[Paleopsych] Science: Biodemographic Trajectories of Longevity

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Biodemographic Trajectories of Longevity
Volume 280, Number 5365, Issue of 8 May 1998, pp. 855-860.

Review

James W. Vaupel, * James R. Carey, Kaare Christensen, Thomas E. Johnson, 
Anatoli I. Yashin, Niels V. Holm, Ivan A. Iachine, Väinö Kannisto, Aziz A. 
Khazaeli, Pablo Liedo, Valter D. Longo, Yi Zeng, Kenneth G. Manton, James W. 
Curtsinger

Old-age survival has increased substantially since 1950. Death rates decelerate 
with age for insects, worms, and yeast, as well as humans. This evidence of 
extended postreproductive survival is puzzling. Three biodemographic 
insights--concerning the correlation of death rates across age, individual 
differences in survival chances, and induced alterations in age patterns of 
fertility and mortality--offer clues and suggest research on the failure of 
complicated systems, on new demographic equations for evolutionary theory, and 
on fertility-longevity interactions. Nongenetic changes account for increases 
in human life-spans to date. Explication of these causes and the genetic 
license for extended survival, as well as discovery of genes and other survival 
attributes affecting longevity, will lead to even longer lives.

J. W. Vaupel is at the Max Planck Institute for Demographic Research, D-18057 
Rostock, Germany; Odense University Medical School, DK-5000 Odense C, Denmark; 
the Center for Demographic Studies, Duke University, Durham, NC 27706, USA; and 
Andrus Gerontology Center, the University of Southern California, Los Angeles, 
CA 90089-0191, USA. J. R. Carey is in the Department of Entomology, University 
of California at Davis, Davis, CA 95616-8584, USA. K. Christensen, N. V. Holm, 
I. A. Iachine, and V. Kannisto are at Odense University Medical School, DK-5000 
Odense C, Denmark. T. E. Johnson is at the Institute for Behavioral Genetics, 
University of Colorado at Boulder, Boulder, CO 80309-0447, USA. A. I. Yashin is 
at the Max Planck Institute for Demographic Research, D-18057 Rostock, Germany, 
and the Center for Demographic Studies, Duke University, Durham, NC 27706, USA. 
A. A. Khazaeli and J. W. Curtsinger are in the Department of Ecology, 
Evolution, and Behavior, University of Minnesota, St. Paul, MN 55108, USA. P. 
Liedo is with El Colegio de la Frontera Sur, Tapachula 30700, Mexico. V. D. 
Longo is at the Andrus Gerontology Center at the University of Southern 
California, Los Angeles, CA 90089-0191, USA. Y. Zeng is at the Max Planck 
Institute for Demographic Research, D-18057 Rostock, Germany, and the Institute 
of Population Research, Peking University, Beijing 100871, China. K. G. Manton 
is at the Center for Demographic Studies at Duke University, Durham, NC 27706, 
USA. * To whom correspondence should be addressed at the Max Planck Institute 
for Demographic Research, Doberaner Strasse 114, D-18057 Rostock, Germany. 
E-mail: jwv at demogr.mpg.de

Humanity is aging. The social, economic, and health-care consequences of the 
new demography (Table 1) will drive public policy worldwide in coming decades 
(1). Growth of the older population is fueled by three factors. Baby-boom 
generations are growing older. The chance of surviving to old age is 
increasing. And the elderly are living longer--because of remarkable, largely 
unexplained reductions in mortality at older ages since 1950 (2-4). 
Biodemography, the mating of biology and demography, is, we argue, spawning 
insights into the enigma of lengthening longevity (5).

Table 1. Estimated population, proportion of population, and growth of 
population above age 60 for the world and for selected countries in 1970 and 
1997 and projected for 2025. Countries are ranked by percentage 60+ in 1997. 
Data are from (46). Country Millions 60+ Percent 60+ Growth 1970 1997 2025 1970 
1997 2025 1997/1970 2025/1997 World 300.0 530.0 1200.0 8 9 15 1.8 2.3 Italy 9.0 
13.0 18.0 16 23 33 1.4 1.4 Sweden 1.6 2.0 2.7 20 22 29 1.3 1.4 Germany 15.0 
18.0 28.0 20 21 32 1.2 1.6 Japan 11.0 27.0 40.0 11 21 33 2.5 1.5 U.S.A. 29.0 
44.0 83.0 14 17 25 1.5 1.9 China 57.0 118.0 290.0 7 10 20 2.1 2.5 India 29.0 
64.0 165.0 6 7 12 2.2 2.6 Mexico 3.0 6.5 18.0 6 7 13 2.2 2.7 Increases in 
Old-Age Survival For Sweden, accurate statistics on mortality are available 
going back for more than a century. Female death rates at older ages have 
fallen since 1950, with large absolute reductions at advanced ages (Fig. 1). 
The pattern is similar for males, although from conception to old age males 
suffer higher death rates than females, and progress in reducing male mortality 
has generally been slower than for females. Consequently, most older people in 
Sweden--and nearly all other countries--are women. 
<http://www.sciencemag.org/content/vol280/issue5365/images/small/se1886503001.gif> 
Fig. 1. Shaded contour maps (47) of death rates (48) for Swedish females from 
age 0 to 112 and years 1875 to 1995 (49), with contours on a ratio scale of 
mortality doublings (A) and on an arithmetic scale (B). The color of each small 
rectangle denotes the level of the death rate at that age and year. White 
rectangles indicate ages and years when no female deaths were recorded. Dark 
red rectangles at the highest ages mark the deaths of the last survivor of a 
cohort. The vertical black line marks the year 1950, when increases in old-age 
survival accelerated. The horizontal black line is at age 85. The large 
relative reductions in mortality at younger ages, especially before 1950, are 
apparent when a ratio scale is used to set contours (A). The vertical light 
line at 1919 in (A) is a consequence of deaths from the Spanish flu epidemic. 
The low level of mortality at ages below age 70 and the large absolute 
reductions in mortality at advanced ages are highlighted when an arithmetic 
scale is used (B). [View Larger Version of this Image (44K GIF file)]

