Law of universal mortality

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 66, Issue 1, 2002, Pages

  Azbel’, Mark Ya ^a  

^a TEL AVIV UNIVERSITY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

BIOMEDICAL ENGINEERING; GENES; LAWS AND LEGISLATION; MATHEMATICAL MODELS; PHASE EQUILIBRIA; PROBABILITY; THERMODYNAMICS;

HUMAN BIRTH; HUMAN MORTALITY; INFANT MORTALITY; THERMODYNAMIC MECHANISM;

INVARIANCE;

EID: 41349089880     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.66.016107     Document Type: Article

References (37)

1. C. E. Finch, Longevity, Senescence and Genome (Chicago University Press, Chicago, 1990);B. Charlesworth, Evolution in Age-Structured Populations (Cambridge University Press, Cambridge, 1994);K. W. Wachter and C. E. Finch, Between Zeus and Salmon. The Biodemography of Longevity (National Academic, Washington, D.C., 1997);C. E. Finch and T. B. Kirkwood, Chance, Development and Aging (Oxford University Press, New York, 2000);
2. T. B. L. Kirkwood and S. N. Austad, Nature (London) 408, 233 (2000).
3. A. J. Coale, P. Demeny, and B. Vaughan, Regional Model Life Tables and Stable Populations, 2nd ed. (Academic, New York, 1993);
4. R. D. Lee and L. R. Carter, J. Am. Stat. Assoc. 87, 659 (1993);Indirect Techniques for Demographic Estimation, Manual X (UN, New York, 1993), pp. 12–21, and references therein.
5. D. Stauffer, in Biological Evolution and Statistical Physics, edited by M. Lässig and A. Valleriani (Springer, Berlin, 2002), and references therein.
6. See a reliability theory of mortality by L. A. Gavrilov and N. S. Gavrilova, J. Theor. Biol. 213, 527 (2001).
7. Australian Life Tables (Australian Government Actuary, Canberra, 1999);Die Sterbentafels (Statistischen Nachrichten, Wien, Austria, 1999);Tables de Mortalité (Statistics Belgium, Brussels, 1999);Berkeley Mortality Database, http://demog.berkeley.edu/wilmoth/mortality;Life Tables for Japan (Ministry of Health and Welfare, Tokyo, 1994);Life Tables for Canada and Provinces (Bureau of Statistics, Ottawa, 1995);Historical Database of Mortality for England and Wales (The Government Actuary’s Department, London, UK, 1999);Life Tables for Finland (Statistics Finland, Helsinkr, 1999);Statistics Figures for Everyone (Federal Statistics Office, Wiesbaden, Germany, 1986);Life Tables for Iceland (Statistics Iceland, Rykyavik, Iceland, 1999);Life Tables for Ireland (Statistics, Dublin, 1995);Life Tables for Switzerland (Swiss Federal Statistical Office, Zürich, 1995);S.-E. Mamaelund and J.-K. Borgan, Cohort and Period Mortality in Norway, Aktuelle Beforkningstung (Statistics Norway, Oslo-Kongsvinger, 1996/1999);Life Tables (Registrar General for Scotland, Edinburgh, 1995);National Central Bureau of Statistics (1974), Statistical Abstracts of Sweden (1996), Life Tables (1891–1995), Stockholm, Sweden;Vital Statistics of the United States, Life Tables (National Center or Health Statistics, Hyattsville, MD, 1997).
8. The rate (Formula presented) where (Formula presented) is the number of survivors up to age x. It significantly changes with the country (in 1947 the female infant mortality (Formula presented) was three times higher in Japan than in Sweden), time (in Japan (Formula presented) halved from 1947 till 1955), age specific factors (from 1851 till 1900 English female mortality decreased 2.6 times for 10 yr olds and by 5% for breast fed infants, prevented from contaminated food and water), deceases (the 1918 flu pandemic in Europe increased Swedish female mortality threefold at 28 yr, but changed it little for newborns and elderly), wars (French male mortality at 40 yr was 2.5 times higher in 1915 than in 1913), genotype and its life history (acquired components yield significantly different mean lifespans of even genetically identical populations in a uniform environment 178), and genetic and environmental heterogeneity. Mortality rates in the same calendar year and country are significantly different for different population subgroups (e.g., in 1891/1900 Swedish female (Formula presented) was almost twice higher in Stockholm than in the rural area).
