Full text of DOI:10.1093/gerona/56.10.B432

Journal of Gerontology: BIOLOGICAL SCIENCES
Copyright 2001 by The Gerontological Society of America
2001, Vol. 56A, No. 10, B432–B442
Have the Oldest Old Adults Ever Been Frail in
the Past? A Hypothesis That Explains Modern
Trends in Survival
Anatoli I. Yashin,1,7 Svetlana V. Ukraintseva,1,2 Giovanna De Benedictis,3 Vladimir N. Anisimov,1,4
Alexander A. Butov,1,5 Konstantin Arbeev,1,5 Dmitri A. Jdanov,1,5 Serge I. Boiko,1
Alexander S. Begun,1 Maximiliano Bonafe,6 and Claudio Franceschi6
1Max Planck Institute for Demographic Research, Rostock, Germany.
2Research Center for Medical Genetics, Russian Academy of Medical Sciences, Moscow.
3Department of Cell Biology, University of Calabria, Rende, Italy.
4N. N. Petrov Institute of Oncology, St. Petersburg, Russia.
5Ulyanovsk State University, Russia.
6Department of Molecular Pathology, University of Bologna, Italy.
7Center for Demographic Studies, Duke University, Durham, North Carolina.
Three important results concerning the shape and the trends of the human mortality rate were
discussed recently in demographic and epidemiological literature. These are the deceleration of
the mortality rate at old ages, the tendency to rectangularization of the survival curve, and the
decline of the old age mortality observed in the second part of the 20th century. In this paper we
show that all these results can be explained by using a model with a new type of heterogeneity
associated with individual differences in adaptive capacity. We first illustrate the idea of such a
model by considering survival in a mixture of two subpopulations of individuals (called “labile”
and “stable”). These subpopulations are characterized by different Gompertz mortality patterns,
such that their mortality rates cross over. The survival chances of individuals in these subpopu-
lations have different sensitivities to changes in environmental conditions. Then we develop a
more comprehensive model in which the mortality rate is related to the adaptive capacity of an
organism. We show that the trends in survival patterns experienced by a mixture of such individ-
uals resemble those obtained in an analysis of empirical data on survival in developed countries.
Lastly, we present evidence of the existence of subpopulations of phenotypes in both humans
and experimental organisms, which were used as prototypes in our models. The existence of
such phenotypes provides the possibility that at least part of today’s centenarians originated
from an initially frail part of the cohort.
ECENT demographic studies of aging and survival re-
veal three important features characterizing mortality
vival improvement in the United States, Canada, France, It-
aly, England and Wales, and Japan are similar to those ob-
served in Sweden.
R
rates and survival dynamics in populations of developed
parts of the world. The first feature is the deceleration of the
age-specific mortality rate at old ages (1). The second fea-
ture deals with the age pattern of mortality and survival im-
provement (2,3). The third characterizes changes in such a
pattern during the 20th century. Figure 1 shows two main
patterns of change in survival of Swedish females in the
20th century.
One can see from this figure that the distinct rectangular-
ization pattern of survival improvement observed in the first
part of the 20th century was replaced by a near-parallel shift
of survival curves to the right with an increase in old-age
survival. The unprecedented growth in the proportion of
centenarians in developed countries is a good illustration of
the latter changes (4). Our analysis shows that trends in sur-
An explanation of the mortality-deceleration effect was
given by Vaupel and colleagues (1) in terms of a frailty
model. Long debates about the compression of morbidity
(2,5,6) resulted in an admission of the fact that both the ef-
fect of rectangularization of the survival curve and the
lengthening of the tail of survival distribution do take place
in modern survival patterns. In this paper we show that the
rectangularization trend in survival improvement that domi-
nated in the first part of the 20th century was replaced by a
near-parallel shift of the survival curve to the right in the
second part. We also show that the deceleration of old-age
mortality, the rectangularization trend, and observed changes
in survival patterns with years can be explained by dynamic
properties of mortality and survival in a heterogeneous pop-
B432

MODERN TRENDS IN SURVIVAL
B433
Figure 1. The change in the pattern of survival (top panels) and mortality (middle and bottom panels) improvement in Sweden. The bottom
panels show the changes in the logarithm of age-specific mortality after the age of 40 years.
ulation. The goal of this paper is not to fit model to the data,
but to show that all three features can be explained by using
the model of population heterogeneity in which the loga-
rithms of mortality rates in subpopulations cross over. We
also provide evidence that such populations exist in nature.
For simplicity, we consider the mixture of two such sub-
populations, which we call “labile” and “stable.” We also
assume that survival in these two groups has different re-
sponses to environmental changes. An improvement in liv-
ing standards increases the proportion of initially frail (la-
bile) individuals in such a mixture in the old part of the
population. This is an interesting property, because it shows
that today’s centenarians might not be among the longest-
lived individuals if they were born two centuries ago. We

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YASHIN ET AL.
discuss the plausibility of the latter model, in the light of re-
cent findings about the aging process in humans and labora-
tory animals and of the wide data on genetics and physiol-
ogy of extremely old individuals (centenarians). We discuss
empirical evidence of the presence of subpopulations of in-
dividuals with different slopes of the mortality curve, and
we describe possible mechanisms by which an initially frail
organism may become robust (or vise versa) later in life.
These mechanisms include the following: (i) the antagonis-
tic gene action; (ii) slower aging, which may be associated
with not optimal health parameters in some ages; and (iii)
the antagonistic change in stress resistance during an indi-
vidual life.
