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that have to be understood and explained. There were reports that in some cases the organisms die according to the Weibull (power) law (see the section on basic failure models). The Weibull law is more commonly applicable to technical devices (Barlow and Proschan, 1975; Rigdon and Basu, 2000; Weibull, 1951), while the Gompertz law is more common in biological systems (Finch, 1990; Gavrilov and Gavrilova, 1991; Strehler, 1978). As was already noted, the exponential Gompertzian increase in age-specific mortality is observed for many biological species including fruit flies Drosophila melanogaster, nematodes, mosquitoes, human lice, flour beetles, mice, rats, dogs, horses, mountain sheep, baboons and humans. Comparative meta-analysis of 129 life tables for fruit flies as well as 285 life tables for humans demonstrates that the Gompertz law of mortality provides a much better data fit for each of these two biological species, compared to the Weibull law (Gavrilov and Gavrilova, 1991, pp. 55-56, 68-72). Possible explanations why organisms prefer to die according to the Gompertz law, while technical devices typically fail according to the Weibull law are provided elsewhere (Gavrilov and Gavrilova, 1991; 2001; 2005) and will be discussed later in this chapter (see the section on theoretical models of systems failure in aging).

Both the Gompertz and the Weibull failure laws have a fundamental explanation rooted in reliability theory (Barlow and Proschan, 1975) and are the only two theoretically possible limiting extreme value distributions for systems whose lifespans are determined by the first failed component (Gumbel, 1958; Galambos, 1978). In other words, as the system becomes more and more complex (contains more vital components, each being critical for survival), its lifespan distribution may asymptotically approach one of the only two theoretically possible limiting distributions—either Gompertz or Weibull (depending on the early kinetics of failure of system components). The two limit theorems in the statistics of extremes (Gumbel, 1958; Galambos, 1978) make the Gompertz and the Weibull failure laws as fundamental as are some other famous limiting distributions known in regular statistics, e.g., the normal distribution and the Poisson distribution. It is puzzling, however, why organisms prefer to die according to the Gompertz law, while technical devices typically fail according to the Weibull law. One possible explanation of this mystery is suggested later in this chapter.

Thus, 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 mortality growth with age (Austad, 2001; Finch, 1990; Haranghy and Balazs, 1980; 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 and Gavrilova, 1991)?

Any theory of human aging has to explain these last three rules, known collectively as mortality, or failure, laws. And reliability theory, by way of a clutch of equations, covers all of them (see the section on theoretical models of systems failure in aging, and Gavrilov and Gavrilova, 1991, 2001, 2005).

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