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The Journals of Gerontology Series A: Biological Sciences and Medical Sciences 59:B697-B704 (2004)
© 2004 The Gerontological Society of America

The Future of Aging Interventions

The Human Life Span Is Not That Limited: The Effect of Multiple Longevity Phenotypes

Robert Arking1,, Vassily Novoseltsev2 and Janna Novoseltseva2

1 Department of Biological Sciences, Wayne State University, Detroit, Michigan.
2 Institute of Control Sciences, Russian Academy of Sciences, Moscow.

Address correspondence to Dr. Robert Arking, Department of Biological Sciences, Biological Sciences Building, 5705 Gullen Mall, Wayne State University, Detroit, MI 48202. E-mail: rarking{at}biology.biosci.wayne.edu


    Abstract
 Top
 Abstract
 Summary of the Arguments
 Animal Studies
 Discussion
 Appendix
 References
 
There is an ongoing debate as to whether or not human longevity is approaching its limits. The debate and its outcome are important since they might affect public policy. We review the evidence presented by both schools. We add our empirical observation that there exist multiple longevity phenotypes, each of which arises from the alteration of fundamental aging processes. The current debate only considers two of the three known mammalian longevity phenotypes. The overlooked phenotype is the delayed onset of senescence phenotype, which can be induced by various interventions, including pharmaceuticals. The existence of multiple phenotypes means that an overview of potential life expectancy outcomes for a species should be based on the analysis of all longevity phenotypes likely to occur in that species.


An ongoing debate within the biogerontological community focuses on the question as to whether or not human longevity is approaching its limits. Theoretical bases for estimating longevity limits exist but are indirect. As a result, much of the ensuing discussion necessarily focuses on the robustness of the approach or the interpretation of the data used in the extrapolation. One school of thought, summarized in Olshansky and Carnes (1), and exemplified by the writings of Carnes and colleagues (2) and Olshansky and colleagues (3,4), suggests that human longevity is most likely approaching a statistical maximum. Their analysis suggests that there is in fact a lower limit to death rates, and thus an upper limit to life expectancy. A different school, illustrated by the views of Oeppen and Vaupel (5), contends that the entire history of estimating human longevity limits has been a dismal failure since almost every estimate has been falsified by events, and it is likely that the same will happen to the few remaining estimates.

The debate and its outcome are important since they might affect public policy. The United States' Social Security program requires that the responsible officials make forecasts of the number of future beneficiaries so as to determine the future solvency of the program. As described by Carnes and colleagues (2), this forecasting method has often involved linear extrapolation of past trends in mortality and/or life expectancy. Given the extraordinary continued success in reducing premature mortality during the past century, it was only to be expected that past data would underestimate future changes, thereby raising real concerns about the validity of future estimates. The Social Security program as well as other public and private programs need biologically realistic estimates of life expectancies if they are to plan well for the future. These needs apply to other developed countries as well.


    SUMMARY OF THE ARGUMENTS
 Top
 Abstract
 Summary of the Arguments
 Animal Studies
 Discussion
 Appendix
 References
 
The Oeppen–Vaupel argument rests on the fact that world record life expectancy at birth in the developed nations has been increasing steadily since 1840 at an overall rate of 2.5 years per decade. It must be noted that such trends have not been observed for any single country during this time period. Nonetheless, some countries (e.g., Japan) have had higher yearly increases in longevity over shorter periods of time as compared to the mean world rate. This has been due to a multitude of continuing small improvements in various aspects of our environment. If this trend should continue, then a life expectancy of 100 years would be reached in about six decades. Given the adage that the past is the best predictor of the future, it is argued that policy makers should "... base their calculations on the empirical record of mortality improvements over corresponding spans of the past" (5, p. 1031; note that this is the same protocol often used by the Social Security System). But there are different measures of mortality improvement. Since the Carnes–Olshansky-postulated limit to human life expectancy covers a range of 82–97 years (more realistically perhaps 82 for men and 88 for women) (2), and since the life expectancy of many cohorts alive today is approaching the lower boundaries of this life span limit, then we should expect to see signs of a deceleration in the rate of increase of life expectancy at birth and at age 65. This has been observed (3). However, one might also expect to see signs of an acceleration in the late life qx values. This is not observed, at least in the sense that maximum longevity continues to increase (6). Rather, what is observed is a continuing deceleration of the late life qx values (6–8). Thus each argument uses somewhat different predictions, each of which is supported by some data. Given these contradictions between their predictions and observation, Oeppen and Vaupel (5) conclude that human longevity is not approaching a detectable limit, should one even exist.