Finally, we develop a mathematical model of mortality
and aging, which illustrates one possible mechanism of an-
tagonistic change in relative risk in the course of an individ-
ual’s life. This model explains the possibility of a centenar-
ian’s origin from an initially frail part of a cohort. It
describes survival of two kinds of individuals, which origi-
nally have different sensitivities to changes in environmen-
tal conditions and different abilities to adapt to these
changes. The model establishes interrelations between these
characteristics and survival. We show that the trends in sur-
vival patterns experienced by a mixture of such individuals
resemble those observed in humans during the previous
century.
curves for two subpopulations around the age of 85 years
manifests antagonistically changing relative risk (frailty) in
two respective subpopulations. Individuals from the first
(labile) subpopulation are originally frailer than individuals
from the second one. (Their mortality rate is initially higher
than that of the second subpopulation, but its rate of in-
crease is slower.) After intersection (in our example, at age
85 years), the proportion of labile individuals starts to in-
crease. This is because at old ages they become more robust
than individuals from the stable population. This intersec-
tion indicates that because of significant mortality reduction
in the population of labile individuals, some portion of to-
day’s centenarians may originate from an initially frail part
of the population. It also shows that at least part of today’s
centenarians would not be among the longest-lived individ-
uals if the progress in mortality reduction had stopped ap-
proximately a century ago.
Figure 4 shows how survival function corresponding to
Swedish females in 1861 can be approximated as a mixture
of two survival functions. The lower survival function cor-
responds to labile individuals; the higher survival function
represents stable individuals. Figure 5 shows how the sur-
vival function for Swedish females in 1995 can be approxi-
mated as a mixture of survival functions for labile and sta-
ble individuals with the same properties. In this figure the
survival function for labile individuals intersects that of sta-
ble individuals around age 70 years. This intersection hap-
pens as a result of faster progress in the mortality reduction
in the labile subpopulation.
THE MODEL
To explain observed trends in human survival, we hy-
pothesize that each cohort in a human population is a mix-
ture of two subcohorts of individuals—the labile and the
stable. The mortality rate in the population of labile individ-
uals is initially higher, but its rate of increase with an in-
crease of age is slower than that of stable individuals. Be-
cause of this difference in mortality rates, labile individuals
are also referred to as initially frail individuals. In this case,
frailty defined as the ratio of mortality rate in labile popula-
tions to the respective rate in stable populations (relative
risk) declines with age.
In the next section we describe a model that incorporates
physiological and environmental changes. These changes
produce two different survival responses in two subpopula-
tions.
Model of Difference in Stress Response That Produces
an Intersection of Mortality Rates
We suggest a model of physiological aging and survival
in which adaptation to the stresses of life has a metabolic
cost. The model shows that today’s centenarians may origi-
nate from an initially frail part of a cohort. The model de-
scribes survival of two kinds of individuals, the labile and sta-
ble. These individuals have different sensitivities to changes
in environmental conditions, and so different amplitudes of
the response to stress. The model establishes interrelations
between amplitude and survival. The low amplitude of the re-
sponse to stress corresponds to stable individuals; the higher
amplitude corresponds to labile ones. The mathematical de-
velopment is reported in the Appendix; here a qualitative
description is given.
For simplicity, we assume that at any age an organism
may be in one of two possible states. One is the state of nor-
mal functioning. The other is a state of stress, disease, or
other tension (arousal), induced by some external or internal
conditions, in which the systems of an organism are func-
tioning with an “overload” (7). A long stay in this state must
have a cost for an organism: when it accumulates, the sur-
vival chances of an organism decline. The response of an
organism to stress is regulated by the parameter ꢀ, called the
rate of recovery, or the adaptation rate (see the Appendix).
The lability property is associated with small values of ꢀ;
Antagonistically Changing Frailty in the Process of an
Individual’s Life
Let us assume that the human population is a mixture of
two subpopulations of individuals, both with Gompertz mor-
tality rates, but with different slopes of a logarithm of mor-
tality. At the beginning of the century the mortality rate for
one subpopulation with lower slope is higher than that of
the other. The intersection of such curves happens at an age
that is beyond the observed range of the human life span
(say, at 130 years, or more). The improvements in the stan-
dards of living produce a significant reduction of the mor-
tality rate for the first (labile) subpopulation, and less signif-
icant changes in the survival chances in the second (stable)
subpopulation (see Figure 2).
As a result, the middle-century mortality rate for the first
population crosses the mortality curve for the second one at the
age of ꢀ85 years. After this time the two curves evolve together
(shift to the right) with almost the same speed (Figure 3).
Such an evolution produces the pattern of changes similar
to those shown in Figure 1. The overcrossing of mortality

MODERN TRENDS IN SURVIVAL
B435
Figure 2. Secular trends in survival calculated in accordance with the model of mortality in a mixture of two subpopulations with different
slopes of the Gompertz curve, adjusted to the mortality data on Swedish females for the years 1910 and 1950, respectively.
stability is associated with high ones. Because those who
cannot adapt properly die first, the survival function of indi-
viduals with a small adaptation rate (i.e., labile individuals)
is initially lower than that of individuals with high values of
this rate (i.e., stable individuals). This means that stable in-
dividuals have a survival advantage earlier in life. The
model establishes interrelations between the rate of adapta-
tion and the accumulation of damage: a high rate yields a
metabolic cost included in the definition of allostatic load;
see Equation (3) of the Appendix. Then, at older ages, indi-
viduals with smaller values of the adaptation rate may have
higher survival chances than those with higher values of ꢀ.