For other developed countries, trends in mortality since 1900 have been roughly 
similar to those in Sweden. For example, old-age survival has also increased 
since 1950 for female octogenarians in England, France, Iceland, Japan, and the 
United States (Fig. 2). If there were an impending limit to further declines in 
death rates at older ages, countries with low levels of mortality would tend to 
show slow rates of reduction. There is, however, no correlation between levels 
of mortality and rates of reduction (2). In most developed countries the rate 
of reduction has accelerated, especially since 1970 (2, 4). Japan, which enjoys 
the world's longest life expectancy and lowest levels of mortality at older 
ages, has been a leader in the quickening pace of increase in old-age survival 
(Fig. 2). Since the early 1970s female death rates in Japan have declined at 
annual rates of about 3% for octogenarians and 2% for nonagenarians. Mortality 
among octogenarians and nonagenarians has been low in the United States (Fig. 
2). The reasons for the U.S. advantage and the recent loss of this advantage to 
Japan and France are not well understood (4, 6). 
<http://www.sciencemag.org/content/vol280/issue5365/images/small/se1886503002.gif> 
Fig. 2. Deaths per 1000 women at ages 80 to 89 from 1950 to 1995 for Japan 
(dashed black line), France (blue line), Sweden (green line), England and Wales 
(red line), Iceland (gray line), the United States (light blue line), and U.S. 
whites (brown line). The U.S. data (light blue line) may be unreliable, 
especially in the 1960s. Source: (49, 50). [View Larger Version of this Image 
(26K GIF file)]

The reduction in death rates at older ages has increased the size of the 
elderly population considerably (2, 4, 7). In developed countries in 1990 there 
were about twice as many nonagenarians and four to five times as many 
centenarians as there would have been if mortality after age 80 had stayed at 
1960 levels. Reliable data for various developed countries indicate that the 
population of centenarians has doubled every decade since 1960, mostly as a 
result of increases in survival after age 80 (7).

The decline in old-age mortality is perplexing. What biological charter permits 
us (or any other species) to live long postreproductive lives (8)? A canonical 
gerontological belief posits genetically determined maximum life-spans. Most 
sexually reproducing species show signs of senescence with age (9), and 
evolutionary biologists have developed theories to account for this (10). The 
postreproductive span of life should be short because there is no selection 
against mutations that are not expressed until reproductive activity has ceased 
(11-13).

