[Paleopsych] GRG: EvolutionaryTheories of Aging and Mortality Deceleration
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From: Leonid Gavrilov <gavrilov at longevity-science.org>
Date: Mon, 11 Apr 2005 21:33:14 -0500
To: Gerontology Research Group <grg at lists.ucla.edu>
Subject: [GRG] EvolutionaryTheories of Aging and Mortality Deceleration
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Reply-To: Gerontology Research Group <grg at lists.ucla.edu>
Here are our comments to the following recent publication:
"How is the evolutionary biological theory of aging holding up against
American Aging Association Newsletter, March 2005
Dr. George M. Martin, Department of Pathology, University of Washington
Any feedback would be greatly appreciated. Thanks!
Comments on discussion piece "How is the evolutionary biological theory of
aging holding up against mounting attacks?"
Leonid A. Gavrilov, Ph.D., and Natalia S. Gavrilova, Ph.D.
Center on Aging, NORC/University of Chicago
An interesting discussion piece "How is the evolutionary biological theory
of aging holding up against mounting attacks?" by Dr. George Martin is an
inspiration for many possible comments. Here we focus on one particular
topic raised by Dr. George Martin -- the departures of mortality
trajectories from the Gompertz curve -- a paradoxical phenomenon known in
scientific literature as late-life mortality deceleration, mortality
levelling-off, and late-life mortality plateaus.
In many biological species, including Drosophila and humans, death rates
increase exponentially with age for much of the life span (the famous
Gompertz curve). However, at extreme old ages a "mortality deceleration"
occurs -- the pace of mortality growth decelerates from an expected
exponential curve. Sometimes this mortality deceleration progresses to the
extent that mortality "levelling off" is observed, leading eventually to a
"mortality plateau." Thus at extreme old ages a paradoxical situation is
observed when one of the major manifestations of aging -- increasing death
rate -- apparently fades away or even disappears. This phenomenon
represents a challenge for many theories of aging, including the
evolutionary theories (as correctly mentioned by Dr. George Martin).
It is important, however, to put the discussion of "mortality deceleration"
phenomenon in a historical context. Contrary to some recent outrageous
claims, the phenomenon of mortality deceleration is not a new scientific
discovery, but rather an old and well documented observation, which has
been known for a long time. For an excellent historical review of studies
on mortality deceleration at extreme old ages, we would strongly recommend
an article by S. Jay Olshansky, "On the biodemography of aging: a review
essay." Population and Development Review 24, pp. 381-393, 1998.
The first person who noticed that the Gompertz curve is not applicable to
extreme old ages was Benjamin Gompertz himself (see Gompertz B.,
Philosophical Transactions of the Royal Society, 115: 513-585,1825;
reviewed by Olshansky, 1998).
In 1867, another British actuary William Makeham noted that for humans "the
rapidity of the increase in the death rate decelerated beyond age 75" (see
page 346 in Makeham, W.M. 1867. On the law of mortality. Journal of the
Institute of Actuaries 13, 325-358.).
In 1919, a British statistician J. Brownlee wondered whether it is
"possible that a kind of Indian summer occurs after the age of 85 years is
passed, and that conditions improve as regards length of life" (cited from
page 385 in Brownlee, J. 1919. Notes on the biology of a life-table.
Journal of the Royal Statistical Society, 82, 34-77).
Later in 1932, the British actuary W. Perks observed that "the graduated
curve [of mortality] starts to decline in the neighborhood of age 84", and
suggested to substitute the Gompertz law of mortality with a logistic
formula (see page 15 at Perks, W. 1932. On some experiments in the
graduation of mortality statistics. Journal of the Institute of Actuaries
In 1939, the British researchers Greenwood and Irwin published a research
article, "Biostatistics of Senility," with the intriguing finding that
mortality force stops increasing with age at extreme old ages and becomes
constant (see Greenwood, M., Irwin, J.O. 1939. "The biostatistics of
senility." Human Biology, vol. 11, 1-23). Their study and findings were
considered to be so important that they were featured on the front page of
the academic journal "Human Biology" where their study was published.
This study, accomplished by the famous British statistician and
epidemiologist Major Greenwood, is directly related to the topic of this
discussion. The first important finding was formulated by Greenwood and
Irwin in the following way: "
the increase of mortality rate with age
advances at a slackening rate, that nearly all, perhaps all, methods of
graduation of the type of Gompertzs formula overstate senile mortality"
(Greenwood, Irwin, 1939, p. 14). This observation was confirmed later by
many authors (see review in Gavrilov L.A., Gavrilova N.S. 1991. The Biology
of Life Span: A Quantitative Approach, NY: Harwood Academic Publishers),
and it is known as the late-life mortality deceleration.
The authors also suggested "the possibility that with advancing age the
rate of mortality asymptotes to a finite value" (Greenwood, Irwin, 1939, p.
14). Their conclusion that mortality at exceptionally high ages follows a
first-order kinetics (also known as the law of radioactive decay with
exponential decline in survival probabilities) was confirmed later by other
researchers, including A.C. Economos ("Kinetics of metazoan mortality," J.
Social Biol. Struct. 1980, 3: 317-329). Economos demonstrated the
correctness of this law for humans and laboratory animals (linear decrease
for the logarithm of the numbers of survivors). This observation is known
now as the "mortality leveling-off" at advanced ages, and as the "late-life
Moreover, Greenwood and Irwin made the first estimates for the asymptotic
value of human mortality (one-year probability of death, qx) at extreme
ages using data from the life insurance company. According to their
the limiting values of qx are 0.439 for women and 0.544 for
men" (Greenwood and Irwin, 1939, p. 21). It is interesting that these first
estimates are very close to estimates obtained later using more numerous
and accurate human data, including recent data on supercentenarians.