Carnes and Olshansky do not accept the above analysis because it is based on the prior one-time victories over various aspects of premature mortality. In those cases, relatively small investments yielded large increases in life expectancy. But these easy victories in which the life expectancies of younger individuals have been increased have been won already, and there is no reason to think that comparable life expectancy increases can be obtained by various interventions with older individuals. The difficulty of continuing to increase the life spans of elderly persons will ensure that the increases in life expectancy will slow and eventually come to an end. In addition, the analysis of 50 years worth of morbidity and mortality records for animals raised under controlled conditions at the Argonne National Laboratories led Carnes and colleagues (9) to conclude that the intrinsic mortality signatures of mice, beagles, and humans were indistinguishable. This finding led Carnes and Olshansky to the concept of a "biological warranty period"—that is, biological senescent processes set a statistical limit on the length of time that humans can survive before the increased age-related pathology load causes their functional ability to drop below some critical threshold. The essential aspect of the Carnes–Olshansky analysis is that the continued extension of postreproductive life span in humans is fundamentally contradicted by the evolutionary theory of aging, which posits that somatic maintenance processes should decline as reproduction draws to a close (10,11). Much work has shown that this theoretical relationship does occur and that it does determine the particulars of a species' aging processes. Thus, the Carnes–Olshansky argument is that attributes of reproduction of humans and other species are relatively fixed biological attributes, and if senescence is an inadvertent byproduct of attributes of reproduction, then age-dependent declines in physiological attributes of humans and other species are expected. They point out that such declines can be modified by biomedical interventions precisely because they are not programmed. To test the relationship between reproduction and senescence, they calculated what they term the "effective end to reproduction" (EER), which occurs at the age when 75% of the reproduction that will be accomplished by females has been accomplished. They used mouse data to calculate the regression equation describing the relationship between the EER and the "median age at death" (MAD) of female mice. Assuming that humans and mice follow the same kinetics in this case, they then calculated that women with an EER of 32–38 years would have a MAD of 82–97 years (Note, however, that this procedure does not take into consideration the debate as to whether the age at human menarche decreases and that of human menopause increases as economic development proceeds (12–16). If it does occur, then this would indicate that both EER and MAD may be significantly influenced by more than one variable). Human data on the loss of testosterone in men (17) is generalized to suggest that approximately 80% of functional capacity in all systems is lost by the age of 80 years, and further extended to suggest that most postreproductive females are suffering from various age-related pathologies [although a different approach estimates an approximately 30% loss of function by age 80 (18), there is general consensus that there is a significant loss of function by age 80 years]. They calculate that it would take an 85% decline in all-cause mortality rates from the 1985 level to yield a life expectancy of 50 years at age 50 (4). Such a decline is beyond our present capabilities, and so they conclude that, "Barring major advance in the development and use of life extending technologies or the alteration of human aging at the molecular level, the period of rapid increases in life expectancy in developed nations has come to an end" (4, p. 637).


    ANIMAL STUDIES
 Top
 Abstract
 Summary of the Arguments
 Animal Studies
 Discussion
 Appendix
 References
 
One fact that has emerged from the past several decades of aging research is that aging is not simple. The work that my colleagues and I have done on Drosophila longevity bears this out in a manner pertinent to the current debate. We reported that aging in our Ra strain of wild-type flies is rather complex, being characterized by at least three different extended longevity phenotypes, each of which was induced by specific stimuli and had different demographic mortality and survival profiles (19). As shown in Figure 1A, the first longevity phenotype (Type 1) is a delayed onset of senescence, which leads to a significant increase in both mean and maximum life span of the experimental strain. The second longevity phenotype (Type 2), shown in Figure 1B, is an increased early survival, which leads to a significant increase in mean but sometimes not in maximum life span. The third longevity phenotype (Type 3), shown in Figure 1C, is an increased later survival, which leads to a change in the maximum (LT90) but not in the median life spans.