The logic of this theory and the absence of compelling countertheories (14) 
have led many to discount the evidence of substantial declines in old-age 
mortality. Often it is assumed that the reductions are anomalous and that 
progress will stagnate (15). Only time can silence claims about the future. And 
empirical observations are not fully acceptable until they are explicable. We 
have therefore focused on testing hypotheses and developing new concepts. 
Mortality Deceleration A key testable hypothesis is that mortality accelerates 
with age as reproduction declines. We estimated age trajectories of death rates 
(Fig. 3) for Homo sapiens, Ceratitis capitata (the Mediterranean fruit fly), 
Anastrepha ludens, Anastrepha obliqua, and Anastrepha serpentina (three other 
species of true fruit fly), Diachasmimorpha longiacaudtis (a parasitoid wasp), 
Drosophila melanogaster, Caenorhabditis elegans (a nematode worm), and 
Saccharomyces cerevisiae (baker's yeast). To peer into the remote realms of 
exceptional longevity we studied very large cohorts. 
<http://www.sciencemag.org/content/vol280/issue5365/images/small/se1886503003.gif> 
Fig. 3. Age trajectories of death rates (48). (A) Death rates from age 80 to 
122 for human females. The red line is for an aggregation of 14 countries 
(Japan and 13 Western European countries) with reliable data, over the period 
from 1950 to 1990 for ages 80 to 109 and to 1997 for ages 110 and over (49). 
The last observation is a death at age 122, but data are so sparse at the 
highest ages that the trajectory of mortality is too erratic to plot. Although 
the graph is based on massive data, some 287 million person-years-at-risk, 
reliable data were available on only 82 people who survived past age 110. The 
exponential (Gompertz) curve that best fits the data at ages 80 to 84 is shown 
in black. The logistic curve that best fits the entire data set is shown in 
blue (16). A quadratic curve (that is, the logarithm of death rate as a 
quadratic function of age) was fit to the data at ages 105 and higher; it is 
shown in green. (B) Death rates for a cohort of 1,203,646 medflies, Ceratitis 
capitata (17). The red curve is for females and the blue curve for males. The 
prominent shoulder of mortality, marked with an arrow, is associated with the 
death of protein-deprived females attempting to produce eggs (51). Until day 
30, daily death rates are plotted; afterward, the death rates are averages for 
the 10-day period centered on the age at which the value is plotted. The 
fluctuations at the highest ages may be due to random noise; only 44 females 
and 18 males survived to day 100. (C) Death rates for three species of true 
fruit flies, Anastrepha serpentina in red (for a cohort of 341,314 flies), A. 
obliqua in green (for 297,087 flies), and A. ludens in light blue (for 851,100 
flies), as well as 27,542 parasitoid wasps, Diachasmimorpha longiacaudtis, 
shown by the thinner dark blue curve. As for medflies, daily death rates are 
plotted until day 30; afterward, the death rates are for 10-day periods. (D) 
Death rates for a genetically homogeneous line of Drosophila melanogaster, from 
an experiment by A.A.K. and J.W.C. The thick red line is for a cohort of 6338 
flies reared under usual procedures in J.W.C.'s laboratory. The other lines are 
for 17 smaller cohorts with a total of 7482 flies. To reduce heterogeneity, 
eggs were collected over a period of only 7 hours, first instar larvae over a 
period of only 3 hours, and enclosed flies over a period of only 3 hours. Each 
cohort was maintained under conditions that were as standardized as feasible. 
Death rates were smoothed by use of a locally weighted procedure with a window 
of 8 days (52). (E) Death rates, determined from survival data from population 
samples, for genetically homogeneous lines of nematode worms, Caenorhabditis 
elegans, raised under experimental conditions similar to (53) but with density 
controlled (21). Age trajectories for the wild-type worm are shown as a solid 
red line (on a logarithmic scale given to the left) and as a dashed red line 
(on an arithmetic scale given to the right); the experiment included about 
550,000 worms. Trajectories for the age-1 mutant are shown as a solid blue line 
(on the logarithmic scale) and as a dashed blue line (on the arithmetic scale), 
from an experiment with about 100,000 worms. (F) Death rates for about 10 
billion yeast in two haploid strains: D27310b, which is a wild-type strain, 
shown in red; and EG103 (DBY746), which is a highly studied laboratory strain, 
shown in blue (34). Surviving population size was estimated daily from samples 
of known volume containing about 200 viable individuals. Death rates were 
calculated from the estimated population sizes and then smoothed by use of a 
20-day window for the EG103 strain and a 25-day window for the D27310b strain. 
Because the standard errors of the death-rate estimates are about one-tenth of 
the estimates, the pattern of rise, fall, and rise is highly statistically 
significant. (G) Death rates for automobiles in the United States, estimated 
from annual automobile registration data. An automobile "dies" if it is not 
re-registered (26, 54). The blue and dashed blue lines are for Chevrolets from 
the 1970 and 1980 model years; the red and dashed red lines are for Toyotas 
from the same years. [View Larger Version of this Image (29K GIF file)]

For humans (Fig. 3A), death rates increase at a slowing rate after age 80. A 
logistic curve that fits the data well from age 80 to 105 indicates that death 
rates may reach a plateau (16). A quadratic curve fit to the data at ages 105+ 
suggests a decline in mortality after age 110.

For four species of true fruit flies in two genera and for a parasitoid wasp 
(Fig. 3, B and C), death rates rise and then fall. The data on medflies (Fig. 
3B) generated considerable controversy when published because it was generally 
believed that for almost all species mortality inexorably increases at ages 
after maturity (9, 17). Previously unpublished data on three species from a 
different genus and a species from a different order (Fig. 3C) demonstrate that 
mortality decline is not unique to medflies. Theories of aging will have to 
confront the vexing observation of mortality decline.

Mortality deceleration can be an artifact of compositional change in 
heterogeneous populations (18). Previously unpublished Drosophila data (Fig. 
3D) demonstrate that a leveling off of death rates can occur even when 
heterogeneity is minimized by rearing genetically homogeneous cohorts under 
very similar conditions.

The mortality trajectories for C. elegans (Fig. 3E) are based on data from 
experiments more extensive than earlier ones. The trajectory for the wild-type 
strain decelerates when about a quarter of the cohort is still alive, similar 
to observations for Drosophila. For age-1 mutants mortality remains low 
throughout life, which demonstrates that simple genetic changes can alter 
mortality schedules dramatically.

