The Quest for the General Theory of Aging and Longevity
Leonid A. Gavrilov <firstname.lastname@example.org>
Natalia S. Gavrilova <gavrilova[at]longevity-science.org>
Center on Aging, NORC at the University of Chicago
We would strongly recommend supplementing the reading of this short synopsis by the subsequent study of our original article on related topic:
Gavrilov L.A., Gavrilova N.S. The reliability theory of aging and
Journal of Theoretical Biology, 2001, 213(4): 527-545.
Full text is also available online at:
There is a growing interest to the topic of aging and to the search for a general theory that can explain what aging is and why and how it happens. There is also a need for a general theoretical framework that may allow researchers to handle an enormous amount of diverse observations related to aging phenomena. Empirical observations on aging have become so numerous and abundant that a special 4-volume encyclopedia, The Macmillan Encyclopedia of Aging, is now required for even a partial coverage of the accumulated facts (Ekerdt, 2002). To transform these numerous and diverse observations into a comprehensive body of knowledge, a general theory of species aging and longevity is required. This theory is also important for understanding and forecasting the trends of human mortality and longevity.
A general theory of aging may come in the future from a synthesis between systems theory (reliability theory) and specific biological knowledge. Reliability theory is a general theory about systems failure, which allows researchers to predict age-related failure kinetics for a system of given architecture (reliability structure) and given reliability of its components (Gavrilov & Gavrilova, 1991; 2001). As for specific biological knowledge, many researchers believe that it could be provided by biodemographic studies of aging and longevity (Carey & Judge, 2001).
Attempts to develop a fundamental quantitative theory of aging, mortality, and lifespan have deep historical roots. In 1825, the British actuary Benjamin Gompertz discovered a law of mortality, known today as the Gompertz law. Specifically, he found that the force of mortality (known in modern science as mortality rate, hazard rate, or failure rate) increases in geometrical progression with the age of adult humans. According to the Gompertz law, human mortality rates double over about every 8 years of adult age. Gompertz also proposed the first mathematical model to explain the exponential increase in mortality rate with age (Gompertz, 1825). The Gompertz law of exponential increase in mortality rates with age is observed in many biological species (Strehler, 1978; Finch, 1990), including humans, rats, mice, fruit flies, flour beetles, and human lice (Gavrilov & Gavrilova, 1991), and, therefore, some general theoretical explanation for this phenomenon is required. Many attempts to provide such theoretical underpinnings for the Gompertz law have been made (see reviews in Strehler, 1978; Gavrilov & Gavrilova, 1991), and the problem now is to find out which of these models is correct.
Gompertz also found that at advanced ages mortality rates increase less rapidly than an exponential function, thus forestalling two centuries ago the recent fuss over 'late-life mortality deceleration', 'mortality leveling off', and 'late-life mortality plateaus'. For a more in-depth analysis of the previous extensive studies on mortality leveling-off (Makeham, 1867; Brownlee, 1919; Perks, 1932; Greenwood & Irwin, 1939; Mildvan & Strehler; 1960; Strehler, 1960; Economos, 1979; 1980; 1983; 1985; Gavrilov & Gavrilova, 1991) see the review by Olshansky (Population and Development Review, 1998, 24: 381-393). Here we would like to bring more attention to one particular seminal paper, which was published more than 60 years ago (Greenwood & Irwin, 1939). This study, accomplished by the famous British statistician and epidemiologist, Major Greenwood, may be interesting to discuss again now because this 1939 article correctly describes and forestalls the main specific regularities of mortality at advanced ages.
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 Gompertz’s formula over-state senile mortality” (Greenwood, Irwin, 1939, p.14). This observation is confirmed now 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) was confirmed later by other researchers, including A.C. Economos (1979; 1980; 1983; 1985), who demonstrated the correctness of this law for humans and laboratory animals. This observation is known now as the “mortality leveling-off” at advanced ages, and as the “late-life mortality plateau.” 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 estimates, “… 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 (those who survive to age 110).
A comprehensive theory of species aging and longevity should provide answers to the following questions:
(1) Why do most biological species deteriorate with age (i.e., die more often as they grow older) while some primitive organisms do not demonstrate such a clear age dependence for mortality increase (Haranghy & Balázs, 1980; Finch, 1990; Martinez, 1998)?
(2) Specifically, why do mortality rates increase exponentially with age in many adult species (Gompertz law)? How should we handle cases when the Gompertzian mortality law is not applicable?
(3) Why does the age-related increase in mortality rates vanish at older ages? Why do mortality rates eventually decelerate compared to predictions of the Gompertz law, occasionally demonstrate leveling-off (late-life mortality plateau), or even a paradoxical decrease at extreme ages?
