Supplemental Data

Full Text
Broken Limits to Life Expectancy
Jim Oeppen and James W. Vaupel

Supplementary Material

This supplementary material is organized as follows:
  • Data sources
  • A brief history of life-expectancy limits, with references
  • Further arguments and evidence about life-expectancy limits
  • Supplementary figures 1 to 5
  • Supplementary tables 1 and 2
Data Sources

Statistics in this article are from,, N. Keyfitz and W. Flieger, World Population: An Analysis of Vital Data (Univ. of Chicago Press, Chicago, 1968); S. H. Preston, N. Keyfitz and R. Schoen, Causes of Death: Life Tables for National Populations (Seminar Press, New York, 1972); and life table collections at the Cambridge Group for the History of Population and Social Structure and the Max Planck Institute for Demographic Research. For further information about online data available from the Max Planck Institute, see

A Brief History of Life-Expectancy Limits, with References

Purported limits to life expectancy and the years when they were broken are summarized in Fig. 1 of the main text and in supplementary table 1. The following paragraphs provide some context and supply references not given in the main text.

Louis Dublin, who became Chief Actuary of the Metropolitan Life Insurance Company, seems to have been the first demographer to publish a reasoned estimate of a ceiling to life expectancy. As noted in the main text, when he published his limit in 1928 it had already been breached by non-Maori women in New Zealand.

In 1936, joined by Alfred Lotka, the creator of modern mathematical demography, Dublin assessed a revised life-expectancy limit using data for New Zealand, as well as for the United States [L. I. Dublin, A. J. Lotka, Length of Life: A Study of the Life Table (Ronald Press, New York, 1936), p. 193]. Dublin and Lotka's "hypothetical table promises an eventual expectation of life at birth of 69.93 years." Women on Iceland surpassed this maximum in 1941. Trying yet again, Dublin published in 1941 a third ostensible cap: 70.8 years [reported in his memoirs: L. I. Dublin, The Facts of Life: From Birth to Death (Macmillan, New York, 1951), p. 392]. Women in Norway broke this limit in 1946.

Dublin's memoirs suggest that revising the ceiling upward was a feature of his career with the Metropolitan Life Insurance Company. As he observed half a century ago, "experience has shown that our optimistic views regarding prospects for improved longevity are generally conservative."

As noted in the main text, Olshansky and colleagues used methods and rhetoric similar to Dublin's to estimate limits to life expectancy. In addition to their articles in Science cited in note (8, 9) of the main text, they have written a book: S. J. Olshansky, B. A. Carnes, The Quest for Immortality (Norton, New York, 2001). See J. R. Wilmoth, Pop. Dev. Rev. 27, 791 (2001) for a critical review.

Jean Bourgeois-Pichat [Population 3, 381 (1952) and Pop. Bull. U.N. 11, 12 (1978)] classified deaths into extrinsic causes that potentially could be eliminated and intrinsic causes that could not; he calculated a life table with the extrinsic causes excluded. Similarly, James F. Fries [Milbank Q. 67, 208 (1990) and N. Engl. J. Med. 303, 130 (1980)] distinguished between premature mortality, which is tractable, and senescent mortality, which is not.

P. K. Whelpton identified the lowest age-specific death rates at each age in various countries and estimated life expectancy if a population enjoyed best-practice rates at all ages: see P. K. Whelpton, Forecasts of the Population of the United States 1945-1975 (Bureau of the Census, Washington, DC, 1947), a report notorious for missing the baby boom. Whelpton focused his discussion on life-expectancy limits for U.S. native-born white males. He concluded that for this population a life expectancy in the year 2000 of 72.1 years was the upper limit of what could be achieved by the largest mortality "declines that seem reasonable" and close to what could be attained at the "biological minimum of mortality."