Data from about 10 billion individuals in two strains of S. cerevisiae were 
used to estimate mortality trajectories (Fig. 3F). Because the yeast were kept 
under conditions thought to preclude reproduction, death rates were calculated 
from changes in the size of the surviving cohort. Although they need to be 
confirmed, the observed trajectories suggest that for enormous cohorts of 
yeast, death rates may rise and fall and rise again.

The trajectories in Fig. 3 differ greatly. For instance, human mortality at 
advanced ages rises to heights that preclude the longevity outliers found in 
medflies (3, 16, 17). Such differences demand explanation. But the trajectories 
also share a key characteristic. For all species for which large cohorts have 
been followed to extinction (Fig. 3), mortality decelerates and, for the 
biggest populations studied, even declines at older ages. A few smaller studies 
have found deceleration in additional species (19). For humans, the insects, 
and the worms, the deceleration occurs at ages well past normal reproductive 
ages.

If older individuals contribute to the reproductive success of younger, related 
individuals, then they promote the propagation of their genes. Hence, in social 
species, the effective end of reproduction may be much later than indicated by 
fertility schedules (20). The deceleration of human mortality, however, occurs 
after age 80 and the leveling off or decline after age 110, ages that were 
rarely if ever reached in the course of human evolution (8) and ages at which 
any reproductive contribution is small.

In our early experiments, flies and worms were held in containers, with the 
density of living individuals declining with age. To check whether mortality 
deceleration could be an artifact of such changes in crowding, we held density 
constant--and still observed deceleration (21). Biodemographic Explanations It 
is not clear how to reconcile our two key findings--that mortality decelerates 
and that human mortality at older ages has declined substantially--with theory 
about aging. The proximate and ultimate causes of postreproductive survival are 
not understood (12, 22). Theories that leave "non-zero late survival ... 
unexplained" are unsatisfactory (13). Three biodemographic concepts--mortality 
correlation, heterogeneity in frailty, and induced demographic schedules--point 
to promising directions for developing theory.

Mortality correlation. Demographers have long known that death rates at 
different ages are highly correlated across populations and over time (23). In 
addition to environmental correlation, there may be genetic correlation: 
Mutations that raise mortality at older ages may do so at younger ages as well, 
decreasing evolutionary fitness (12). A pioneering Drosophila experiment found 
mortality correlation and no evidence of mutations with effects only at late 
ages (24). Postreproductive life-spans might be compared with postwarranty 
survival of equipment (25). Although living organisms are vastly more complex 
than manufactured products, they too are bound by mechanical constraints that 
may impose mortality correlations. The trajectory of mortality for automobiles 
(Fig. 3G) decelerates, suggesting the possibility that both deceleration and 
mortality correlation are general properties of complicated systems (26).

Heterogeneity in frailty. All populations are heterogeneous. Even genetically 
identical populations display phenotypic differences. Some individuals are 
frailer than others, innately or because of acquired weaknesses. The frail tend 
to suffer high mortality, leaving a select subset of survivors. This creates a 
fundamental problem for analyses of aging and mortality: As a result of 
compositional change, death rates increase more slowly with age than they would 
in a homogeneous population (18).

The leveling off and even decline of mortality can be entirely accounted for by 
models in which the chance of death for all individuals in the population rises 
at a constant or increasing rate with age (18). A frailty model applied to data 
on the life-spans of Danish twins suggests that mortality for individuals of 
the same genotype and with the same nongenetic attributes (such as educational 
achievement and smoking behavior) at some specified age may increase even 
faster than exponentially after that age (27). On the other hand, mortality 
deceleration could result from behavioral and physiological changes with age.

Verification of the heterogeneity hypothesis hinges on empirical estimation of 
the variation in frailty within a population. If at specified ages cohorts of 
Drosophila (or some other species) could be subjected to a stress that killed 
the frail and left the survivors neither weaker nor stronger, then comparison 
of the trajectories of mortality for the stressed cohorts with the trajectories 
for control cohorts would reveal the degree of heterogeneity (28). In practice, 
however, stresses generally weaken some survivors and strengthen others. 
Experiments with multiple intensities of stress, including nonlethal levels, 
may permit experimental estimates of heterogeneity in frailty.

Induced demographic schedules. A key construct underlying evolutionary theory 
is the Lotka equation, which determines the growth rate of a population (or the 
spread of an advantageous mutation) given age schedules of fertility and 
survival (29). The simplistic assumption in the Lotka equation that fertility 
and survival schedules are fixed is surely wrong for most species in the wild: 
Environments in nature are uncertain and changing (30). Many species have 
evolved alternative physiological modes for coping with fluctuating conditions, 
including dauer states (C. elegans), stationary phase (yeast), diapause 
(certain insects), and hibernation. In social insects the same genome can be 
programmed to produce short-lived workers or long-lived queens (9). That is, 
alternative demographic schedules of fertility and survival can be induced by 
environmental conditions.