(4) How do we explain the so-called compensation law of mortality (Gavrilov & Gavrilova, 1991)? This paradoxical phenomenon refers to the observation that high mortality rates in disadvantaged populations (within a given species) are compensated for by a low apparent 'aging rate' (longer mortality doubling period). As a result of this compensation, the relative differences in mortality rates tend to decrease with age within a given biological species. This is true for male-female comparisons, for international comparisons of different countries within the same sex, as well as for within-species comparisons of animal stocks (Gavrilov & Gavrilova, 1991). The theory of aging and longevity has to explain this paradox of mortality convergence.
Following a long-standing tradition of biological thought, the search for a general biological theory to explain aging and longevity has been made mainly in terms of evolutionary biology (Medawar, 1946; 1952; Williams, 1957; 1966; Hamilton, 1966; Rose, 1991; Carnes & Olshansky, 1993; Charlesworth, 1994) and genetics (Finch, 1990; Jazwinski, 1996; 1998; Finch & Tanzi, 1997; Carnes et al., 1999). However, the first attempts to explain 'late-life mortality plateaus' using evolutionary theory (Mueller & Rose, 1996) have failed because they required highly specialized and unrealistic assumptions (see critical reviews by Charlesworth & Partridge, 1997; Pletcher & Curtsinger, 1998; Wachter, 1999, as well as another attempt to explain mortality plateaus by Charlesworth, 2001). It looks like the evolutionary theory is more appropriate to explain early successes of biological species (e.g., reproductive success), rather than their later failures (aging and death). There seems to be a missing piece in the theoretical arsenal of evolutionary biologists trying to explain aging, and this missing piece is about the general theory of system failures. This theory, known as the theory of reliability (Lloyd & Lipow, 1962; Barlow & Proshan, 1965; 1975; Kaufmann et al., 1977; Crowder et al., 1991; Aven & Jensen, 1999; Rigdon & Basu, 2000), allows researchers to understand many puzzling features of mortality and lifespan (Gavrilov, 1978; 1987; Gavrilov et al., 1978; Abernethy, 1979; ?oubal, 1982; Gavrilov & Gavrilova, 1991; 1993; 2001; Bains, 2000) not readily explainable otherwise (i.e., the Gompertz law, mortality plateaus, and the compensation law of mortality).
The purpose of this paper is to introduce the ideas and methods of
theory to researchers interested in understanding the mechanisms of
mortality, survival, and longevity.
Reliability Theory of Aging and Longevity
The findings and conclusions made in our original theoretical article (Gavrilov, Gavrilova, 2001) could be summarized in the following way.
Reliability theory is a general theory about systems failure. It allows researchers to predict the age-related failure kinetics for a system of given architecture (reliability structure) and given reliability of its components. The theory provides explanations of the following fundamental problems regarding species aging and longevity:
(1) Reliability theory explains why most biological species deteriorate with age (i.e., die more often as they grow older) while some primitive organisms do not demonstrate such a clear age dependence for mortality increase. The theory predicts that even those systems that are entirely composed of non-aging elements (with a constant failure rate) will nevertheless deteriorate (fail more often) with age, if these systems are REDUNDANT in irreplaceable elements. Aging, therefore, is a direct consequence of systems redundancy. Moreover, the 'apparent aging rate' (the relative rate of age-related mortality acceleration corresponding to parameter a in the Gompertz law) increases, according to reliability theory, with higher redundancy levels. Therefore, a negligible 'apparent aging rate' in primitive organisms (Haranghy & Balázs, 1980; Finch, 1990; Martinez, 1998) with little redundancy is a predicted observation for reliability theory.
(2) The reliability theory explains why mortality rates increase exponentially with age in many adult species (Gompertz law) by taking into account the INITIAL FLAWS (DEFECTS) in newly formed systems. It also explains why organisms 'prefer' to die according to the Gompertz law, while technical devices usually fail according to the Weibull (power) law. Moreover, the theory provides a sound strategy for handling those cases when the Gompertzian mortality law is not applicable. In this case, the second best choice would be the Weibull law, which is also fundamentally grounded in reliability theory. Theoretical conditions are specified when organisms die according to the Weibull law: organisms should be relatively free of initial flaws and defects. An unwritten but prevalent assumption is that all living systems also begin more or less in an optimal state, created from perfect or near-perfect parts. However, in contrast to technical (artificial) devices, which are constructed out of previously manufactured and tested components, organisms form themselves in ontogenesis through a process of self-assembly out of de novo forming and externally untested elements (cells). From the point of conception, the cells from which biological systems are built are infused with faults and defective elements that would kill primitive organisms. Nobody can test the quality of each particular cell, so living systems are formed by self-assembly as they are and can be loaded with significant initial damage. But humans and other complex organisms have built-in redundancies, which help them survive random, destructive assaults, ensuring increased reliability and life span. However, these redundancies also ensure organisms will age. Hence, aging, according to this theory, is a direct consequence or trade-off of systems redundancy exhaustion.