Jacob S. Siegel [NIH Publ. 80-969 (National Institutes of Health, Bethesda, MD, 1980), pp. 17-82] carried Whelpton's general approach a step further by estimating life expectancy on the basis of best-practice cause-specific and age-specific rates. See A. Nizard and J. Vallin, Population 25, 847 (1970); G. Wunsch, Eur. Demogr. Infor. Bull. 5(1), 2 (1974); and K. Uemura, World Health Stat. Q. 42, 26 (1989) for calculations similar to Whelpton's and Siegel's.

Whelpton assumed that mortality improvements would decelerate as an ultimate cap was approached. This notion was later used by Tomas Frejka [The Future of Population Growth (Wiley, New York, 1973) and Pop. Dev. Rev. 7, 489 (1981)]. Both these publications focus on population growth rather than life expectancy. In the first, Frejka writes, "within broad limits mortality can be fairly well predicted." He believes that life expectancy will approach a limit and that 77.5 is the most likely limit. He notes, however, that "mortality might even take a course absolutely different from what has been assumed."

Other forecasts in which life expectancy asymptotically approaches a limit include projections by the World Bank [P. Demeny, Pop. Dev. Rev. 10, 103 (1984); R. A. Bulatao and E. Bos, Policy Research Working Paper 337 (World Bank, Washington, DC, 1989)]; and the United Nations (United Nations, World Population Prospects (New York, various years including 1973, 1986, 1989, 1999, 2001).

In most such asymptotic forecasts, judgment, rather than empirical calculation, is used to specify the maximum life expectancy. Research by the eminent demographer Ansley J. Coale provides a notable exception. Coale [IUSSP Int. Conf. Manila 4, 35 (1981); A. J. Coale and G. Guo, Pop. Bull. U.N. 30, 1 (1991)] tried to empirically estimate the upper limit of life expectancy by fitting an asymptotic function.

An account of official life-expectancy projections before 1970 is provided by Samuel H. Preston, World Health Stat. Rep. 27, 719 (1974).

H. Cruijsen and H. Eding [in E. Tabeau, A. van den Berg Jeths, and C. Heathcote, Eds., Forecasting Mortality in Developed Countries (Kluwer Academic, Dordrecht, Netherlands, 2001), p. 243] review mortality forecasting in 13 European Union countries in the early and mid 1990s. They found that all assumed mortality improvements would decelerate and 10 constrained life expectancy to reach an ultimate limit by a target date.

For recent forecasts for Japan, see National Institute of Population and Social Security Research, Population Projection of Japan, 1996-2050 (Tokyo, 1997) and For a recent U.S. forecast, see Board of Trustees, Social Security Administration, 1999 Annual Report (Government Printing Office, Washington, DC, 1999). Ronald D. Lee [Pop. Dev. Rev. 26, 137 (2000)] provides a critical account of the low mortality assumptions used by the U.S. Social Security Administration.

In the early 1940s, when he was a student at Princeton University, Ansley Coale developed and applied a method that computed the average rapidity of improvement in age-specific death rates over many decades and then used this information to project death rates over coming decades [F. W. Notestein, I. B. Taeuber, D. Kirk, A. J. Coale, L. K. Kiser, The Future Population of Europe and the Soviet Union (League of Nations, Geneva, 1944), pp. 5, 183-189]. Today vastly superior data resources are available and powerful, practicable methods have been developed to do more than Coale attempted. These methods use information about fluctuations in the speed of change in the past to estimate confidence bounds for the uncertainty enveloping life expectancy in the future. See references (2) and (3) of the main text and J. Alho, Rev. Stat. Finland 4, 1 (1998).

For further information about methods for forecasting life expectancy, see J. R. Wilmoth, Science 280, 395 (1998); J. W. Vaupel, Science 280, 986 (1998); J. Bongaarts, R. A. Bulato, Eds., Beyond Six Billion: Forecasting the World's Population (National Academy Press, Washington, DC, 2000); W. Lutz, W. Sanderson, S. Scherbov, Nature 412, 543 (2001); and J. Bongaarts and G. Feeney, Pop. Dev. Rev. 28, 234 (2002). S. J. Olshansky, B. A. Carnes, and A. Désesquelles [Science 292, 1654 (2001)] use changes in age-specific probabilities of death over the decade from 1985 to 1995 to make long-term projections, one out to the year 2577. It is more appropriate to base long-term projections on long-term historical data and to use changes in central death rates. See R. D. Lee, Science 292, 1654 (2001), as well as the references given above.

For information about record longevity, see B. Jeune and J. W. Vaupel, Eds., Exceptional Longevity (Odense Univ. Press, Denmark, 1995) online at; B. Jeune and J. W. Vaupel, Eds., Validation of Exceptional Longevity (Odense Univ. Press, Denmark, 1999); and J. R. Wilmoth, L. J. Deegan, J. Lundstrom, and S. Horiuchi, Science 289, 2366 (2000).

Further Arguments and Evidence about Life-Expectancy Limits

S. J. Olshansky, B. A. Carnes, and A. Désesquelles [Science 292, 1654 (2001)] emphasize a theoretical barrier to longer life expectancy: "entropy in the life table means that small but equal incremental gains in life expectancy require progressively larger reductions in mortality.... Projections based on biodemographic principles that recognize the underlying biology within the life table would lead to more realistic forecasts of life expectancy that reflect the demographic reality of entropy in the life table." Entropy in the life table is merely the statistic -Integration Symbols(a,t)ln s(a,t)da/Integration Symbols(a,t)da, where s(a,t) is the probability of surviving from birth to age a at age-specific death rates prevailing at time t. Contrary to Olshansky et al.'s claim, in countries with long life expectancies a continuing rate of decline in age-specific death rates of N percent per year will increase life expectancy at birth by about N years per decade [J. W. Vaupel, Pop. Stud. 40, 147 (1986); J. W. Vaupel and V. Canudas Romo, in E. J. Docker et al., Eds., Optimization, Dynamics, and Economic Analysis: Essays in Honor of Gustav Feichtinger (Physica Verlag, New York, 2000), pp. 345-352, online at]. Note that steady rates of change in mortality levels produce steady absolute increases in life expectancy: This relationship may underlie the linear trend of record life expectancy. In any case, valid biodemographic principles impose no insurmountable barriers to longer lives. See references in note (14-16) of the main text of this article and K. W. Wachter, C. E. Finch, Eds., Between Zeus and the Salmon: The Biodemography of Longevity (National Academy Press, Washington, DC, 1997); J. R. Carey, D. S. Judge, Pop. English Select. 13, 9 (2001); and J. R. Carey, D. S. Judge, Pop. Dev. Rev. 27, 411 (2001).

If the expectation of life in developed countries were approaching an imminent maximum, then the pace of improvement in mortality in the countries with the highest life expectancies would be slower than the pace in countries with shorter life expectancies. There is, however, no correlation between the level of life expectancy and the pace of improvement. Indeed, in the current life-expectancy leader, Japan, death rates are falling exceptionally rapidly. Furthermore, as life expectancy rose over the course of the 20th century, the pace of mortality improvement at older ages accelerated. Even after age 100, death rates are falling. Female life expectancy is higher than the male level in long-lived countries, but female life expectancy is increasing somewhat more rapidly. See reference (13) of the main text and V. Kannisto, Development of Oldest-Old Mortality, 1950-1990 (Odense Univ. Press, Denmark, 1994) online at; V. Kannisto, The Advancing Frontier of Survival (Odense Univ. Press, Denmark, 1996) online at; A. R. Thatcher, V. Kannisto, J. W. Vaupel, The Force of Mortality at Ages 80 to 120 (Odense Univ. Press, Denmark, 1998), online at; J. W. Vaupel, Philos. Trans. R. Soc. London B 352, 1799 (1997); and J. R. Wilmoth, in K. W. Wachter and C. E. Finch, Eds., Between Zeus and the Salmon: The Biodemography of Longevity (National Academy Press, Washington, DC, 1997).

The conventional view is that "future gains in life expectancy cannot possibly match those of the past, because they were achieved primarily by saving the lives of infants and children-something that happens only once for a population" [S. J. Olshansky, B. A. Carnes, and A. Désesquelles, Science 292, 1654 (2001)]. The sustained improvement in best-practice life expectancy belies this contention.

Reinforcing processes may help sustain the increase in record life expectancy. For instance, the decline in childhood diseases may lead to fitter adults and fewer premature deaths may reduce bereavement effects, an important risk factor for mortality. The improvements also increase the number of people who survive to be elderly, leading to greater attention to health at those ages. Increasingly prosperous, educated populations aided by armies of researchers, physicians, nurses, and public-health workers incessantly seize opportunities to push death back. Economy, politics, and society may adapt to reflect the changing age-structure of the population.

This argument was proposed by Tuljapurkar et al. in seeking to explain the universal pattern of mortality decline in the richest countries over the past 50 years [reference (3) in main text]. They highlight "the roughly constant long-run exponential rates of decline" in age-specific death rates and seek to explain this remarkable "linear" (i.e., on a log scale) pattern of decline. Their work provides another critique of the pessimism of mortality forecasts and suggests that the exponential increase in national income per capita in advanced countries may have been enough to offset the increasing marginal costs of reducing morbidity and death.

Note, however, that while the United States may be one of the richest countries in the world, it has not been the healthiest. Similarly high levels of life expectancy are now enjoyed by much poorer countries, such as Chile and Costa Rica. International transfers of health technology over the past century have contributed to both rising and converging life expectancy around the globe [C. Wilson, Pop. Dev. Rev. 28, 234 (2001)]..

Supplemental Figure 1. Female life expectancy in the record-holding country, based on the annual data shown in supplementary table 1. The fitted trend has a slope of 0.243 and r2 = 0.982.

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Supplemental Figure 2. Male (blue squares) and female (red circles) life expectancy in the record-holding country, based on the annual data shown in supplementary table 1. For males the fitted line has a slope of 0.222 and r2 = 0.980.

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Supplemental Figure 3. Female life expectancy in the record-holding country (bold red circles) and in the second-best country (green circles), based on the annual data shown in supplementary table 1. The line for second-best life expectancy has a slope of 0.260 and r2 = 0.979.

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Supplemental Figure 4. Male life expectancy in the record-holding country (bold blue squares) and in the second-best country (green squares), based on the annual data shown in supplementary table 1. The line for second-best life expectancy has a slope of 0.240 and r2 = 0.975.

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Supplemental Figure 5. Female life expectancy in the record holding country based on the simplified data shown in supplementary table 1 as well as additional data for years before 1840. The data before 1840 pertain to nonmetropolitan parishes in England [E. A. Wrigley et al., English Population History from Family Reconstitution: 1580-1837 (Cambridge Univ. Press, Cambridge, 1997)]. Available national data on life expectancy in Denmark, Norway and Sweden before 1840 suggest that female life expectancy in these countries was similar to that in England. For Sweden, see the Human Mortality Database or For Denmark, see H. C. Johansen and J. Oeppen, Danish Population Estimates 1665-1840, Research Report 21, Danish Center for Demographic Research, Odense, Denmark.

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Supplemental Table 1. Estimates of maximum average longevity for females. Limits pertain to female life expectancy at birth, with two exceptions (*). Fries asserted that if all premature death were eliminated, ages at death would follow a normal distribution with a mean of 85 and a standard deviation that he gave as 5 in 1980 and as 7 in 1990. In normal distributions, the mode and median equal the mean. The modal (i.e., most common) age of death was 86 in the 1985 Japanese female life table. The median age of death exceeded 85 in the 1994 life table and the mean age of death after age 50 exceeded 85 in the 1996 life table. For Olshansky et al., the value of 85 shown in this table is 50 plus remaining life expectancy at age 50, which they assert will not exceed 35 years. The text of their article implies that this assertion holds for women as well as for men. The maxima set by Dublin, Dublin and Lotka, Siegel, and Fries also hold for both men and women, whereas the other limits given in this table hold for women only: male caps are lower. References are given in the Supplemental Material, above.
SourceLimit*Date publishedDate exceededExceeded by females in
Dublin64.819281921New Zealand
Dublin and Lotka69.919361941Iceland
United Nations77.519731972Sweden
United Nations80.019791976Iceland
World Bank82.519841993Japan
United Nations82.519851993Japan
United Nations87.51989
World Bank90.01989
Olshansky et al. 85.0*19901996Japan
Coale and Guo84.91991
United Nations92.51998
Olshansky et al. 88.02001

Supplemental Table 2. Level of male and female life expectancy at birth [e(0)] in best-practice and second-best countries from 1840 to 2000. The simplified data in the second column were used to produce Fig. 1, as well as supplementary fig. 5. The annual data in subsequent columns were used to produce suppl. table 1 and supplementary figs. 1 to 4, as well as the regression lines in Fig. 1 and 2. After 1948 the simplified data are the same as the annual data. Before 1948 there are gaps in the simplified data. The gaps arise for three reasons. First, we omitted data for 1914-1919 (World War I and influenza) and 1939-1945 (World War II). Second, life tables that covered several years of time, sometimes five or even ten years, were often published before 1948. In the simplified data, we include the life expectancy from such life tables only at the mid-year of the period covered. If it appears that the country was the record holder for the entire period, we do not include life expectancy values for other years in the period. Third, there were sometimes gaps before 1948 between life tables published for specific countries. If it appeared likely that a country was the record-holder even in years when there was a gap in the life tables for that country, then we do not include life expectancy values during the gap in the simplified data. In contrast, in the annual data the life expectancy published for a period of years is assumed to hold for every year during that period: this is what produces the horizontal patterns in supplementary figs. 1 to 4. Furthermore, the record-holder in a year is chosen from among the countries that have published life expectancy estimates for that year: countries that did not publish estimates for that year are not considered. It is reassuring that the linear trend in life expectancy is not affected by the use of simplified vs. annual data and that a linear trend holds for males as well as females and for the second-best country as well as the best-practice country. The slope of the regression line for best-practice female life expectancy is 0.243 regardless of whether the simplified or annual data are used and r2 is 0.992 for the simplified data and 0.982 for the annual data.
Simplified data
Annual data
2nd e(0)
2nd e(0)
187654.22New Zealand54.22New Zealand48.3351.99New Zealand45.57
188057.26New Zealand53.2554.44New Zealand50.48
188157.26New Zealand56.3254.44New Zealand52.75
188257.26New Zealand50.8454.44New Zealand47.20
188357.26New Zealand50.8454.44New Zealand48.50
188457.26New Zealand52.0354.44New Zealand49.54
188557.26New Zealand52.3054.44New Zealand49.76
188657.26New Zealand57.26New Zealand52.8754.44New Zealand50.48
188757.26New Zealand52.9854.44New Zealand50.57
188857.26New Zealand53.5754.44New Zealand51.03
188957.26New Zealand53.3554.44New Zealand51.09
189057.26New Zealand51.7754.44New Zealand49.12
189158.09New Zealand57.2655.29New Zealand54.44
189258.09New Zealand57.2655.29New Zealand54.44
189358.09New Zealand58.09New Zealand54.7655.29New Zealand51.06
189458.09New Zealand54.7655.29New Zealand51.06
189558.09New Zealand55.4755.29New Zealand52.89
189659.95New Zealand55.8957.37New Zealand52.22
189759.95New Zealand55.6757.37New Zealand52.84
189859.95New Zealand59.95New Zealand56.1557.37New Zealand53.21
189959.95New Zealand54.7657.37New Zealand51.06
190059.95New Zealand55.1457.37New Zealand51.79
190160.55New Zealand58.8458.09New Zealand55.20
190260.55New Zealand58.8458.09New Zealand55.20
190360.55New Zealand60.55New Zealand58.8458.09New Zealand55.20
190460.55New Zealand58.8458.09New Zealand55.20
190560.55New Zealand58.8458.09New Zealand55.20
190661.76New Zealand58.8459.17New Zealand55.64
190761.76New Zealand58.8459.17New Zealand55.75
190861.76New Zealand61.76New Zealand58.8459.17New Zealand55.24
190961.76New Zealand59.5759.17New Zealand57.22
191061.76New Zealand59.4759.17New Zealand56.47
191163.48New Zealand61.1160.96New Zealand57.35
191263.48New Zealand59.7860.96New Zealand57.13
191363.48New Zealand63.48New Zealand60.0860.96New Zealand57.26
191463.48New Zealand59.9160.96New Zealand57.00
191563.48New Zealand59.7860.96New Zealand56.39
192165.93New ZealandDagger Symbol63.3162.58New ZealandDagger Symbol60.30
192265.43New Zealand65.56New Zealand63.3163.07New Zealand60.30
192365.14New Zealand63.8762.59New Zealand61.81
192467.02New Zealand63.5163.76New Zealand62.19
192566.72New Zealand65.1164.07New Zealand62.26
192666.57New Zealand66.27New Zealand64.4763.38New Zealand62.23
192766.96New Zealand64.3264.03New Zealand61.82
192866.79New Zealand64.6364.11New Zealand62.87
192966.95New Zealand63.8363.69New Zealand61.38
193067.47New Zealand66.5964.32New Zealand63.89
193167.88New Zealand67.90New Zealand65.6065.05New Zealand63.60
193268.40New Zealand67.1466.28New Zealand64.70
193369.25New Zealand67.1466.20New Zealand65.36
193468.54New Zealand67.6665.83Netherlands65.60
193569.25New Zealand67.2466.34New Zealand65.74
193668.45New Zealand68.56New Zealand67.4066.05Netherlands65.75
193768.51New Zealand67.7066.19Netherlands65.87
193969.02New Zealand69.0066.90Netherlands65.76
194069.59New Zealand68.5766.15New Zealand65.35
194470.30Iceland70.0066.58New Zealand66.16
194771.70New Zealand71.6368.32Norway68.31

*In 1853 and in some subsequent years, the life expectancy given in the simplified data differs from that for the same country given in the annual data. The simplified data are sometimes based on life tables that pertain to a period of several years, usually five or ten years, whereas the annual data are based on calculations for the specific year.

Dagger SymbolData for New Zealand pertain to the non-Maori population. Data for the Maori population are of very poor quality until 1926. From 1926 to the present the quality of the data has gradually improved but there are still serious problems of age misreporting at older ages. See Ian Pool, Te Iwi Maori: A New Zealand Population: Past, Present and Projeced (Auckland Univ. Press, Auckland, 1991); I. Pool, N. Z. Pop. Rev. 8, 2 (1982); V. Kannisto, The Advancing Frontier of Survival (Odense Univ. Press, Odense, 1996), p. 17. From 1921 through 1955 the annual data in supplementary table 2 are derived from S. K. Jain, Source Book of Population Data: New Zealand, Non-Maori Population 1921-1967, Vols. 1-3 (Research School of Social Sciences, Australian National Univ., Canberra, 1972). Because Jain's life tables end with the interval 75+, he based his life-expectancy calculations on an estimate of the life years lived above age 75, L75+. Jain used an approximation that consistently underestimates life expectancy at birth compared with the official life tables for New Zealand. We estimated life expectancy from Jain's data by using the approximation L75+ = l75/m75+, where l75is the life-table probability of survival to age 75 and m75+ is the central death rate above age 75. Our estimates are consistent with the official estimates over the period from 1921 through 1955.