To reproduce medflies need protein--and this is only occasionally available in 
the wild. Medflies fed sugar and water can survive to advanced ages and still 
reproduce when fed protein. Regardless of when medflies begin reproducing, 
their subsequent mortality starts low and rises rapidly. This is a striking 
example of how, depending on the environment, organisms can manipulate their 
age-specific fertility and survival (31).

In nematodes, exposure to nonlethal heat shock or other stresses early in life 
induces increases in both stress resistance and longevity (32). In Drosophila, 
stress can also produce increases in subsequent longevity, attributable in part 
to the induction of molecular chaperones (33). Deletion of the RAS2 gene in S. 
cerevisiae doubles the mean chronological life-span of yeast in stationary 
phase (34). RAS2 mutants exhibit striking similarities to long-lived nematode 
mutants, including increases in stress resistance (32, 34). Rodents raised on 
restricted diets have extended life-spans and increased resistance to 
environmental carcinogens, heat, and reactive oxidants (35). These findings 
suggest that stress-related genes and mechanisms may affect longevity across a 
broad range of species (32-35).

In sum, induced physiological change can lower mortality substantially. There 
is also evidence for physiological remolding to cope with damage in organisms 
(9, 36). An individual does not face fixed fertility and survival schedules, 
but dynamically adopts alternative schedules as the environment and the 
individual's capabilities change. For this and other reasons (30, 37), 
Lotka-based evolutionary theory needs rethinking. Post-Lotka equations should 
incorporate "grandparental and multigenerational terms, ... homeostatic 
feedback and fluctuating environments" (37), as well as induced demographic 
schedules.

Although simplistic, the Lotka equation captures a fundamental insight: It is 
reproductive success that is optimized, not longevity. Deeper understanding of 
survival at older ages thus hinges on intensified research into the 
interactions between fertility and longevity (19, 31, 38).

Survival Attributes

The concepts of mortality correlation, heterogeneity in frailty, and induced 
demographic schedules can be tied together by a general question: How important 
are an individual's survival attributes (that is, persistent characteristics, 
innate or acquired, that affect survival chances) as opposed to current 
conditions in determining the chance of death? For humans, nutrition and 
infections in utero and during childhood may program the development of risk 
factors for several important diseases of middle and old age (39). Conflicting 
evidence suggests that current conditions may affect old-age survival chances 
much more than conditions early in life (2, 40).

A frailty model applied to Danish twin data sheds some even-handed light on 
this controversy. The model suggests that about 50% of the variation in human 
life-spans after age 30 can be attributed to survival attributes that are fixed 
for individuals by the time they are 30; a third to a half of this effect is 
due to genetic factors and half to two-thirds to nongenetic survival attributes 
(related to, for example, socioeconomic status or nutritional and disease 
history). The model suggests that the importance of survival attributes may 
increase with a person's life expectancy. For persons who at age 30 can expect 
to survive into their 90s, more than 80% of the variation in life-span may be 
due to factors that are fixed by this age (41).

How many survival attributes account for most of the variation in life-spans? 
The number required to "survive ad extrema" may be "hundreds, not 
tens-of-thousands" (37); research over the next decade may resolve this 
question. For nematode worms and yeast, the mutation of a single gene can 
result in a qualitative change in the age trajectory of mortality (Fig. 3E) 
(34). For other species, including Drosophila and humans, no genes with such 
radical demographic effects have yet been discovered, but some polymorphisms, 
such as ApoE alleles in humans, alter substantially the chance of surviving to 
an advanced age (42). The emerging field of molecular biodemography seeks to 
uncover how variation at the microscopic level of genetic polymorphisms alters 
mortality trajectories at the macroscopic level of entire populations.

Analyses of data on Danish twins and other populations of related individuals 
indicate that 20 to 25% of the variation in adult life-spans can be attributed 
to genetic variation among individuals; heritability of life-span is also 
modest for a variety of other species (43). The possibility that genetic 
polymorphisms may play an increasing role with age is supported by evidence of 
increases with age in the genetic component of variation in both cognitive and 
physical ability (44).

Although genes and other survival attributes are fixed for individuals, their 
distribution in a cohort changes with age as the frail die. Hence, it is 
possible to develop survival attribute assays based on demographic analysis of 
changes with age in the frequency of fixed attributes. In longitudinal research 
in progress, we are gathering information on lifestyle and environmental 
conditions as well as DNA from 7000 Chinese octogenarians and nonagenarians, 
3000 Chinese centenarians, and 14,000 elderly Danes. Survival-attribute assays 
applied to these data may uncover a suite of genetic and nongenetic 
determinants of longevity.