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Figure 1. A, Survival curves of the normal-lived Ra strain and of two long-lived strains (La and 2La) sequentially derived from it by a direct selection for delayed female fecundity. The data points represent the observed survival data, and are based on the age-specific values obtained from two or three replicate cohorts consisting of at least 250 mixed sex individuals each. The Ra, La, and 2La curves are significantly different (log-rank test = 530.16, df = 2, p <.0001). See Arking and colleagues (19,50) for experimental details. The continuous lines are the Weibull approximations of the empirical data. See Arking and colleagues (19) for statistical details. B, Survival curves of the normal-lived Ra strain and the PQR strain selected from it by direct selection for paraquat resistance. The data points represent the observed survival data, and are based on the age-specific values obtained from mixed sex cohorts of 250–450 animals each. The two curves are significantly different (log-rank test = 24.76, df = 1, p <.00005). The continuous lines are the Weibull approximations of the empirical data. See Vettraino and colleagues (51) and Arking and colleagues (19) for experimental details. C, Survival curves of the normal-lived Ra control strain and the longer-lived Ra heat-treated strain. The animals were subjected to a non-lethal heat shock (37°C for 90 minutes) early in life at days 5–7 after eclosion. They were then maintained under controlled optimal conditions and their survival monitored. The two curves are significantly different (log rank test = 17.84, df = 1, p <.00005). See Keuther and Arking (52) and Arking and colleagues (2002<--?4-->) for experimental details. The continuous lines are the Weibull approximations of the empirical data

 
Analysis of the mortality data supports these statements. The Type 1 phenotype yields a Gompertz curve that is significantly different from that of the control strain (Figure 2A). Analysis of the data suggests that the Type 1 phenotype involves a 33% reduction in the mortality rate doubling time (MRDT) of the long-lived strain relative to the normal-lived strain. The MRDT is a commonly used indicator of comparative aging rates (20). However, neither the Type 2 long-lived populations (Figure 2B) nor the Type 3 long-lived populations (Figure 2C) show any alteration in aging rates relative to their controls.



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Figure 2. Age-specific logarithmic mortality curves and their Gompertz approximations. See Arking and colleagues (19) for experimental details. A, Age-specific logarithmic mortality curves of the normal-lived Ra strain and of two long-lived strains (La and 2La). The data points and their Gompertz approximations are presented (RaG, LaG, and 2LaG). The curves Ra and La (as well as Ra and 2La) are significantly different (p = 0) whereas La and 2La strains have no significant difference. B, Age-specific logarithmic mortality curves of the normal-lived Ra strain and the PQR strain. The data points and their Gompertz approximations are shown (RaG and PQRG). Statistical analysis confirms that the curves Ra and PQR differ significantly (p <.0036), the intercepts are significantly different whereas the slopes Ra and PQR have no significant difference. C, Age-specific logarithmic mortality curves of the normal-lived Ra control strain and the longer-lived heat-treated strain (RaHx). The experimental points and the Gompertz approximations (RaG and RaHxG) are shown. Statistical analysis does not reveal a significant difference between the curves Ra and RaHx (p <.35). The intercepts do not differ significantly

 
Moreover, it should be pointed out that the same phenotype may be induced by multiple different stimuli. For example, the Type 1 delayed onset of senescence phenotype may be induced in flies by (a) caloric restriction (CR) (21), (b) temperature shifts (22), (c) the down-regulation of the insulin-like signaling pathway (23,24), (d) up-regulation of the antioxidant defense system (ADS) plus altered mitochondrial properties (25), and (e) additive effects of mechanisms (c) and (d) combined (Hwangbo and colleagues, in preparation). These presumptive mechanisms in flies probably exert varied specific effects, but all seem to lead to high levels of somatic maintenance and thus to a significant delay in the onset of observable loss of function (i.e., senescence). This empirical evidence demonstrates that not only do multiple longevity phenotypes exist but that each of them may be induced by a variety of stimuli, some of which may interact in an additive manner.