That is why the survival curves for these two groups of indi-
viduals may intersect. Another important parameter of the
model ꢁ characterizes permanently acting environmental
disturbances. The higher the ꢁ, the higher the level of dis-
turbances. The life-span distribution in this model is ob-
tained by simulation of individual life spans for a large sam-
ple of individuals (see the Appendix). Figure 6 shows
survival patterns, generated by the model, in hypothetical
populations of labile (small ꢀ) and stable (large ꢀ) individu-
als, for two values of ꢁ: the two values of ꢁ represent the
transition from low standards of living (high value of ꢁ) to
improved ones (lower value of ꢁ).
One can see that the survival functions for labile and sta-
ble individuals have different shapes. Even for large values
of disturbance factor ꢁ, respective survival functions inter-
sect. The age at intersection moves to the left when the level
of disturbances declines. Perhaps the most striking result
shown by the simulation is that the variation of ꢁ (an in-
crease in living standards) has a small impact on the stable
population, whereas it substantially increases the survival of
the labile one, which exceeds that of the stable population at
older ages.
Figure 7 shows the survival patterns of a mixture of labile
and stable individuals (with survival functions shown in
Figure 6) before and after an improvement in living stan-
dards. One can see from this figure that the resulting sur-
vival function shows both features. It became more rectan-
gular, and it has a longer tail than the initial one.
THE GENES: EXPERIMENTAL DATA
Individual lability–stability could be regarded as a pheno-
typic trait resulting both from the individual specific envi-
ronmental history and from the individual specific genetic
equipment. However, different genes are expected to affect
the trait in different ways, according to their role and effec-
tiveness in stress response. Because centenarians living to-

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YASHIN ET AL.
Figure 3. Secular trends in survival calculated in accordance with the model of mortality in a mixture of two subpopulations with different
slopes of the Gompertz curve, adjusted to the mortality data on Swedish females for the years 1950 and 1995, respectively.
day experienced dramatic social and cultural changes (from
high to low ꢁ values) with respect to those of younger indi-
viduals (low ꢁ), the cohort of centenarians should be
formed by both labile and stable individuals (Figure 6). The
model discussed above can be checked by comparing the
levels of genetic homogeneity between centenarians and
younger individuals (20–60 years old) extracted from the
same population. Let us consider a stress responder gene,
with A and a alleles conferring lability (small values of ꢀ)
and stability (high values of ꢀ), respectively. Let us assume
that the frequencies of A and a at the birth of the cohort are
pA ꢂ pa, and that the population is in Hardy–Weinberg
equilibrium. When survival selection operates under high ꢁ
(thin lines in Figure 4), the allelic pool will tend toward an
increase of a, with a consequent decrease of heterozygosity.
However, as ꢁ decreases (thick lines in Figure 6), A will
tend to remain in the gene pool, and the level of heterozy-
gosity will increase in the cohort of centenarians. Therefore
centenarians are expected to show increasing heterozygos-
ity with respect to youths for stress-responder genes affect-
ing lability–stability. We checked our hypothesis by esti-
mating heterozygosity at 12 autosomal loci in centenarians
and younger individuals, after verification of Hardy–Wein-
berg equilibrium. The results are shown in Table 1.
A trend toward decreasing heterozygosity from youths to
centenarians was observed at the loci denoted with numbers
from 1 to 8 in Table 1. This result is in line with the nega-
tive correlation between population heterozygosity and life
span observed by studying neutral polymorphisms (10). In
contrast, the level of heterozygosity tended to increase from
youths to centenarians for HSP70, THO, INS, and IGF2
loci. It must be noted that THO, INS, and IGF2 loci lie in
the same chromosomal region (11p15.5) and that both INS
and IGF2 markers are in linkage disequilibrium with THO
markers in Table 1 (data not shown). THO and HSP70 are
the only stress-responder genes studied until now with re-
spect to human life span. THO is the rate-limiting enzyme
in cathecolamine biosynthesis, amino acid-derived mole-
cules that act both as hormone (adrenalin) and neurotrans-
mitters (dopamine and noradrenalin). HSP70 is the stress-
responder gene evolutionary conserved from bacteria to hu-
mans. The finding that centenarians are less homogeneous
than younger subjects at both THO and HSP70 loci supports
the model given above.
DISCUSSION
In the following subsections we discuss how both the as-
sumptions from which the model is built up and the results

MODERN TRENDS IN SURVIVAL
B437
Figure 6. Survival functions in hypothetical subcohorts of labile (ꢀ ꢂ
370, ---, sample size 500) and stable (ꢀ ꢂ 550, —, sample size 1500) in-
dividuals before (ꢁ ꢂ 6.4, — and ---) and after (ꢁ ꢂ 6.0,
and
)
improvement in living conditions. Dotted lines (... and ..., respec-
tively) show changes in respective survival functions, assuming that
an improvement in living conditions (ꢁ ꢂ 6.4 was replaced by ꢁ ꢂ
6.0) happened at the age of 40 years in each subcohorts. The data are
simulated in accordance with the life history model for labile and sta-
ble individuals described in the Appendix.
Figure 4. Survival function in Swedish females in the year 1861 (ꢀ)
approximated by a survival function in a mixture of stable (...) and la-
bile (---) individuals with initial proportions of p1 ꢂ 0.759 and p2 ꢂ
0.241, respectively. The central line (—) refers to a mixture of two hy-
pothetical cohorts of labile and stable individuals.
fore (4). It is clear that both effects may mirror an influence
of the increasing standards of living on the mortality curves
of homogeneous subcohorts, comprising heterogeneous
groups of individuals. This, however, does not explain the
observed trends in survival patterns. The explanation would
be easier to obtain if we assume that a substantial part of the
group of centenarians originates from an initially vulnera-
ble, frail part of a generation, whose deaths at adult age
were prevented by the improvements in health and living
standards gained by industrial progress. Because industrial
progress is likely to increase survival chances for all indi-
provided by it enable us to explain several phenomena ob-
served in human population and experimental studies.
Paradoxes in Centenarians
The progress in health and living standards experienced
by the human population today tends to increase the propor-
tion of originally frail individuals in successive generations
(11,12). The proportion of centenarians in human popula-
tions of developed countries also increases faster than be-
Figure 7. Survival functions in a mixture of hypothetical subco-
horts of labile (ꢀ ꢂ 370, sample size 500) and stable (ꢀ ꢂ 550, sample
size 1500) individuals before (ꢁ ꢂ 6.4, ---) and after (ꢁ ꢂ 6.0, —) im-
provement in living conditions. The initial proportion of labile indi-
viduals is 0.25. The thin solid line shows changes in survival in a
mixed cohort (initial ꢁ ꢂ 6.4) as a result of improvement in living
conditions that occurred at an age of 40 years (at this age ꢁ ꢂ 6.4 was
replaced by ꢁ ꢂ 6.0). The data are simulated in accordance with the
life history model for labile and stable individuals described in the
Appendix.
Figure 5. Survival function in Swedish females in the year 1995 (ꢀ)
approximated by a survival function in a mixture of stable (---) and la-
bile (– – –) individuals with initial proportions of p1 ꢂ 0.759 and p2 ꢂ
0.241, respectively. The central line (—) refers to a mixture of two hy-
pothetical cohorts of labile and stable individuals.

B438
YASHIN ET AL.
Table 1. Heterozygosity in Centenarians and Younger Subjects
Autosomal
Loci
*Allele
No.
Sample
Size
Young Subjects
(20–60 y)
Sample
Size
Gene
REN
Marker
Centenarians
1
2
3
4
5
6
7
8
9
(acag)n.STR
C/T (401)
(gt)n.STR
3ꢃVNTR†
5 (4)
2 (2)
7 (6)
3 (3)
2 (2)
2 (2)
2 (2)
3 (3)
2 (2)
2 (2)
2 (2)
2 (2)
218
187
171
658
575
575
575
179
358
257
257
227
0.429 (0.383–0.472)
0.492 (0.474–0.499)
0.528 (0.464–0.582)
0.558 (0.536–0.575)
0.391 (0.364–0.413)
0.179 (0.153–0.205)
0.243 (0.206–0.260)
0.297 (0.237–0.357)
0.482 (0.470–0.488)
0.268 (0.224–0.316)
0.439 (0.408–0.464)
0.445 (0.411–0.461)
157
167
147
260
194
197
193
210
217
217
217
198
0.352 (0.286–0.411)
0.488 (0.467–0.498)
0.482 (0.415–0.543)
0.549 (0.511–0.582)
0.336 (0.292–0.378)
0.153 (0.105–0.198)
0.238 (0.190–0.287)
0.181 (0.131–0.227)
0.495 (0.485–0.505)
0.301 (0.251–0.345)
0.454 (0.425–0.477)
0.480 (0.459–0.494)
SOD2
PARP
APOB
APOA1
APOC3
APOA4
APOE
THO
MspI-RFLP
SstI-RFLP
HincII-RFLP
ε2/ε3/ε4
(acag)n.STR‡
Fok!-RFLP
AvaII-RFLP
A/C (promoter)
10
11
12
INS
IGF2
HSP70
Note: 95% confidence intervals calculated by bootstrap are reported in parentheses for young and centenarian subjects.
*The number of alleles in centenarians is reported in parentheses.
†Alleles recoded as small, medium, or large (8).
‡Alleles recoded as small and large (9).
viduals in the population, one should find a good reason
why some originally frail individuals get survival advan-
tages at old age. Several examples discussed below provide
compelling evidence about the possibility of the original
frailty of today’s centenarians.
Recent genetic studies in centenarians pointed out some
unexpected findings, as the presence of genetic risk factors
in their gene pool (13). For example, several alleles, known
to be associated with increased cardiovascular risk in mid-
dle age, are present in centenarians at the same frequency as
in younger individuals (14–17). In some cases, such risk
factors occur even more frequently in centenarians than in
younger individuals (18–22). Such counterintuitive accu-
mulation of originally harmful alleles may be easier to un-
derstand if the biological and physiological role of respec-
tive alleles in survival is taken into account.
For example, let us consider the guanine insertion/dele-
tion polymorphism 4G/5G in the promoter of the plasmino-
gen activator inhibitor 1 (PAI-1) gene, a predictor of the risk
of atherothrombotic disease. The 4G4G genotype is associ-
ated with a high plasma level of plasminogen activator in-
hibitor and therefore with an increased risk of athero-
thrombosis and myocardial infarction in adulthood (19).
Unexpectedly, the frequency of the 4G4G genotype is
higher in centenarians than in younger individuals (20). Our
model can explain this apparent paradox on the basis of the
physiological role of the PAI-1 hemostatic protein. The im-
provement in medical care and living conditions in early
and in middle ages (e.g., by saving lives and preventing
deaths of those who would otherwise die) promotes an in-
crease in the proportion of individuals carrying the harmful
genotype. However, this genotype, which is a risk genotype
at middle age, may turn out to be advantageous at older
ages, when the rate of metabolic processes decelerates, and
many processes including a recovery from injury go slower.
In such ages, a higher rate of blood coagulation may be ben-
eficial for faster recovery (e.g., for stopping bleeding). Thus
individuals with potentially harmful alleles, who yet sur-
vived under the pressure of selection and reached old age,
may get an advantage from the same alleles later in life.
Centenarians may also be those individuals whose devel-
opment (and aging) processes go slower than those in other
individuals of the same generation. Such individuals may
have a higher risk of death earlier in life because their health
parameters at young and adult ages may substantially devi-
ate from those “optimized” by the evolution. This is con-
firmed by the fact that the risk of death at a given age re-
garded as a function of physiological parameters can often
be approximated by a U-shaped curve (23). For example,
being both underweight and overweight is associated with
an increased risk of mortality. A person who grows old
slower may have a body mass index as well as other physio-
logical parameters (such as metabolic rate) that are not opti-
mal for survival at early and adult life. But if such a person
survives this period, he or she may have a survival advan-
tage at older ages because of a slower aging phenotype (see
Figure 8). Progress in medicine and health care together with
improvements in living standards increases survival of such
Figure 8. Risk as a quadratic function of hypothetical risk factor at
ages of 30 and 90 years. Individual 1 has minimum risk at age 30 but
an increased risk at age 90. Individual 2 has an increased risk at age
30 but a minimum risk at age 90. This happens because both the value
of the physiological risk factor and the parameters of risk function
change with age.

MODERN TRENDS IN SURVIVAL
B439
individuals earlier in life. This yields an increase in the pro-
portion of such individuals in old ages, where they get sur-
vival advantages, and it contributes to the increase in the
proportion of centenarians in a population.
a better-trained vascular system. In this scenario, some
heavy stresses at old ages are likely to be more lethal for the
robust individuals than for the originally vulnerable ones.
Thus, an originally more vulnerable (and primarily more la-
bile) organism may improve the quality of its own response
to stress compared with an originally more robust (and pri-
marily more stable) organism. Such change in the resistance
to stress may give a survival advantage at older ages to the
originally more vulnerable organisms. Because more such
organisms got the chance to survive their adulthood during
the past decades, they may be more present in the popula-
tion of the oldest old, that is, centenarians, today. The in-
crease of heterozygosity at stress-responder loci with re-
spect to younger controls (Table 1) is in line with the above
considerations.
The same considerations can be applied to model organ-
isms. Stress experiments with nematode worms Caenorhab-
ditis elegans reveal an intersection of survival curve in the
population exposed to 4 hours of heat shock with that in the
control group (30). The survival curves corresponding to a
population of some long-lived mutants of C. elegans inter-
sect those of wild-type worms under normal conditions
(31).
Stress Resistance and Longevity:
Labile–Stable Individuals
A positive correlation between stress resistance and lon-
gevity has been confirmed by many experimental studies in
model organisms (24–27) and has been hypothesized in hu-
man longevity too (18,28,29). Stress resistance means faster
response of the organism to destabilizing factors, and
quicker stabilization of homeostatic equilibrium. However,
the high level of stability has a metabolic cost, and the price
must be paid by an organism, if not at the adult age then at
the late ages. Thus, high stress resistance may be profitable
for the survival of an organism at young and adult ages but
have deleterious consequences later in life. For instance,
some individuals may be more resistant to fluctuations of
temperature and atmospheric pressure than others, who are
more susceptible to environmental changes. Such vulnera-
ble individuals have fluctuations of their vascular state in
parallel with the waves of ambient temperature and atmo-
spheric pressure. In contrast, the first-type individuals are
more robust when they are at adult ages, having better
health and lower chances of death than the vulnerable indi-
viduals. For many years of life, their cardiovascular system
has had less variability in parameters. As a result, this sys-
tem may be trained much less than that of vulnerable indi-
viduals. However, if the latter manage to survive to adult
ages, they may get a survival advantage later on, because of
Experiments with rodents give one more confirmation of
the existence of the labile phenotype. In aging studies on ro-
dents, rats and mice exposed to high doses (0.5 mg/rat) of
pineal gland preparation epithalamin (known as geroprotec-
tor) show lower survival earlier in life and better survival
later in life than those in the control group (Figure 9). These
rodents also manifested both increased maximal life span
and postponed aging (32–34). That is, treated rodents lived
Figure 9. Effect of succinic acid on survival and tumor incidence of female C3H/Sn mice (adapted from Anisimov and Konrashova, 1979). A,
survival curves; B, fatal tumor yield curves; C, simulated survival curves; 1, control; 2, treated with succinic acid. The treatment with succinic acid
prolonged an average and maximum life span and decreased spontaneous mammary adenocarcinoma development. The survival curve for the
treated group has a crossing at early age with the survival curve for the control group.

B440
YASHIN ET AL.
Acknowledgments
longer and aged slower (by a number of physiological pa-
rameters). At the same time, they are frailer at their young
and adult ages, and they are more robust at old ages than ro-
dents in the control group. Furthermore, in populations with
lower survival earlier in life and higher survival later in life,
tumorigenesis is going slower (32). This observation is ex-
pected in the population of labile individuals, in which the
accumulation of damage associated with the excess of meta-
bolic activity is slower than in the stable individuals. A sim-
ilar antagonistic change of survival in adult and in old ages
was observed in some experiments on rodents exposed to
caloric restriction, a treatment known to increase longevity
and postpone aging (35).
This research was partly supported by National Institutes of Health/Na-
tional Institute on Aging Grant 7P01AG08761-09 and by Russian Fund of
Basic Research Grant 99-01-00185. The authors thank James W. Vaupel
for the opportunity to use facilities of the Max Planck Institute for Demo-
graphic Research in Rostock, Germany, during this study, and Baerbel
Splettstoesser and Karl Brehmer for help in preparing this paper for publi-
cation. Dr. Yashin is now also affiliated with the Sanford Institute for Pub-
lic Policy, Duke University, Durham, NC.
Address correspondence to Anatoli Yashin, Max Planck Institute for
Demographic Research, Doberaner Strasse 114, 18057 Rostock, Germany.
E-mail: yashin@demogr.mpg.de
References
Experimental studies show that labile and stable pheno-
types may be the result of gene–environment interactions
(36). It means that individuals who are stable in one set of
environmental conditions may manifest a labile phenotype
in case of another set of conditions and vice versa. In any
case, all the above data agree with the existence of labile
and stable individuals assumed in our model.
1. Vaupel J, Carey J, Christensen K, et al. Biodemographic trajectories of
longevity. Science. 1998;280:855–860.
2. Fries JF. Aging, natural death and the compression of morbidity. N
Engl J Med. 1980;303(3):130–135.
3. Fries JF. Compression of morbidity of the elderly. Vaccine. 2000;
18(16):1584–1589.
4. Vaupel JW, Jeune B. The emergence and proliferation of centenarians.
In: Jeune B, Vaupel JW, eds. Experimental Longevity: from Prehistory
to the Present. Odense, Denmark: Odense University Press; 1995:
109–116.
Evolutionary Adaptation May Produce an Intersection
of Mortality Curves
5. Myers GC, Manton KG. Compression of mortality: myth or reality?
Gerontol. 1984;24(4):346–359.
The intersection of survival curves may have evolution-
ary reasons. The evolutionary theories suggest that genes
that would enhance fitness earlier in life may be selected
for, even if they produce detrimental effects later in life
(37). Because the notion of fitness involves fertility as well
as mortality, one may assume that mortality rates for geno-
types may have a spectrum of possible shapes (the average
fertility rates for the populations of these genotypes must
also be different). These theories link the life span with the
quality of maintenance and repair systems in the cells of an
organism. However, they do not provide an explicit descrip-
tion of possible mechanisms, which relate characteristics of
physiological and biological aging with demographic sur-
vival curves. The idea of disposable soma suggested by
Kirkwood (38) looks promising; however, it requires addi-
tional specification of resource-allocation strategies that
may depend on environmental conditions. In addition, none
of the theories explains why some individuals in a popula-
tion are more sensitive to industrial progress than the others.
6. Manton KG, Tolley HD. Rectangularization of the survival curve: im-
plications of an ill-posed question. J Aging Health. 1991;3(2):172–
193.
7. Sterling P, Eyer J. Allostasis: a new paradigm to explain arousal pa-
thology. In: Fisher S, Reason J, eds. Handbook of Life Stress,
Cognition and Health. New York: Wiley; 1988:629–649.
8. De Benedictis G, Carotenuto L, Carrieri G, De Luca M, Falcone E,
Rose G, Cavalcanti S, Corsonello F, Feraco E, Baggio G, Bertolini S,
Mari D, Mattace R, Yashin AI, Bonafè M, Franceschi C. Gene/longev-
ity association studies at four autosomal loci (REN, THO, PARP,
SOD2). Eur J Hum Genet. 1998;6:534–541.
9. De Benedictis G, Carotenuto L, Carrieri G, De Luca M, Falcone E,
Rose G, Yashin AI, Bonafe M, Franceschi C. Age-related changes of
the 3ꢃ APOB VNTR genotype pool in ageing cohorts. Ann Hum Genet.
1998;62:115–122.
10. Altukhov YP, Sheremetjeva VA. Genomic heterozygosity and human
longevity. Doklady Biol Sci. 2000;371:197–199.
11. Fogel RW, Costa DL. A theory of technophysio evolution, with some
implications for forecasting population, health care costs and pension
costs. Demography. 1997;(34)1:49–66.
12. Ukraintseva SV. Evolution of morbidity in human history. Clin Geron.
1998;4:61–65.
13. Robine JM, Forette C, Franceschi C. The Paradoxes of Longevity.
New York: Springer-Verlag; 1999.
14. Faure-Delanef L, Quere I, Zouali H, Cohen D. Human longevity and
R506Q factor V gene mutation. Thromb Haemost. 1997;78(3):1160.
15. Harman D. The aging process. Proc Natl Acad Sci USA. 1981;78(11):
7124–7128.
16. Brattstromm L, Zhang Y, Hurtig M, et al. A common methylenetet-
rahydrofolate reductase gene mutation and longevity. Atherosclerosis.
1998;1412:315–319.
17. Bladbjerg EM, Andersen-Ranberg K, de Maat MP, et al. Longevity is
independent of common variations in genes associated with cardiovas-
cular risk. Thromb Haemost. 1999;82:1100–1105.
18. Schächter, F. Causes, effects, and constraints in the genetics of human
longevity. Am J Hum Genet. 1998;62(5):1008–1014.
19. Galinsky D, Tysoe C, Bryne C, et al. Analysis of the ApoE/ApoC-1,
ACE genes as candidates affecting human longevity. Atherosclerosis.
1997;129:(2)177–183.
20. Mannucci PM, Mari D, Merati G, et al. Gene polymorphisms predict-
ing high plasma levels of coagulation and fibrinolysis proteins. A
study in centenarians. Arterioscler Thromb Vasc Biol. April 1997;17:
4, 755.
Conclusions
Mortality decline in the human population forms a sur-
vival pattern, which shows signs of both the rectangulariza-
tion of the survival curve and the lengthening of the tails of
survival distributions (5,39,40). In this paper we propose a
mixed stochastic–deterministic mathematical model of sur-
vival, which incorporates parameters directly related to
qualitative features such as adaptive capacity and sensitivity
to environmental changes of an individual. The qualitative
analysis and the simulation experiments show that the ob-
served pattern of mortality as well as trends in human sur-
vival can be explained in terms of a mixture of two subpop-
ulations. An important feature of these subpopulations is
that their mortality rates intersect, thus giving a solid inter-
pretation to the intersection of mortality curves often ob-
served in the studies of aging and survival, including human
and nonhuman subjects.
21. Pepe G, Di Perna V, Resta F. In search of a biological pattern for human
longevity: Impact of apo A-IV genetic polymorphisms on lipoproteins

MODERN TRENDS IN SURVIVAL
B441
and the hyper-Lp(a) in centenarians. Atherosclerosis. 1998;137(2):407–
417.
internal conditions. For simplicity, we assume that there are only
two possible states—“0” and “1.” State 0 is characterized by the
absence of stress, disease, or other conditions that require substan-
tial adaptational efforts. State 1 is an arousal state. It is character-
ized by elevated metabolic activity (as in the case of stress, dis-
22. Yashin AI, De Benedictis G, Vaupel JW, et al. Genes, demography,
and life span: the contribution of demographic data in genetic studies
on aging and longevity. Am J Hum Genet. 1999;5:1178–1193.
23. Yashin AI, Manton KG, Lowrimore GR. Evaluating partially observed
survival histories: retrospective projection of covariate trajectories.
Appl Stoch Mod Data Anal. 1997;13:1–13.
24. Hoffman AA, Parsons PA. Evolutionary Genetics and Environmental
Stress. Oxford, England: Oxford University Press; 1991.
25. Parsons PA. Habitats, stress, and evolutionary rates. J Evol Biol. 1994;
7:387–397.
ease, etc.). The process N ꢂ (Nt)t
describes random changes
0
ꢆ
between these states. The process ꢄt characterizes the intensity of
transitions (incidence of disease, stress hits) resulting in an arousal
state
νt = eδA
(1)
t
26. Jazwinski SM. Longevity, genes, and aging. Science. July 1996;273:
54–59.
27. Luckinbill LS. Selection for longevity confers resistance to low-tem-
perature stress in Drosophila melanogaster. J Gerontol Biol Sci. 1998;
53A:B147–B153.
where ꢇ is a nonnegative parameter. This process depends on At,
the fifth process contributing to aging, which we associate with the
price for staying in the arousal state. The process ꢅt describes the
rate of recovery from the arousal state. We assume that
28. Kirkwood TB, Franceschi C. Free radicals: only part of the story? Ag-
ing. 1993;5(1):1–2.
µt = m exp(bXt – At)
(2)
29. Mecocci P, Polidori MC, Troiano L, et al. Plasma antioxidants and
longevity: a study on healthy centenarians. Free Radic Biol Med.
2000;28(8):1243–1248.
30. Yashin AI, De Benedictis G, Vaupel JW, et al. Genes and longevity:
lessons from studies of centenarians. J Gerontol Biol Sci. 2000;55A:
B319–B328.
Here m and b are nonnegative parameters. The process A ꢂ (At)t ꢆ 0
describes the accumulation of damage, that is, a cost paid by an or-
ganism associated with its stay in the arousal state (e.g., an allo-
static load; 7,41,42). It seems reasonable to assume that A ꢂ (At)t ꢆ 0
depends on the history of the process X up to time t, for example,
31. Larsen PL, Albert PS, Riddle DL. Genes that regulate both develop-
ment and longevity in Caenorhabditis elegans. Gen USA. 1995;
139(4):1567–1583.
32. Anisimov VN. Carcinogenesis and Aging. Vol. 1, 2. Boca Raton: FL:
CRC Press; 1987.
33. Anisimov VN. Age as a risk factor in multistage carcinogenesis. In:
Balducci L, Ershler WB, Lyman G, eds. Comprehensive Geriatric On-
cology, Amsterdam: Harwood; 1998:157–178.
34. Anisimov VN. Means of the prevention of premature aging (geropro-
tectors). Adv Gerontol. 2000;4:55–74.
At = aλ t Xudu
(3)
∫
0
where a and ꢀ are nonnegative parameters. We also assume that
the process X is related to process N by the equation
dXt = –λ(Xt – Nt)dt + σdWt, X0 = 0.
(4)
Here W ꢂ (Wt)t ꢆ 0 is the standard Wiener process, and parame-
ters ꢀ and ꢁ ꢈ 0 are fixed for all genetically identical individuals.
This equation contains deterministic and stochastic components.
The deterministic part represents the homeostatic feedback mecha-
nism by which process X adapts to the level of N. The stochastic
component characterizes permanently acting disturbances, for ex-
ample, oxidative stress or immunological stress, which disturbs
homeostasis. It is important to note that parameter ꢀ influences
both the X process and the A process. In the first case it character-
izes the rate of adaptation of an organism to changes in the state.
The higher the value of ꢀ, the faster the organism adapts. The vari-
ance of fluctuations of the process Xt is ꢁ2/2ꢀ; that is, it is inversely
proportional to parameter ꢀ. Thus the weaker the adaptive capacity
of an organism, the higher the fluctuations of X. The high rate of
adaptation is, however, not for free. It has a metabolic cost in-
cluded in the definition of allostatic load (7,41). Note that accord-
ing to Fries (3), even for the same trajectories of X the allostatic
load will be accumulated faster for an individual with larger values
of ꢀ. Thus any jump of Nt from 0 to 1 induces an increase of an av-
erage level of X. An increase in Xt causes faster accumulation of al-
lostatic load At and finally results in a reduction of a stress resis-
tance ꢅt and in an increase of intensity of diseases ꢄt.
35. Turturrro A, Witt W, Lewis S, et al. Growth curves and survival char-
acteristics of the animals used in the biomarkers of aging program. J
Gerontol Biol Sci. 1999;54A:B492–B501.
36. Doubal S, Klemera P. The effect of antioxidants and dietary restriction
on mortality curves. Age. 1999;22:101–105.
37. Medawar PB. An unsolved problem of biology. In: Medawar PB, ed.
The Uniqueness of the Individual. London: Methuen;1957:44–70.
38. Kirkwood TBL. Human senescence. BioEssays. 1996;18(12):1009–
1016.
39. Wilmoth JR, Horiuchi S. Rectangularization revisited: variability of
age at death within human populations. Demography. 1999;36:475–
495.
40. Caselli G, Lopez AD. Health and Mortality Among Elderly Populations,
International Studies in Demography. Oxford, England: Clarendon
Press; 1996.
41. Seeman TE, Singer BH, Rowe JW, Horwitz RI, McEwen BS. Price of
adaptation—allostatic load and its health consequences. MacArthur
studies of successful aging. Arch Intern Med. 1997;157:2259–2268.
42. McEwen BS. Protective and damaging effects of stress mediators. N
Engl J Med. 1998;338:171–179.
Three possible causes of death were considered in this model.
The first is associated with a decrease of vital characteristics below
the admissible level (in the example given below, Xt ꢉ ꢊ1). The
second arises when the recovery rate falls below its admissible
level (in the example given below, ꢅt ꢉ 0.01). The third arises
when X exceeds the admissible level (in the example given below,
Xt ꢈ 2).
Received January 29, 2001
Accepted May 11, 2001
Decision Editor: John Faulkner, PhD
Appendix
The Model
Simulation of the Modern Pattern of Survival
We introduce five main dynamic components of the processes
of aging and mortality, denoted by X, N, ꢄ, ꢅ, and A. The first, X ꢂ
(Xt)t ꢆ 0, characterizes the rate of metabolic processes. It may be re-
garded as a difference between metabolic rates in the state of nor-
mal functioning and in the arousal state. The dynamics of this pro-
cess reflects changes in metabolic characteristics during the
adaptation to the new state of an organism induced by external or
We simulated life-span data by using a computer experiment
with our model and calculated survival functions for different sets
of parameter values. The control set (F1) of the parameters is ꢀ ꢂ
370, ꢀ ꢂ550, ꢁ1 ꢂ 6.4, ꢁ2 ꢂ 6.0 a ꢂ 0.00066, ꢇ ꢂ 0.2, b ꢂ 0.5,
and m ꢂ 10. The statistics is based on 2000 independent random
realizations consisting of two cohorts: 25% (500 individuals) with

B442
YASHIN ET AL.
ꢀ ꢂ 370 and 75% with ꢀ ꢂ 550 (1500 individuals); T* ꢂ 40 years.
The sample size of simulated data is 2000 individuals.
gidity (with smaller ꢀ). The main cause of the mortality among in-
dividuals with strong feedback (large values of ꢀ) is the fast
decrease in the recovery rate caused by accumulation of damage
(allostatic load). The individuals with low feedback (weak homeo-
static mechanisms, small values of ꢀ) die mostly because of cross-
ing the admissible boundary by the process Xt.
Thus individuals with the large values of ꢀ usually do not die
from the fluctuations of Xt, because they are small. However, the
accumulation of allostatic load for them is going faster. Individuals
with small ꢀ have higher levels of fluctuations in Xt (are more la-
bile). Thus they die more often at the beginning of life. However,
the allostatic load in these individuals increases at a slower rate,
which gives them better survival chances later in life compared
with more stable individuals.
The parameter ꢀ in this model is supposed to be genetically de-
termined and fixed for all individuals in a given birth cohort. As it
defines the rate of adaptation and is inversely proportional to the
variance of Xt, an increase in ꢀ leads to an increase in survival
probability for the younger ages, where the allostatic load is small
and most of the deaths occur because of fluctuations of Xt. Because
the allostatic load increases faster with age for such individuals,
the survival curve for them goes steeper to zero. Thus we can sim-
ulate the phenomenon of the intersection of the survival curves by
assigning different values of parameter ꢀ to respective populations
of individuals. Note that the old-age survival probability is signifi-
cantly higher for the organisms with a lower level of feedback ri-