Experiments with insects, worms, yeast, and other organisms permit alternative 
approaches for discovering survival attributes; the diet and stress experiments 
sketched above provide examples. That genes can alter mortality trajectories is 
now certain; research on the mechanisms will shed new light on aging and 
longevity (45). The importance of diet, stress, and reproduction in inducing 
alternative mortality schedules has been demonstrated, but the potential of 
such studies to clarify causal relationships is just beginning to be tapped. 
The emerging dialogue between biologists and demographers (5) is changing the 
terms of discourse and opening new vantage points for research on aging.

REFERENCES AND NOTES

    1. In China the 60+ population in 2050 may number around half a billion 
people, about the number worldwide today (Table 1). To keep the proportion over 
60 to a quarter that size, population size would have to rise from 1.25 to 2 
billion [J. W. Vaupel and Y. Zeng, Policy Sci. 24, 389 (1991); Y. Zeng, J. W. 
Vaupel, Z. Wang, Math. Pop. Stud. 6, 187 (1997)]. More generally, see J. W. 
Vaupel and A. E. Gowan, Am. J. Public Health 76, 430 (1986) [Abstract] and D. 
A. Wise, Ed., Advances in the Economics of Aging (Univ. of Chicago Press, 
Chicago, IL, 1996).

    2. V. Kannisto, J. Lauritsen, A. R. Thatcher, J. W. Vaupel, Pop. Dev. Rev. 
20, 987 (1994); V. Kannisto, Development of Oldest-Old Mortality 1950-1990 
(Odense Univ. Press, Odense, Denmark, 1994); V. Kannisto, The Advancing 
Frontier of Survival (Odense Univ. Press, Odense, Denmark, 1996); J. R. Wilmoth 
in (5), p. 38.

    3. B. Jeune and J. W. Vaupel, Eds., Exceptional Longevity: From Prehistory 
to the Present (Odense Univ. Press, Odense, Denmark, 1995).

    4. J. W. Vaupel, Philos. Trans. R. Soc. London Ser. B 352, 1 (1997) 
[CrossRef][ISI] .

    5. K. W. Wachter and C. E. Finch, Eds., Between Zeus and the Salmon: The 
Biodemography of Longevity (National Academy Press, Washington, DC, 1997).

    6. K. G. Manton and J. W. Vaupel, N. Engl. J. Med. 333, 1232 (1995) 
[Abstract/Free Full Text] .

    7. J. W. Vaupel and B. Jeune, in (3), p. 109.

    8. Remaining life expectancy at age 65 for Paleolithic populations may have 
been about 7 years [R. E. Lee, in (5), p. 212]. For Swedish females in 1900, 
1950, and 1995 it was 12.9, 14.3, and 19.8 years, and for Japanese females in 
1995 it was over 20.8 years, triple the Paleolithic level. Remaining life 
expectancy at age 50 from the stone age through the middle ages may have varied 
from 10 to 16 years [J. R. Wilmoth in (3), p. 125], compared with values of 
23.8, 26.4, and 33.0 for Swedish females in 1900, 1950, and 1995.

    9. C. E. Finch, Longevity, Senescence, and the Genome (Univ. of Chicago 
Press, Chicago, IL, 1990).

   10. P. B. Medawar, An Unsolved Problem in Biology (Lewis, London, 1952); G. 
C. Williams, Evolution 11, 398 (1957) [ISI] ; W. D. Hamilton, J. Theor. Biol. 
12, 12 (1966) [ISI][Medline] ; B. Charlesworth, Evolution in Age-Structured 
Populations (Cambridge Univ. Press, New York, 1994); P. Abrams and D. Ludwig, 
Evolution 49, 1055 (1995) [ISI] ; L. Partridge in (5), p. 78. For discussion of 
the mixed empirical support for this theory, see (13); J. W. Curtsinger, P. M. 
Service, T. Prout, Am. Nat. 144, 210 (1994) [CrossRef][ISI]; D. E. L. 
Promislow, M. Tatar, A. A. Khazaeli, J. W. Curtsinger, Genetics 143, 839 (1996) 
[Abstract/Free Full Text] .

   11. J. W. Curtsinger, Genetica 96, 187 (1995) [ISI] ; S. Tuljapurkar, in (5), 
p. 65.

   12. B. Charlesworth and L. Partridge, Curr. Biol. 7, R440 (1997) 
[ISI][Medline] .

   13. The quote, from (12, p. R441), pertains to L. D. Mueller and M. R. Rose, 
Proc. Natl. Acad. Sci. U.S.A. 93, 15249 (1996) [Abstract/Free Full Text] ; also 
see S. D. Pletcher and J. W. Curtsinger, Evolution, in press.

   14. L. Keller and M. Genoud, Nature 389, 958 (1997) [CrossRef][ISI] .

   15. N. Keilman, J. Off. Stat. 13, 245 (1997); J. F. Fries, N. Engl. J. Med. 
303, 130 (1980) [Abstract] ; S. J. Olshansky, B. A. Carnes, C. Cassel, Science 
250, 634 (1990) [ISI][Medline] .