These three longevity phenotypes are empirical observations. They do not, however, arise from random events with limited significance. They in fact represent the operation of the organism's homeostatic mechanisms, and can be mathematically modeled as the outcome of variations in antioxidant defense, environmental conditions, or energy allocations to reproduction (Figure 3 and Appendix). These factors are generally agreed to be fundamental to the biology of aging. It therefore follows that the appearance of multiple longevity phenotypes may be anticipated in any species subject to these fundamental factors. This finding suggests that an overview of potential life expectancy outcomes for a species should be based on the analysis of all longevity phenotypes likely to occur in that species.



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Figure 3. Simulation of different types of aging in Drosophila. A, Type I: effect of increased antioxidant defense ß. The simplest way to reproduce Type I aging is to change the corresponding genetic mean value ß. We simulate three populations in which the oxidative vulnerability decreases (ß = 1.2 x 10–4; 1.0 x 10–4; 0.8 x 10–4). The other parameters are unchanged; S0 = const, {sigma}S = 0.001; W = const, {sigma}S = 0.001. Similar patterns can be created by simultaneous changes in ß, S0, and W (not shown). C, Type II: rectangularization of a survival pattern by a decrease in external mortality. External mortality in a population is described by a Makeham coefficient, m = const. When m decreases (m = 0.01; 0.005; 0.0001), the survival pattern moves right to the pattern with m = 0; mortality becomes closer to that caused by the natural senescence only. The final pattern is that for a randomized rate of aging, Rr = R0 · {xi}R, where {xi}R is Gaussian variable with mean = 1.0 and = 0.02. B, Type III: manipulations with reproduction. High mortality in an initial population is caused by the extreme reproductive effort (the energy proportion devoted to reproduction is shown). Fecundity pattern for an R-strain with the plateau Wr = 42.6 eggs/day is presented by the thick curve (55). Thin line shows the original fecundity scores (53). D, Type III: manipulations with reproduction. Decreased investment to reproduction (Wr = 50, 45, and 40 eggs/day) results in a reshaping of the survival pattern by moving it to the right

 
As expected, this diversity of longevity phenotypes is not restricted to insects. All three are known in mice. The Type 1 delayed onset of senescence phenotype is known to occur in calorically restricted mice (26), in dwarf mice (27), in mice lacking the insulin receptor in their adipose tissue (28), and in mice expressing a down-regulation of the insulin-like growth factor-1 (IGF-1) receptor (29). The Type 2 increased early survival phenotype is noted in exercising mice (30). The Type 3 increased late survival phenotype is observed when comparing the survival of inbred mice with that of their F1 hybrids [for example, BALB/cJ or DBA/2J mice to that of their F1 BDA hybrid (31)].

However, only two of these three longevity phenotypes are known to occur in humans. The reduced early mortality and increased mean life span but unchanged maximum life span observed in the Type 2 phenotype is characteristic of exercising humans versus their sedentary controls (30), while the increased late survival characteristic of the Type 3 phenotype is characteristic of human centenarians (32–34). Both of these phenotypes have been taken into account in the Carnes–Olshansky analysis, but the potential contribution of the Type 1 delayed senescence phenotype has been overlooked. It may be argued that it was overlooked due to the absence of its occurrence in humans. But the whole point of using the fly and mouse as model systems is to identify evolutionarily conserved mechanisms and processes not clearly observable in humans (35–39).

The occurrence of these three longevity phenotypes in mice strongly implies their parallel existence in humans. There is every reason to believe that the Type 1 phenotype can be expressed in primates. For example, it certainly appears as if the caloric restriction-induced Type 1 phenotype is expressed in macaque monkeys (40) and humans (41) subjected to caloric restriction. This is almost certainly a conserved longevity mechanism and a conserved longevity phenotype. In addition, there are suggestions of shifts in certain human mortality curves consistent with such a phenotype (42,43).