Interestingly, Greenwood and Irwin suggested the same explanation for
mortality levelling off, as it was offered by Dr. George Martin in his
"cocoon" hypothesis: "With advancing years the disabilities, forcefully
described by a large number of poets whom it is needless to quote, restrict
activities. Even the juvenile of 60, if ordinarily intelligent, eschews the
violent exercises of the child of 40. Centenarians rarely appear in public.
A statistical rate of mortality might show no increase with age, if the
demands made on the vital forces diminished pari passu with the decay of
vigor." (cited from page 14 in Greenwood, M., Irwin, J.O. 1939. "The
biostatistics of senility." Human Biology, vol. 11, 1-23).
In 1960, journal Science published an article on a "General theory of
mortality and aging" that listed some "... essential observations which
must be taken into account in any general theory of mortality." (Strehler &
Mildvan, 1960, p.14). The first of these essential observations was the
Gompertz law of mortality, while the second essential observation stated
that "the Gomperzian period is followed by a gradual reduction in their
rate of increase of the mortality" (see page 14 in Strehler, B. L., &
Mildvan, A. S. 1960. General theory of mortality and aging. Science, 132,
Biologists and biogerontologists became well aware of mortality
levelling-off since the 1960s. For example a biologist P.J. Lindop (1961)
applied the Perks (logistic) formula in order to account for mortality
deceleration at older ages in mice (Lindop P.J. Growth rate, lifespan and
causes of death in SAS/4 mice. Gerontologia, 5: 193-208, 1961). George
Sacher (1966) believed that the observed mortality deceleration in mice and
rats can be explained by population heterogeneity: "one effect of such
residual heterogeneity is to bring about a decreased slope of the
Gompertzian at advanced ages. This occurs because sub-populations with the
higher injury levels die out more rapidly, resulting in progressive
selection for vigour in the surviving populations" (see page 435 in Sacher
G.A. The Gompertz transformation in the study of the injury-mortality
relationship: Application to late radiation effects and aging. In: P.J.
Lindop and G.A. Sacher (eds.) Radiation and ageing, 1966, pp. 411-441,
Taylor and Francis, London).
This observation of mortality deceleration was confirmed in 1979 for
several other biological species including Drosophila and nematode C.
elegans (Economos, A.C. 1979. A non-Gompertzian paradigm for mortality
kinetics of metazoan animals and failure kinetics of manufactured products.
AGE, 2, 74-76). The author concluded "...that after a certain
species-characteristic age, force of mortality and probability of death
cease to increase exponentially with age ... and remain constant at a high
level on the average for the remainder of the life span." (page 74). The
author called these findings "a non-Gompertzian paradigm for mortality
kinetics" (Economos, 1979, p. 74). A year later the same author analyzed
data for thoroughbred horses (mares), Dall mountain sheep, houseflies and
some other species, and came to a conclusion that "Gompertz's law is only
an approximation, not valid over a certain terminal part of the lifespan,
during which force of mortality levels off." (see page 317 in Economos,
A.C. 1980. Kinetics of metazoan mortality. Journal of Social and Biological
Structures, 3, 317-329).
Prior to 1990 the most popular explanation of mortality plateaus was based
on the idea of initial population heterogeneity, suggested by British
actuary Robert Eric Beard (1911-1983). Beard developed a mathematical model
in which individuals were assumed to have exponential increase in their
risk of death as they age (Gompertz law), but their initial risks differed
from individual to individual and followed a gamma distribution (Beard, R.
E. 1959. Note on some mathematical mortality models, In: The Lifespan of
Animals, G. E. W. Wolstenholme and M. OConnor, eds. Little, Brown,
Boston). This model produces a logistic function for mortality kinetics
that is very close to the exponential function at younger ages, but then
mortality rates decelerate and reach a plateau in old age. This
compositional interpretation of mortality plateaus explained them as an
artifact of mixture, perhaps reducing their intrinsic interest to biologists.
The situation changed in 1991, when it was found that the general theory of
systems failure (known as reliability theory) predicts an inevitable
mortality levelling-off as a result of redundancy exhaustion, even for
initially identical individuals (Gavrilov L.A., Gavrilova N.S. The Biology
of Life Span: A Quantitative Approach, NY: Harwood Academic Publisher,
1991, 385p.). Thus, a testable prediction from this theory was that
mortality deceleration should be observed even for genetically identical
individuals kept in strictly controlled laboratory conditions. This
prediction was confirmed later for inbred strains of Drosophila
melanogaster (Curtsinger, J.W., et. al., 1992. Demography of genotypes:
Failure of the limited life-span paradigm in Drosophila melanogaster.
Science, 258, 461-463).
In conclusion, we agree with Dr. George Martin that the evolutionary theory
of aging needs to be reconciled with many empirical observations, including
the late-life mortality deceleration. In 2002, we reviewed the evolutionary
theories of aging, and came to the following conclusion: "Evolutionary
theories of aging are useful when they open new opportunities for research
by suggesting testable predictions, but they should never be used to impose
limitations on aging studies. This is because the evolutionary theories
of aging are not in fact completed theories, but rather a set of ideas that
themselves require further elaboration and validation." (see page 353 in
Gavrilov, L.A., Gavrilova, N.S. Evolutionary theories of aging and
longevity. The Scientific World JOURNAL, 2002, 2: 339-356. Available:
Leonid A. Gavrilov, Ph.D., and Natalia S. Gavrilova, Ph.D.
Center on Aging, NORC/University of Chicago
1155 East 60th Street
Chicago, IL 60637-2745
Fax: (773) 256-6313, Phone: (773) 256-6359
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