   16. A. R. Thatcher, V. Kannisto, J. W. Vaupel, The Trajectory of Mortality 
from Age 80 to 120 (Odense Univ. Press, Odense, Denmark, 1998).
   17. J. R. Carey, P. Liedo, D. Orozco, J. W. Vaupel, Science 258, 457 (1992) 
[ISI][Medline] ; J. R. Carey, Demography 34, 17 (1997) [ISI][Medline] .

   18. J. W. Vaupel, K. G. Manton, E. Stallard, ibid. 16, 439 (1979) 
[ISI][Medline]; J. W. Curtsinger, H. H. Fukui, D. R. Townsend, J. W. Vaupel,

Science 258, 461 (1992) [ISI][Medline] ; J. W. Vaupel and J. R. Carey, ibid. 
260, 1666 (1993) [ISI][Medline]; A. I. Yashin, J. W. Vaupel, I. A. Iachine, 
Mech. Aging Dev. 74, 1 (1994).

   19. M. Tatar, J. R. Carey, J. W. Vaupel, Evolution 47, 1302 (1993) [ISI] ; D. 
L. Wilson, Mech. Aging Dev. 74, 15 (1994). But most smaller studies have not 
found deceleration (9).

   20. J. R. Carey and C. Gruenfelder, in (5), p. 127; S. N. Austad, ibid., p. 
161.

   21. J. R. Carey, P. Liedo, J. W. Vaupel, Exp. Gerontol. 30, 605 (1995) 
[CrossRef][ISI][Medline] ; A.A. Khazaeli, L. Xiu, J. W. Curtsinger, J. 
Gerontol. 52, 48 (1995) ; A. A. Khazaeli, L. Xiu, J. W. Curtsinger, Genetica 
98, 21 (1996) [ISI][Medline] . In our nematode experiments, the volume of the 
container was reduced as worms died, to keep density constant.

   22. K. Christensen and J. W. Vaupel, J. Int. Med. 240, 333 (1996).

   23. A. Coale and P. Demeny, Regional Model Life Tables and Stable Populations 
(Academic Press, New York, 1983); R. D. Lee and L. R. Carter, J. Am. Stat. 
Assoc. 87, 659 (1992) [ISI] .

   24. S. D. Pletcher, D. Houle, J. W. Curtsinger, Genetics 148, 287 (1998) 
[Abstract/Free Full Text] .

   25. L. Hayflick, How and Why We Age (Ballantine Books, New York, 1994); L. S. 
Gavrilov and N. S. Gavrilova, The Biology of Life Span (Harwood, Chur, 
Switzerland, 1991). Contrary to J. F. Fries and L. M. Crapo [Vitality and Aging 
(Freeman, San Francisco, 1981)] and R. Dawkins [Sci. Am. 273, 80 (November 
1995)], reliability engineering constraints make it virtually impossible for 
organisms to approximate the "one-hoss shay" of Oliver Wendell Holmes, which 
ran perfectly until one day when all of its pieces fell apart simultaneously.

   26. J. W. Vaupel, in (5), p. 17.

   27. A. I. Yashin and I. A. Iachine, Demography 34, 31 (1997) [ISI][Medline] .

   28. J. W. Vaupel, A. I. Yashin, K. G. Manton Math. Pop. Studies 1, 21 (1988); 
J. W. Curtsinger and A. A. Khazaeli, Exp. Gerontol., in press.

   29. A.J. Lotka, Theorie Analytique des Associations Biologiques (Hermann, 
Paris, 1939). The equation is 1 = [int ] e [-] rxl(x)m(x)dx, where r is the 
intrinsic rate of growth of the population, l(x) is the proportion of females 
surviving to age x, and m(x) is the average number of female offspring to 
females at age x.

   30. S. Orzack and S. Tuljapurkar, Am. Nat. 133, 901 (1989) [CrossRef][ISI]; 
M. Mangel and C. W. Clark, Dynamic Modeling in Behavioral Ecology (Princeton 
Univ. Press, Princeton, NJ, 1988).

   31. J. R. Carey, P. Liedo, H.-G. Müller, J.-L. Wang, J. W. Vaupel, in 
preparation.

   32. G. Lithgow, T. M. White, S. Melov, T. E. Johnson, Proc. Natl. Acad. Sci. 
U.S.A. 92, 7540 (1995) [Abstract] ; S. Murakami and T. E. Johnson, Genetics 
143, 1207 (1996) [Abstract/Free Full Text] .

   33. M. Tatar, A. A. Khazaeli, J. W. Curtsinger, Nature 390, 30 (1997) 
[CrossRef][ISI][Medline] .

   34. V. Longo et al., in preparation.

   35. E. J. Masoro and S. N. Austad, J. Gerontol. 51A, B387 (1996) [ISI] ; S. 
M. Jazwinski, Science 273, 54 (1996) [Abstract] .

