Between Zeus and the Salmon The Biodemography of Longevity (1997) / Chapter Skim
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3 In Search of Limits
3 In Search of Limits
Pages 38-64
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From page 38... ...
Two common beliefs that have gained an almost mythical status are that human life expectancy is bounded by a limit of around 85 years and that the maximum human life span is around 120 years. There are numerous means of approaching the question of whether such limits exist.
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be the probability density function describing the distribution of life spans in this population. The cumulative density function, F(x)
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From page 40... ...
Three hypotheses about possible limits to human longevity can be described in a similar way. These hypotheses, known as the limited-life-span hypothesis, the compression-rectangularization hypothesis, and the limit-distribution hypothesis, are illustrated in Figures 3-2 to 3-4.
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From page 41... ...
JOHN R WILMOTH 1.0 0.8 0.6 x 0.4 0.2 0.0 1.000 x x 0.100 0.010 0.001 0.12 0.10 0.08 0.06 0.04 0.02 0.0 Survival function 1900 \ 1992 \ \ ,, , , , , _ '1` 1 0 20 40 60 80 100 Age Hazard function I , - - 1992 it- '' 0 20 40 60 80 100 Age Density function \ 1900 - "~1992 1 0 20 40 60 80100 Age FIGURE 3-l Mortality curves for U.S.
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From page 42... ...
. Similarly, the density function equals zero above this age.
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From page 43... ...
Note: Changes in these three curves are interrelated: over time the hazard function falls more rapidly at younger than older ages, the area under the survival function grows larger as the curve becomes more rectangular, and the density function shifts to the right and becomes more compressed. The distribution may or may not be truncated at some maximum age.
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From page 44... ...
Likewise, the limit distribution may or may not have a finite right-hand boundary.
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From page 45... ...
According to Webster's dictionary, life span is either "the longest period over which the life of any plant or animal organism or species may extend, according to the available biological knowledge concerning it," or "the longevity of an individual." Thus, the life span of an individual refers to his or her age at death; the life span of a species refers to the maximum potential length of life for the most robust members of the species; and the mean life span (of individuals) is equivalent to the familiar concept of life expectancy.
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From page 46... ...
A complete analysis of the trend shown in Figure 3-5 breaking it into components related to the trend in births, the probability of survival until old age, and the probability of survival within old age is still lacking. Nevertheless, if the mortality distribution were truncated on the right, this trend would be subject to an upper limit, regardless of the increasing size of the centenarian population.
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From page 47... ...
, whose mortality rates appear to level off in old age (Curtsinger et al., 1992; Carey et al., 1992; Fukui et al., 1993; Vaupel et al., 1994~. Of course, it is possible that there exists a maximum human life span at a point that is well beyond current experience.
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From page 48... ...
until just before the upper limit of the life span and only then shoot abruptly toward infinity. However, such a situation even if it were the reality could never be observed and documented using our present methods.
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. As life expectancy increases in these model life tables, the coefficient of variation declines.
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From page 50... ...
Furthermore, there is no reason to believe that an extrapolation of the relationship between level and variability in Coale-Demeny model life tables is an accurate prediction of the course of future mortality changed Alternatively, it is at least theoretically possible that the variability in ages at death could decrease more slowly relative to the increase in life expectancy than predicted by the Coale-Demeny model tables. Thus, Figure 3-3 provides an example of the compression-rectangularization hypothesis in the absence of apparent limits on either the maximum life span or life expectancy.
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From page 51... ...
Limit-Distribution Hypothesis A third hypothesis about limits to human longevity asserts that there exists a limiting distribution that mortality curves may approach but not surpass. In terms of the hazard function, this limiting distribution can be written as h*
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From page 52... ...
. Therefore, for the purpose of discussing ultimate mortality limits, I assume that the forces of Darwinian selection and genetic drift will have only a negligible impact on the genetics of human longevity over the time horizon of interest to demographers and social planners, which is perhaps 50-100 years.
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(x) , which thus implies an upper limit to the mean life span, or life expectancy (but not necessarily a finite maximum life span)
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From page 54... ...
The absence of deceleration in the rate of mortality decline, then, is taken as evidence that we are not currently approaching a lower limit in mortality rates. For example, the reduction in age-specific death rates for most developed countries has been a stable, long-term process.
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Total death rates were standardized using the 1980 census population.
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the average annual reduction in death rates (in percent) for ages 80-89 and 90-99 in an aggregate of eight European countries plus Japan from the 1950s through the 1980s.
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From page 57... ...
~ ~ 0.5 a) 1861-1 990 -\\\ \ \ - - - - 1936/40-1956/60 \ \ -- -- -- - 1956/60-1986/90 \ \\ 1861/65- 1936/40 \ \ \ \ _ _ _ _ _ 80 90 100 / aft\, ,: ," 1 ~ i \\,, ,''"""' / \ we'd / \ \ \/ ~/~" 1955/60 - 1961/65 -- -- -- -- - 1961/65- 1966/70 1966/70- 1976/80 -1976/80- 1986/90 50 55 60 65 7075 80 85 90 95 100 Age 57 FIGURE 3-9 Average annual rates of mortality decline by age in Sweden for women only in various years during 1861-1990.
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From page 58... ...
CONCLUSION The demographic debate about the limits of human longevity can be expressed in terms of three hypotheses: limited life span, compression-rectangu
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From page 59... ...
Men 3.0 2.5 is_ ~ 2.0 .E 1.5 1.0 0.5 0.0 -0.5 59 J Nl Au |~. AU Ic Ch NF S Ew I E Sc B Ok Nz Ir La Ea 1 1 Sf Gw Lx A pa Ge H Cz 1 1 1 1 1 1 1 1 1 1 1 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 Average death rate E Au Ch lo N S Nl Ok J F Ew Sf Gw A pa Lx I Nz B SO Ea H La PI Ge 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 Average death rate FIGURE 3-10 Average death rate in the 1970s plotted against the average annual rate of mortality decline from the 1970s to 1980s, women and men, ages 80-99 combined, 27 developed countries.
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From page 60... ...
. This hypothesis implies limits in the mean life span, or life expectancy, and in other parameters of the probability distribution of ages at death, including the median, the variance, and so forth.
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Nemeskeri 1970 History of Human Life Span and Mortality. Budapest: Akademiai Kiado.
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Stallard, and H.D. Tolley 1991 Limits to human life expectancy: Evidence, prospects, and implications.
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Cassel 1990 In search of Methuselah: Estimating the upper limits to human longevity. Science 250:634-640.
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From page 64... ...
64 IN SEARCH OF LIMITS Wilmoth, J.R., and H Lundstrom 1996 Extreme longevity in five countries: Presentation of trends with special attention to issues of data quality.
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