Because our aim is insight and not prediction, we assume that fertility rates stay unchanged and that net migration amounts to zero: these simplifications avoid obscuring the effects of mortality change with fertility or migration change...

The LEXIS Program for Creating Shaded Contour Maps of Demographic Surfaces

The LEXIS computer program, which was developed at the International Institute for Applied Systems Analysis (IIASA) and Duke University, is intended to aid demographers in the analysis of large arrays of data. Its application as a supplement t o other methods of graphic display is demonstrated in 'Thousands of Data at a Glance: Shaded Contour Maps of Demographic Surfaces" (Vaupel, Gambill, and Yashin, 1985) and will not be discussed here. This paper provides instructions on the use of the program, gives some hints concerning the art and craft of using the program in a creative way, and briefly describes the algorithm used in designing the program. A diskette containing a copy of the LEXIS program may be obtained from the authors or from IIASA. The program is copyrighted but the diskette is not protected against copying: please feel free to make and distribute copies. By making the program available to demographers and others interested in mapping the contours of surfaces, we hope to encourage the development of this method of data analysis. We would, of course, sincerely appreciate it if we and the International Institute for Applied Systems Analysis were acknowledged when the program or some modified version of it is used to produce maps for presentation or publication. Comments and suggestions are welcome

Targetting Lifesaving: Demographic Linkages Between Population Structure and Life Expectancy

A computer-assisted mathematical modeling method that emphasizes the interaction between analysts and computers is presented. It combines algebraic and graph-theoretic approaches to extract a trade-off between human mental models and models based on the use of data collected from the system under study. The method is oriented to the modeling of the so-called "gray box" systems which often involve human behavioral aspects and also knowledge of the experts in relevant fields. By recursive dialogues with the computer, the modeler finds a system model which can be nonlinear with respect to descriptive variables. The structure of the computer program packages is also presented