9. Everywhere in this paper, I escape any adjustment by using “raw” life table variables, e.g., an integer age x (in years for humans and in days for flies), the mortality rate (Formula presented) [and mortality force (Formula presented)] rather than (Formula presented) the life expectancy (Formula presented) at age x rather than (Formula presented) All universal quantities are related to (Formula presented) rather than to (Formula presented) Note that only (Formula presented) and (Formula presented) are piecewise linear in (Formula presented) and (Formula presented) The only normalization condition is (Formula presented) it implies (Formula presented)
10. J. W. Curtsinger, H. H. Fukui, D. R. Townsend, and J. W. Vaupel, Science 258, 461 (1992);J. R. Carey, Applied Demography for Biologists (Oxford University Press, New York, 1993);
11. J. R. Carey, P. Liedo, D. Orozdo, and J. W. Vaupel, Science 258, 4547 (1992);
12. S. D. Pletcher and J. E. Curtsinger, Evolution (Lawrence, Kans.) 52, 454 (1993).
13. S. M. Jazwinski, Science 263, 54 (1996);
14. A. A. Puca, M. J. Daly, S. J. Brewster, T. C. Matise, J. Barrett, M. Shea-Drinkwater, S. Kang, E. Joyce, J. Nicoli, E. Benson, L. M. Kunkel, and T. Perls, Proc. Natl. Acad. Sci. U.S.A. 98, 10 505 (2001).
15. M. Ya. Azbel’, Proc. Natl. Acad. Sci. U.S.A. 96, 3303 (1999);
16. Proc. Natl. Acad. Sci. U.S.A.M. Ya. Azbel’96, 15 368 (1999).
17. M. Ya. Azbel’, Physica A 297, 235 (2001). The piecewise linear dependence in Eq. (2) is related to the invariance only. The age dependence of (Formula presented) and the actual number of linear segments are determined by the minimal relative mean square deviation of (Formula presented) from (Formula presented) The latter is remarkably low (<0.1 for (Formula presented) and <0.2 for (Formula presented)) and may be refined in further studies, especially of specific subgroups.
18. The first life tables were compiled by the discoverer of the famous comet, E. Halley, Philos. Trans. R. Soc. London 17, 596 (1693);and the great L. Euler, Histoire de l’Academie Royale des Sciences et Belle-Lettres (1760), p. 144.
19. In 1825 the first mortality law was suggested by B. Gompertz, Philos. Trans. R. Soc. London A115, 513 (1825). Thereafter the search for the universal mortality law went on 16. Equation (2) demonstrates that the exact universal law does exist, but only for a certain, accurately defined, universal fraction of mortality (rather than for the total life table mortality).
20. V. Kannisto, Development of Oldest-Old Mortality, 1950–1990 (Odense University Press, Odense, Denmark, 1994);A. R. Thatcher, V. Kannisto, and J. W. Vaupel, The Force of Mortality of Ages 80 to 120 (Odense University Press, Odense, Denmark, 1994);
21. S. Horiuchi and J. R. Wilmoth, Demography 35, 391 (1998);
22. DemographyJ. R. Wilmoth and S. Horiuchi, 36, 475 (1999);
23. J. R. Wilmoth, L. J. Deagan, H. Lundstrom, and S. Horiuchi, Science 289, 2366 (2000);
24. S. Tuljapurkar, N. Li, and C. Boe, Nature (London) 405, 789 (2000), and references therein.
25. This is consistent with C. Osmond and D. J. P. Barker, Environ. Health Perspect. 108, 543 (2000).
26. L. B. Medawar, An Unsolved Problem of Biology (Lewis, London, 1952).
27. P. Hasty, Mech. Ageing Dev. 122, 1651 (2001);
28. W. A. Van Voorties, Exp. Gerontol. 36, 55 (2001);
29. G. M. Martin, Mech. Ageing Dev. 123, 65 (2002).
30. (a) S. J. Olshansky and B. A. Carnes, Demography 34, 1 (1997);
31. S. J. OlshanskyB. A. Carnes(b) Exp. Gerontol. 36, 1423 (2001), special issue on molecular aging.
32. M. Ya. Azbel’, Proc. Natl. Acad. Sci. U.S.A. 91, 12 453 (1994).
33. A. Brooks, G. J. Lithglow, and T. R. Johnson, Science 263, 668 (1994).
34. G. C. Williams, Evolution (Lawrence, Kans.) 11, 398 (1957).
35. T. B. L. Kirkwood, Nature (London) 270, 301 (1977).
36. L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon, Oxford, 1989), Chap. VIII, Sec. 11.
37. M. Ya. Azbel’, Exp. Gerontol. 37, 859 (2002).