In those cases when neither the Gompertz nor the Weibull mortality law is appropriate, reliability theory offers more general failure law applicable to adult and extreme old ages. The Gompertz and the Weibull laws are just special cases of this unifying more general law (Gavrilov, Gavrilova, 2001).
(3) Reliability theory also explains why the age-related increase in mortality rates vanishes at older ages. It predicts the late-life mortality deceleration with subsequent leveling-off, as well as the late-life mortality plateaus, as an inevitable consequence of REDUNDANCY EXHAUSTION at extreme old ages. This is a very general prediction of reliability theory: it holds true for systems built of elements connected in parallel, for hierarchical systems of serial blocks with parallel elements, for highly interconnected networks of elements (Bains, 2000), and for systems with avalanche-like random failures (Gavrilov & Gavrilova, 1991).
The reliability theory also predicts that the late-life mortality plateaus will be observed at any level of initial damage: for initially ideal systems, for highly redundant systems replete with defects, and for partially damaged redundant systems with an arbitrary number of initial defects.
Furthermore, reliability theory predicts possible paradoxical mortality decline in late life (before eventual leveling-off to mortality plateau) if the system is redundant for non-identical components with different failure rates. Thus, in those cases when 'apparent rejuvenation' is observed (mortality decline among the oldest-old) there is no need to blame data quality or to postulate initial population heterogeneity and 'second breath' in centenarians. The late-life mortality decline is an inevitable consequence of age-induced population heterogeneity expected even among initially identical individuals, redundant in non-identical system components (Gavrilov & Gavrilova, 2001). Recently this general explanation was also supported using computer simulations (Bains, 2000). Late-life mortality decline was observed in many studies (Barrett, 1985; Carey et al., 1992; Khazaeli et al., 1995; Klemera & Doubal, 1997) and stimulated interesting debates (Klemera & ?oubal, 1997; Olshansky, 1998) because of the lack of reasonable explanation. Reliability theory predicts that the late-life mortality decline is an expected scenario of systems failure.
(4) The theory explains the compensation law of mortality, when the relative differences in mortality rates of compared populations (within a given species) decrease with age, and mortality convergence is observed due to the exhaustion of initial differences in redundancy levels. Reliability theory also predicts that those experimental interventions that change 'true aging rate' (rate of elements' loss) will also suppress mortality convergence, providing a useful approach on how to search for factors affecting aging rate.
Overall, reliability theory has an amazing predictive and explanatory power and requires only a few general and realistic assumptions. It offers a promising approach for developing a comprehensive theory of aging and longevity that integrates mathematical methods with biological knowledge including cell biology (Abernethy, 1998), evolutionary theory (Miller, 1989; Charlesworth, 1994) and systems repair principles (Rigdon & Basu, 2000). We suggest, therefore, adding the reliability theory in the arsenal of theoretical methods to study aging and longevity.
Gavrilov L.A., Gavrilova N.S. The reliability
theory of aging and longevity.
Journal of Theoretical Biology, 2001, 213(4): 527-545.
Gavrilov L.A., Gavrilova N.S. The quest
for the theory of human longevity.
The Actuary, 2002, 36(5): 10-13.
Gavrilov L. A. Biodemographic
(reliability) theory of aging and longevity.
Full paper (53 pages) presented at the Annual Meeting of the Population
Association of America (Atlanta, May 9-11, 2002, Session 135
Gavrilov, L.A. & Gavrilova, N.S. (1991) The Biology of Life Span: A Quantitative Approach, New York: Harwood Academic Publisher.
Media coverage and discussion of the aging theory:
A.J.S. Rayl. Aging, in Theory: A
Personal Pursuit. The Scientist, 2002,
16:20, May 13 issue.
Full text is also available online at:
The University Science News - UniSci (February 12, 2002)
Science News, Cosmiverse Daily News (February 13, 2002)
MedServ Medical News
SciWeb: The Life Science Home Page
Healthy Senior, volume 3, number 40 -- March 1, 2002
The National Opinion Research Center (January 25, 2002)
Additional information on the media coverage and discussion of the
theory is available at the following URL: