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Ever since gompertz

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Abstract

In 1825 British actuary Benjamin Gompertz made a simple but important observation that a law of geometrical progression pervades large portions of different tables of mortality for humans. The simple formula he derived describing the exponential rise in death rates between sexual maturity and old age is commonly referred to as the Gompertz equation—a formula that remains a valuable tool in demography and in other scientific disciplines. Gompertz’s observation of a mathematical regularity in the life table led him to believe in the presence of a law of mortality that explained why common age patterns of death exist. This law of mortality has captured the attention of scientists for the past 170 years because it was the first among what are now several reliable empirical tools for describing the dying-out process of many living organisms during a significant portion of their life spans. In this paper we review the literature on Gompertz’slaw of mortality and discuss the importance of his observations and insights in light of research on aging that has taken place since then.

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References

  • Abernathy, J.D. 1979. “The Exponential Increase in Mortality Rate with Age Attributed to Wearing-Out of Biological Components.” Journal of Theoretical Biology 80:333–54.

    Article  Google Scholar 

  • Barinaga, M. 1992. “Mortality: Overturning Received Wisdom.” Science 258:398–99.

    Article  Google Scholar 

  • Beard, R.E. 1959. “Note on Some Mathematical Mortality Models.” Pp. 121–127 in CIBA Foundation Colloquia on Ageing, Vol. 5, edited by G.E.W. Wolstenholme and M. O’Connor. Boston: Little, Brown, and Company.

    Google Scholar 

  • Berlin, N.I. 1960. “An Analysis of Some Radiation Effects on Mortality.” Pp. 121–27 in The Biology of Aging, edited by B.L. Strehler, J.D. Ebert, H.B. Glass, and N.W. Shock. Washington, DC: American Institute of Biological Sciences.

    Google Scholar 

  • Brody, S. 1924. “The Kinetics of Senescence.” Journal of General Physiology 6:245–57.

    Article  Google Scholar 

  • Brooks, A., G.J. Lithgow, and T.E. Johnson. 1994. “Mortality Rates in a Genetically Heterogeneous Population of Caenorhabditis elegans.” Science 263:668–71.

    Article  Google Scholar 

  • Brownlee, J. 1919. “Notes on the Biology of a Life-Table.” Journal of the Royal Statistical Society 82:34–77.

    Article  Google Scholar 

  • Brues, A.M. and G.A. Sacher. 1952. “Analysis of Mammalian Radiation Injury and Lethality.” Pp. 441–65 in Symposium on Ra-diobiology, edited by J.J. Nickson. New York: John Wiley and Sons.

    Google Scholar 

  • Carey, J.R., P. Liedo, D. Orozco, and J.W. Vaupel. 1992. “Slowing of Mortality Rates at Older Ages in Large Medfly Cohorts.” Science 258:457–61.

    Article  Google Scholar 

  • Carnes, B.A. and S.J. Olshansky. 1993. “Evolutionary Perspectives on Human Senescence.” Population and Development Review 19:793–806.

    Article  Google Scholar 

  • Carnes, B.A., S.J. Olshansky, and D.A. Grahn. 1996. “Continuing the Search for a Law of Mortality.” Population and Develop ment Review 22:231–64.

    Article  Google Scholar 

  • Charlesworth, B. 1994. Evolution in Age-Structured Populations. Cambridge: Cambridge University Press.

    Book  Google Scholar 

  • Clark, R.D. 1950. “A Bio-Actuarial Approach to Forecasting Rates of Mortality.” Proceedings of the Centerary Assembly of the Institute of Actuaries 2: 12–27.

    Google Scholar 

  • Connor, A., K.M. Weiss, and S.C. Weeks. 1993. “Evolutionary Models of Quantitative Disease Risk Factors.” Human Biology 65:917–40.

    Google Scholar 

  • Deevey, E.S., Jr. 1947. “Life Tables for Natural Populations of Animals.” Quarterly Review of Bioiogy 22:283–314.

    Article  Google Scholar 

  • Doubal, S. 1982. “Theory of Reliability, Biological Systems and Aging.” Mechanisms of Ageing and Development 18:339–53.

    Article  Google Scholar 

  • Economos, A. 1980. “Kinetics of Metazoan Mortality.” Journal of Social Biology 3:317–29.

    Google Scholar 

  • — 1982. “Rate of Aging, Rate of Dying and the Mechanism of Mortality.” Archives of Gerontological Geriatrics 1:3–27.

    Article  Google Scholar 

  • Failla, G. 1958. “The Aging Process and Cancerogenesis.” Annals of the New York Academy of Sciences 71:1124–40.

    Article  Google Scholar 

  • — 1960. “The Aging Process and Somatic Mutations.” Pp. 170–75 in The Biology of Aging edited by B.L. Strehler, J.D. Ebert, H.B. Glass, and N.H. Shock. Washington, DC: American Institute of Biological Sciences.

    Google Scholar 

  • Finch, C.E. 1990. Longevity, Senescence, and the Genome. Chicago: University of Chicago Press.

    Google Scholar 

  • Finch, C.E., M.C. Pike, and M. Witten. 1990. “Slow Mortality Rate Accelerations During Aging in Some Animals Approximate that of Humans.” Science 249:902–905.

    Article  Google Scholar 

  • Fukui, H.H., L. Xiu, and J.W. Curtsinger. 1993. “Slowing of Age-Specific Mortality Rates in Drosophila melanogaster.” Experi-mental Gerontology 28:585–99.

    Article  Google Scholar 

  • Gavrilov, L.A. and N.S. Gavrilova. 1991. The Biology of Life Span: A Quantitative Approach. Switzerland: Harwood Academic Publishers.

    Google Scholar 

  • Gompertz, B. 1820. “A Sketch on an Analysis and the Notation Applicable to the Estimation of the Value of Life Contingencies.” Philosophical Transactions of the Royal Society of London 110:214–94.

    Article  Google Scholar 

  • — 1825. “On the Nature of the Function Expressive of the Law of Human Mortality and on a New Mode of Determining Life Contingencies.” Philosophical Transactions of the Royal Society of London 115:513–85.

    Article  Google Scholar 

  • — 1862. “A Supplement to Two Papers Published in the Transactions of the Royal Society on the Science Connected with Human Mortality, This is a Supplement Published in 1862 to Papers Published in 1820 and 1825.” Philosophical Transactions of the Royal Society of London 152:511–59.

    Article  Google Scholar 

  • — 1872. “On One Uniform Law of Mortality from Birth to Extreme Old Age, and on the Law of Sickness.” Journal of the Institute of Actuaries 16:329–44.

    Google Scholar 

  • Grahn, D. 1970. “Biological Effects of Protracted Low Dose Radiation Exposure of Man and Animals.” Pp. 101–36 in Late Effects of Radiation edited by R.J.M. Fry, D. Grahn, M.L. Griem, and J.H. Rust. London: Taylor and Francis.

    Google Scholar 

  • Greenwood, M. 1928. “Laws of Mortality from the Biological Point of View.” Journal of Hygiene 28:267–94.

    Article  Google Scholar 

  • Gumbel, E.J. 1954. “Statistical Theory of Extreme Values and Some Practical Applications: A Series of Lectures.” National Bureau of Standards, Applied Mathematics Series No. 33. Washington, DC: National Bureau of Standards.

    Google Scholar 

  • Hamilton, W.D. 1966. “The Moulding of Senescence by Natural Selection.” Journal of Theoretical Biology 12:12–45.

    Article  Google Scholar 

  • Harmon, D. 1992. “Free Radical Theory of Aging.” Mutation Research 275:257–66.

    Article  Google Scholar 

  • Heligman, L. and J.H. Pollard. 1980. “The Age Pattern of Mortality.” Journal of the Institute of Actuaries 107:49–80.

    Google Scholar 

  • Horiuchi, S. and A.J. Coale. 1990. “Age Patterns of Mortality for Older Women: An Analysis Using Age-Specific Rate of Mortality Change with Age.” Mathematical Population Studies 2(4): 245–67.

    Article  Google Scholar 

  • Horiuchi, S. and J. Wilmoth. 1996. “Deceleration in the Age Pattern of Mortality at Older Ages.” Unpublished manuscript. Laboratory of Populations, Rockefeller University.

  • Kirkwood, T.B.L. 1977. “Evolution of Aging.” Nature 270:301–304.