    DISCUSSION
 Top
 Abstract
 Summary of the Arguments
 Animal Studies
 Discussion
 Appendix
 References
 
The Oeppen–Vaupel argument depends on the continued increase of world record life expectancy at a rate comparable to that of the past (i.e., 2.5 years per decade). No mechanistic basis for this prediction is offered, and this absence is a weak aspect of their argument. Given the fact that the easy victories have already been won, as Carnes and Olshansky point out, then this implies that such a large increase will occur only if new techniques allow the slowing down of senescence in postreproductive adults (3) or the delayed onset of senescence in presenescent adults. The genetic results described herein justify the optimism of both Olshansky and colleagues (4) and of Oeppen and Vaupel (5) that such new interventions might someday be developed. They also show that the interventions serve to significantly extend the "biological warranty period" by delaying the onset of senescence and its associated increase in age-specific mortality rates (Figure 2A). In addition, we will point out below how the new data of Mair and colleagues (22) suggest that some future interventions might be effective in postsenescent adults as well.

The Carnes–Olshansky analysis and its reliance on the evolutionary theory of aging sets real limits on the increased life expectancy that might be obtained from interventions on senescing (i.e., postreproductive) humans. Their overlooking the implications of the Type 1 phenotype means they assume that all possible longevity interventions that might affect their predictions are restricted to the postreproductive portion of the life span. They explicitly state that "There are no life-style changes, surgical procedures, vitamins, antioxidants, hormones, or techniques of genetic engineering available today with the capacity to repeat the gains in life expectancy that were achieved during the 20th century. If there is to be another quantum leap in life expectancy at birth (20 to 30 years or more), these large gains will have to come from adding decades of life to the lives of people who reach the ages of 70 and older" (3, p. 1492). But the Type 1 interventions in animal models act prior to the age of EER so as to delay the onset of senescence. As explained in the next paragraph, this intervention effectively "loads" the extra longevity not in the postreproductive senescent phase but rather into the reproductive presenescent phase. This results in the significant temporal extension of the low levels of age-specific mortality characteristic of such organisms.

It is instructive to use the existing mouse data to extrapolate the possible effects of such an intervention on human longevity. For the sake of argument, let us consider a cohort life span to be composed of a "health span," during which the animals are healthy and the mortality rate is low, constant, and age-independent; and a "senescent span," during which the animals are senescing, losing function, and the mortality rate is increasing in an age-dependent manner. Let us define the health span as that period of time beginning with reproductive maturity and lasting until that time when the logqx values begin to increase. For the purposes of the present discussion, we shall arbitrarily define that age to be when 10% of the population will have died (LT10). Consequently, the senescent span will cover the period of time from the LT10 until the last animal in the cohort dies. (By these criteria, the control fly population in Figure 1A would have a health span of approximately 30 days, while the long-lived population would have a health span of ~55 days.) Female mice genetically engineered to have a 50% reduction in the levels of their IGF-1 receptor (IGF-1R) genes have a Type 1 extended longevity due to a delayed onset of senescence (see Figure 2 of ref. 29). The health span of the control female mice covers the period from approximately 3 to 12 months while that of the experimental female mice covers the period from approximately 3 to 21 months. Death occurs at 27 and 32 months, respectively. Thus, the senescent span of the female control mice is approximately 15 months while that of the female experimental mice is approximately 11 months. Not only is there a 33% increase in the mean life spans (756 ± 46 vs 568 ± 49 days) and an approximately 18.5% increase in the maximum life span, but the health span of the treated female animals increased from 9 months to 18 months while the senescent span decreased from 15 months to 11 months. As suggested by Figure 2A, the doubling of the health span likely came about because the age-specific mortality rates of the treated mice did not rise at the same time as did the control, but rather stayed near the low extrinsic level characteristic of their controlled environment. Other genetic interventions that also interfere with the insulin- or glucoregulatory mechanisms of the body bring about a similar phenotype (28). If we assume, as did Carnes and colleagues (2), that mice and humans will react rather similarly, then this means that such an intervention would increase the human female health span from approximately 35 years (ages 20 to 55 years) to approximately 70 years (ages 20 to 90 years) while decreasing the human senescent span from approximately 45 years (ages 55 to 100 years) to approximately 33 years (ages 100 to 133 years). The point of this numerical exercise is not so much the actual numbers as it is to emphasize that the next "... quantum leap in life expectancy at birth ..." will come from intervening in younger adults rather than in older senescent adults.

Note that the effects of these new types of interventions are consistent with the views of both Olshansky and colleagues (3) and Vaupel and colleagues (44), both of whom predict that new interventions will be necessary if life expectancy at birth is to continue to increase.