   36. C. Franceschi, et al., Int. Rev. Immunol. 12, 57 (1995) [Medline] ; E. G. 
Lakatta, Aging 6, 213 (1994) [Medline] .

   37. K. W. Wachter in (5), p. 1.

   38. L. Partridge and M. Farquhar, Nature 294, 580 (1981) [ISI] ; L. Partridge 
and P. Harvey, ibid. 316, 20 (1985) [ISI].

   39. W. Kermack, A. McKendrick, P. McKinlay, Lancet 1, 698 (1934) 
[CrossRef][ISI] ; D. J. P. Barker, Fetal and Infant Origins of Adult Disease 
(British Medical Journal, London, 1992); I. T. Elo and S. H. Preston, Pop. 
Index 58, 186 (1992); R.W. Fogel and D. R. Costa, Demography 34, 49 (1997) 
[ISI][Medline] .

   40. K. Christensen, J. W. Vaupel, N. V. Holm, A. I. Yashin, Br. Med. J. 310, 
432 (1995) [Abstract/Free Full Text] ; V. Kannisto, K. Christensen, J. W. 
Vaupel, Am. J. Epidemiol. 145, 987 (1997) [Abstract] .

   41. Calculation by I. A. Iachine based on frailty model described in (27).

   42. F. Schächter, et al., Nature Genet. 6, 29 (1994) [ISI][Medline] ; G. De 
Benedictis, et al., Hum. Genet. 99, 312 (1997) [CrossRef][ISI][Medline] ; J. 
Maynard Smith, Nature 181, 496 (1958) [ISI][Medline] .

   43. A. M. Herskind, et al., Hum. Genet. 97, 319 (1996) 
[CrossRef][ISI][Medline] ; J.W. Curtsinger, et al., Annu. Rev. Genet. 29, 553 
(1995) [CrossRef][ISI][Medline] ; C. E. Finch and R. E. Tanzi, Science 278, 407 
(1997) [Abstract/Free Full Text] .

   44. G. E. McClearn, et al., Science 276, 1560 (1997) [Abstract/Free Full 
Text] ; K. Christensen et al., in preparation.

   45. A promising line of inquiry we are pursuing focuses on lines of medflies 
(31) and yeast (34) that survive to and reproduce at advanced ages.

   46. Census Bureau International Data Base (updated 10 October 1997), 
available at http://www.census.gov/ipc/www/idbnew.html; United Nations 
Population Division, World Population Prospects: The 1996 Revision, Annex II 
and III (United Nations, New York, 1997).

   47. J. W. Vaupel, Z. Wang, K. Andreev, A. I. Yashin, Population Data at a 
Glance: Shaded Contour Maps of Demographic Surfaces (Odense Univ. Press, 
Odense, Denmark, 1998).

   48. Death rates are the so-called central death rates calculated by dividing 
the number of deaths at the specified age by the years or days of exposure for 
the population at risk.

   49. Own calculations from data in the Kannisto-Thatcher Oldest-Old Database 
and other databases in the Archive of Population Data on Aging maintained by 
Odense University Medical School, Denmark [see (2)], as well as from data in 
the Berkeley Mortality Database (http://demog.berkeley.edu/wilmoth/mortality).

   50. U.S. data are from the Social Security Administration. Data on U.S. 
whites are based on Social Security data supplied to J.W.V. by the Health Care 
Financing Administration. Concerning reliability and calculation methods, see 
(4, 6); B. Kestenbaum, Demography 29, 565 (1992) [ISI][Medline] ; L. B. 
Shrestha and S. H. Preston, Survey Method. 21, 167 (1995).

   51. H.-G. Müller, J.-L. Wang, W. B. Capra, P. Liedo, J. R. Carey, Proc. Natl. 
Acad. Sci. U.S.A. 94, 2762 (1997) [Abstract/Free Full Text] .

   52. T. J. Hastie and R. J. Tibshirani, Generalized Additive Models (Chapman & 
Hall, New York, 1990).

   53. A. Brooks, G. J. Lithgow, T. E. Johnson, Science 263, 668 (1994) 
[ISI][Medline] ; J. W. Vaupel, T. E. Johnson, G. J. Lithgow, ibid. 266, 826 
(1994) [ISI][Medline].

   54. Calculations by J.W.V. and C. R. Owens in manuscript on "Automobile 
Demography."

   55. Our research was supported by the U.S. National Institutes of Health 
(grant AG08761), Danish Research Council, Max Planck Society, Alfred P. Sloan 
Foundation, and Wellcome Trust. We thank K. Andreev, K. Brehmer, C. E. Finch, 
L. G. Harshman, B. Jeune, P. Laslett, H. Lundström, M. K. McGue, H.-G. Müller, 
D. Orozco, C. R. Owens, L. Partridge, S. D. Pletcher, S. H. Preston, D. Roach, 
R. Suzman, M. Tatar, A. R. Thatcher, S. Tuljapurkar, N. G. Vaupel, K. W. 
Wachter, J.-L. Wang, J. R. Wilmoth, and the Moscamed Program in Metapa, Mexico.


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