    Article  Google Scholar 

  • Lawless, J.F. 1982. Statistical Models and Methods for Lifetime Data. New York: John Wiley and Sons.

    Google Scholar 

  • Lederberg, J., R.E. Shope, and S.C. Oaks, Jr. 1992. Emerging Infections: Microbial Threats to Health in the United States. Washington, DC: National Academy Press.

    Google Scholar 

  • Loeb, J. and J.H. Northrop. 1916. “Is There a Temperature Coefficient for the Duration of Life?” Proceedings of the National Academy of Sciences 2:456–57.

    Article  Google Scholar 

  • — 1917a. “What Determines the Duration of Life in Metazoa?” Proceedings of the National Academy of Sciences 3:382–86.

    Article  Google Scholar 

  • —. 1917b. “On the Influence of Food and Temperature upon the Duration of Life.” Journal of Biological Chemistry 32: 102–21.

    Google Scholar 

  • Lorenz, E. 1950. “Some Biologic Effects of Long-Continued Irradiation.” American Journal of Roentgenol Radium Therapy 63:176–85.

    Google Scholar 

  • Makeham, W.M. 1860. “On the Law of Mortality and the Construction of Annuity Tables.” Journal of the Institute of Actuaries 6:301–10.

    Google Scholar 

  • — 1867. “On the Law of Mortality.” Journal of the Institute of Actuaries 13:325–58.

    Google Scholar 

  • — 1872. “Explanation and Example of a Method Constructing Mortality Tables with Imperfect Data; and of the Extension of Gompertz’s Theory to the Entire Period of Life.” Journal of the Institute of Actuaries 16:344–54.

    Google Scholar 

  • — 1889. “On the Further Development of Gompertz’s Law.” Journal of the Institute of Actuaries 28: 152–60, 185–92.

    Google Scholar 

  • — 1890. “On the Further Development of Gompertz’s Law.” Journal of the Institute of Actuaries 29:316–32.

    Google Scholar 

  • Manton, K.G., C.H. Patrick, and E. Stallard. 1980. “Population Impact of Mortality Reduction: The Effects of Elimination of Major Causes of Death on the “Saved’ Population.” International Journal of Epidemiology 9: 111–20.

    Article  Google Scholar 

  • Manton, K.G. and B. Soldo. 1985. “Dynamics of Health Changes in the Oldest Old: New Perspectives and Evidence.” Milbank Memorial Fund Quarterly/Health and Society 63:206–85.

    Article  Google Scholar 

  • Manton, K.G., E. Stallard, J.P. Creason, W.B. Riggan, and M.A. Woodbury. 1985. “Compartment Model Approaches for Estimating the Parameters of a Chronic Disease Process Under Changing Risk Factor Exposures.” Environmental Health Perspectives 19:151–69.

    Google Scholar 

  • Manton, K.G., E. Stallard, and J.W. Vaupel. 1981. “Methods for Comparing the Mortality Experience of Heterogeneous Populations.” Demography 18:389–410.

    Article  Google Scholar 

  • Medawar, P.B. 1952. An Unsolved Problem of Biology. London: Lewis.

    Google Scholar 

  • Mildvan, A. and B.L. Strehler. 1960. “A Critique of Theories of Mortality.” Pp. 216–35 in The Biology of Aging. edited by B.L. Strehler, J.D. Ebert, H.B. Glass, and N.W. Shock. Washington, DC: American Institute of Biological Sciences.

    Google Scholar 

  • Olshansky, S.J. and B.A. Carnes. 1994. “Demographic Perspectives on Human Senescence.” Population and Development Review 20:57–80.

    Article  Google Scholar 

  • Olshansky, S.J., B.A. Carnes, R. Rogers, and L. Smith. Forthcoming. ”Epidemiologic Transitions: The Re-Emergence of Infectious and Parasitic Diseases.” Population Bulletin.

  • Pakin, Y.V. and S.M. Hrisanov. 1984. “Critical Analysis of the Applicability of the Gompertz-Makeham Law in Human Populations.” Gerontology 30:8–12.

    Article  Google Scholar 

  • Patz, J.A., P.R. Epstein, T.A. Burke, and l.M. Balbus. 1996. “Global Climate Change and Emerging Infectious Diseases.” Journal of the American Medical Association 275:217–23.