It may well be argued that genetic alterations of a few mice do not constitute an effective human anti-aging intervention because of (a) the great difficulties associated with genetic engineering of humans and (b) the long time likely to elapse until an effective nongenetical intervention is approved for general use. The point of using genetically altered mice is not to develop genetic engineering techniques suitable for human use but rather to identify the genetic pathways regulating longevity so that one can devise suitable pharmaceutical interventions that will induce the expression of the same longevity phenotype. It was this mindset that led to the recent identification and characterization of the insulin-like signaling pathway (ISP) as a major evolutionary conserved longevity-regulating mechanisms operative in all laboratory models, including humans. Pharmaceutical interventions capable of inducing the expression of a Type 1 longevity phenotype are a reality. The Food and Drug Administration (FDA)-approved drug, 4-phenylbutyrate, induces a delayed onset of senescence in Drosophila by inhibiting certain histone deacetylases and thereby activating various antioxidant and other genes (45). Caloric restriction will bring about a Type 1 longevity phenotype in mice (26) and humans (41), and a similar phenotype can be induced in rats by high doses of the FDA-approved glucoregulatory drug metformin (46). Related FDA-approved glucoregulatory drugs are believed to exert similar effects on laboratory animals. Other laboratories are searching for different caloric restriction mimetic drugs (40). Nonetheless, the phenylbutyrate and metformin cases constitute a proof of concept. It is these types of pharmaceutical interventions applied to presenescent humans that will bring about the next quantum leap in life expectancy at birth. The fact that these drugs are already FDA approved will likely speed up their eventual translation from laboratory to clinic.

There are two major implications of these genetic researches for the current discussion of human demography. The first implication is that humans are likely composed of subpopulations with various longevity phenotypes, all of which should be taken into consideration when estimating the likely longevity limits of our species. Another implication is that the normally rare Type 1 phenotype may be induced in younger animals by means of targeted pharmaceutical modulation of the insulin/glucoregulatory mechanisms. This induced phenotypic plasticity will likely result in a delayed onset of senescence and a significantly extended longevity for some increasingly larger subset of the population.

There is a third implication regarding other future interventions inherent in some recently published data dealing with caloric restriction in Drosophila (22). Shifting flies from an ad libitum diet to a caloric restriction diet, or vice versa, affected the age-specific mortality rates such that the animals after the shift rapidly expressed the mortality rate characteristic of animals raised all their lives on the new diet. In other words, even older animals rapidly lowered their intrinsic mortality rate to a level characteristic of younger animals. This observation is consistent with the recent findings that the caloric restriction effect appears to take place at the cellular level (47), and that caloric restriction is known to exert significant effects at the molecular level within several months after initiation in older rodents (48). Should caloric restriction mimetic drugs be found to bring about a similar decrease in age-specific mortality rates when administered to older mice, then it might be possible in the future to significantly increase the life span of postreproductive humans as well. Administering the drug at this stage would result in an extension of the senescent span. Thus, this option is just an extension of our present efforts to increase the longevity of elderly postreproductive humans. What is interesting is the possibility that a caloric restriction mimetic drug may bring about either a delayed onset of senescence or just a slowed senescence, depending on the age of the recipient.

It is true that these particular anti-aging interventions are still being studied in animals. It is true that the necessary clinically approved human biomarkers are not yet in place. It is true that theoretical possibilities are difficult to model. It is true that one could marshal other practical objections. Whether the clinical use of such interventions takes place in one decade or in three decades is a matter of conjecture at this time—but that it will take place is highly probable. And it is this information that public policy decision makers need to know.

Other probable but presently theoretical events affecting longevity have been modeled. The increasing obesity of the United States population is an indication that many people are following nonhealthy lifestyles. The probable negative effect of this trend on longevity has been modeled (49). It is unlikely that present or future Type 1 pharmaceutical anti-aging interventions will work effectively in an unhealthy background. One can envision a future in which the population stratifies into two components. One component being a subset of people practicing a healthy lifestyle conducive to a pharmaceutically induced extended longevity, while the other comprises a perhaps larger group of people practicing an unhealthy lifestyle refractive to such interventions and perhaps conducive to a shorter than normal longevity. The potential stratification of our society into very long-lived and rather short-lived subpopulations would have ramifications beyond the financial stability of the U.S. Social Security program. It would be useful to have these apparently contrary trends analyzed in detail by the demographic community.

Given these probable developments, it would be useful if the likely effects of such interventions could be factored into the demographic predictions, if only to alert the policy makers that the demographic future is likely to keep changing in unexpected ways. It would be perfectly acceptable to include this information in the more speculative part of the forecast of our future demography until the necessary clinical data are in place. Policy makers need time to adjust to the coming realities, as the past decades of political debate has shown. Their need for time to digest the data will likely be even more prevalent when that future appears to be more complex than that which they may have assumed. The genie is out of the pill bottle, which is an appropriate metaphor to keep in mind as we enter into the century of biology.


    APPENDIX
 Top
 Abstract
 Summary of the Arguments
 Animal Studies
 Discussion
 Appendix
 References
 
Survival Patterns Attainable in Simulated Drosophila Populations.-- To simulate the three types of aging presented above, we will model aging in an individual (A), and in a population (B) via homeostatic model of oxidative stress and aging (54,55). Then we will change the parameters of individual and population aging to yield the types of aging that corresponds to the general types from above.

A. Aging: injuring of individual homeostatic mechanism by oxidative stress
Oxidative stress is accumulated in the organism with age. The rate of accumulation at age x is


where W(x) is the age-related pattern of oxygen consumption rate, and ß is an oxidative vulnerability. We assume ß = const. As for the patterns of oxygen consumption, W(x) = const in males, and W(x) changes in females in agree with individual fecundity pattern.

The main feature of the homeostatic modeling of aging is that the accumulation of oxidative stress injures the homeostatic capacity S(x) of physiological systems in the organism. The damage accumulation results in the age-related "exponential" decrease of S from the initial value, S0:


An energy resource of the organism is assumed to be equal the oxygen level in the cells, Q(x). It is supported by the oxygen delivery system with homeostatic capacity S(x). At age x the current "steady state" exists


where P is atmospheric oxygen pressure. The oxygen resource decreases with age alongside with the decreasing S(x). At some age xD, zero level is achieved: Q(xD) = 0, and senescence-caused death occurs (55).

In the above theory there are only three parameters: ß, S0, and W0. In males, they are assumed to be constants. These parameters dictate the life history patterns S(x) and Q(x) ending with the individual's death.

The parameters values for a typical Drosophila males are as follow: W0 = 80–150 (µl2/day), S0 = 1.5 ÷ 2.5 (µl2/day/mmHg), ß = 0.8 ÷ 2.0 (x·10–4). ß is measured in (1/µl2). For females, a pattern W(x) is governed by the egg production. These parameters (for P = 150 mm. Hg) yield Q0 about 100 (mm. Hg) and LS about 30 ÷ 100 (days).

B. Mimicking a population: addition of phenotypic variability
Usually populations, not individuals are studied. A homogeneous population can be simulated as a set of genetically identical flies with phenotypic variations (N = 500). Phenotypic variability of the population is generated by the Gaussian scattering of the parameters S0 and W0:


Here {xi}S and {xi}W are Gaussian random variables with the mean values equal to unity and the variances {sigma}. The typical are values {sigma}S = 0 ÷ 0.05 and {sigma}W = 0 ÷ 0.02.

Thus the parameters characterizing the population are the genotypic mean values ß, S0, and W0, and phenotypic variances {sigma}S and {sigma}W. Due to phenotypic variability the life spans of individuals differ, and the model produces a "natural" survival pattern Surv0(x). In this pattern only senescence-related mortality is presented. The external influences can be simulated by a Makeham coefficient m(x):


The model allows generating a number of varying survival patterns, which may be related to the patterns observed experimentally in different species. In particular, Figure 3 demonstrates the examples of type I–type III patterns discussed above.


    Footnotes
 
Decision Editor: James R. Smith, PhD

Received December 10, 2003


    References
 Top
 Abstract
 Summary of the Arguments
 Animal Studies
 Discussion
 Appendix
 References
 

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