    Article  Google Scholar 

  • Pearl, R. 1921. “Experimental Studies on the Duration of Life.” The American Naturalist 55:481–509.

    Article  Google Scholar 

  • — 1922. “A Comparison of the Laws of Mortality in Drosophila and in Man.” The American Naturalist 56:398–405.

    Google Scholar 

  • Pearl, R. and J.R. Miner. 1935. “Experimental Studies on the Duration of Life. XIV. The Comparative Mortality of Certain Lower Organisms.” Quarterly Review of Biology 10:60–79.

    Article  Google Scholar 

  • Perks, W. 1932. “On Some Experiments in the Graduation of Mortality Statistics.” Journal of the Institute of Actuaries 63:12–57.

    Google Scholar 

  • Perls, T. 1995. “The Oldest Old.” Scientific American 272:70–75.

    Article  Google Scholar 

  • Pinner, R.W., S.M. Teutsch, L. Simonsen, L.A. Klug, J.M. Graber, M.J. Clarke, and R.L. Berkelman. 1996. “Trends in Infectious Diseases Mortality in the United States.” Journal of the American Medical Association 275: 189–93.

    Article  Google Scholar 

  • Pollard, J.R. and K. Streatfield. 1979. “Factors Affecting Mortality and the Length of Life.” Presented at the Joint Convention of The Institute of Actuaries of Australia, Christchurch, New Zealand.

  • Pollard, J.H. and E. Valkovics. 1992. “The Gompertz Distribution and its Applications.” Genus 48: 15–27.

    Google Scholar 

  • Riggs, J.E. 1993. “The Gompertz Function: Distinguishing Mathematical from Biological Limitations.” Mechanisms of Ageing and Development 69:33–36.

    Article  Google Scholar 

  • Sacher, G.A. 1950a. “The Survival of Mice Under Duration-of-Life Exposure to X-Rays at Various Dose Rates.” Working paper CH-3900, Metallurgical Laboratory, University of Chicago.

  • Sacher, G.A. 1950b. “Preliminary Report: A Comparative Study of Radiation Lethality in Several Species of Experimental Animals Irradiated for the Duration-of-Life.” Pp. 105–22 in quarterly report number ANL-4488, Argonne National Laboratory.

  • — 1955. “A Comparative Analysis of Radiation Lethality in Mammals Exposed at Constant Average Intensity for the Duration of Life.” Journal of the National Cancer Institute 15:112–543.

    Google Scholar 

  • Sacher, G.A. 1956a. “Survival of Mice Under Duration-of-Life Exposure to X-Rays at Various Rates.” Pp. 435–63 in Biological Effects of External X and Gamma Radiation, Part 2, edited by R.E. Zirkle. Washington, DC: AEC TID-5220.

  • — 1956b. “On the Statistical Nature of Mortality, with Especial Reference of Chronic Radiation Mortality.” Radiology 67:250–57.

    Google Scholar 

  • — 1960. “Problems in the Extrapolation of Long-Term Effects from Animals to Man.” Pp. 3–10 in Symposium on the Delayed Effects of Whole-Body Radiation, edited by B.B. Watson. Bethesda: Operations Research Office, Johns Hopkins University.

    Google Scholar 

  • — 1966. “The Gompertz Transformation in the Study of the Injury-Mortality Relationship: Application to Late Radiation Effects and Ageing.” Pp. 411–41 in Radiation & Ageing, edited by P.J. Lindop and G.A. Sacher. London: Taylor and Francis.

    Google Scholar 

  • Sacher, G.A. and D. Grahn. 1964. “Survival of Mice under Duration-of-Life Exposure to Gamma Rays. I. The Dosage-Survival Relation and the Lethality Function.” Journal of the National Cancer Institute 32:277–320.

    Google Scholar 

  • Sacher, G.A. and E. Trucco. 1962. “The Stochastic Theory of Mortality.” Annals of the New York Academy of Sciences 96:985–1007.

    Article  Google Scholar 

  • Shock, N.W. 1961. “Physiological Aspects of Aging in Man.” Annual Review of Physiology 23:97–122.

    Article  Google Scholar 

  • Simms, H.S. 1948. “Logarithmic Increase in Mortality as a Manifestation of Aging.” Journal of Gerontology 1: 13–26.

    Google Scholar 

  • Stearns, S.C. 1992. “Reproductive Life Span and Ageing.” Pp. 180–205 in The Evolution of life Histories. London: Oxford University Press.

    Google Scholar 

  • Strehler, B.L. 1959. “Origin and Comparison of the Effects of Time and High-Energy Radiations on Living Systems.” Quarterly Review of Biology 34: 117–42.

    Article  Google Scholar 

  • — 1960. “Fluctuating Energy Demands as Determinants of the Death Process (A Parsimonious Theory of the Gompertz Function).” Pp. 309–14 in The Biology of Aging. Washington, DC: American Institute of Biological Sciences.

    Google Scholar 

  • — 1977. Time. Cells. and Aging, 2nd edition. New York: Academic Press.

    Google Scholar 

  • Strehler, B.L. and A.S. Mildvan. 1960. “General Theory of Mortality and Aging (A Stochastic Model Relates Observations on Aging, Physiologic Decline, Mortality, and Radiation).” Science 132:14–19.

    Article  Google Scholar 

  • Szilard, L. 1959. “On the Nature of the Aging Process.” Proceedings of the National Academy of Sciences 45:30–45.

    Article  Google Scholar 

  • Vaupel, J.W., K.G. Manton, and E. Stallard. 1979. “The Impact of Heterogeneity on Individual Frailty on the Dynamics of Mortality.” Demography 16:439–54.

    Article  Google Scholar 

  • Weibull, W. 1951. “A Statistical Distribution Function of Wide Applicability.” Journal of Applied Mechanics 18:293–97.

    Google Scholar 

  • Weismann, A. 1891. Essays Upon Heredity and Kindred Biological Problems. Oxford: Clarendon Press.

    Google Scholar 

  • Weiss, K. 1989. “Are the Known Chronic Diseases Related to the Human Lifespan and its Evolution?” American Journal of Human Biology 1:307–19.

    Article  Google Scholar 

  • — 1990. “The Biodemography of Variation in Human Frailty.” Demography 27: 185–206.

    Article  Google Scholar 

  • Weiss, K., R.E. Ferrell, and C.T. Ranis. 1984. “A New World Syndrome of Metabolic Diseases with a Genetic and Evolutionary Basis.” Yearbook of Physical Anthropology 27: 153–78.

    Article  Google Scholar 

  • Williams, G.C. 1957. “Pleiotropy, Natural Selection, and the Evolution of Senescence.” Evolution 11:298–311.

    Article  Google Scholar 

  • Wilson, M.E., R. Levins, and A. Spielman. 1994. Disease in Evolution: Global Changes and Emergence of Infectious Diseases New York: New York Academy of Sciences.

    Google Scholar 

  • Witten, M. 1988. “A Return to Time, Cells, Systems, and Aging: V. Further Thoughts on Gompertzian Survival Dynamics-The Geriatric Years.” Mechanisms of Aging and Development 46: 175–200.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Medicine, University of Chicago, 5841 S. Maryland Avenue, MC 6098, Chicago, IL, 60637

    S. Jay Olshansky

  2. Argonne National Laboratory, USA

    Bruce A. Carnes

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  1. S. Jay Olshansky
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  2. Bruce A. Carnes
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Correspondence to S. Jay Olshansky.

Additional information

The authors thank Shiro Horiuchi and anonymous reviewers for comments on an earlier draft of this manuscript. Funding for this work was provided by the National Institute on Aging (Grant AG-00577-01), the Social Security Administration (Grant 10-P-98347-5-01), and the Office of Health and Environmental Research and Offiee of Epidemiology and Health Surveillance (Contract W-31-109-ENG-38). Portions of this manuscript were presented at the Michigan-RAND Summer Seminar on the Demography and Economics of Aging held in Santa Monica, California in August 1995 and at the annual meetings of the Gerontological Society of America, held in Los Angeles, California in November 1995.

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Olshansky, S.J., Carnes, B.A. Ever since gompertz. Demography 34, 1–15 (1997). https://doi.org/10.2307/2061656

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