contemporary methods of mortality analysis biodemography of mortality and longevity

CONTEMPORARY METHODS OF MORTALITY ANALYSIS

Biodemography of Mortality and Longevity

Lecture 1

Leonid GavrilovNatalia Gavrilova

Center on Aging NORC and the University of Chicago

Chicago, Illinois, USA

CONTEMPORARY METHODS OF MORTALITY ANALYSIS

Empirical Laws of Mortality

The Gompertz-Makeham Law

μ(x) = A + R e αx

A – Makeham term or background mortalityR e αx – age-dependent mortality; x - age

Death rate is a sum of age-independent component (Makeham term) and age-dependent component (Gompertz function), which increases exponentially with age.

risk of death

Gompertz Law of Mortality in Fruit Flies

Based on the life table for 2400 females of Drosophila melanogaster published by Hall (1969).

Source: Gavrilov, Gavrilova, “The Biology of Life Span” 1991

Gompertz-Makeham Law of Mortality in Flour Beetles

Based on the life table for 400 female flour beetles (Tribolium confusum Duval). published by Pearl and Miner (1941).


Gompertz-Makeham Law of Mortality in Italian Women

Based on the official Italian period life table for 1964-1967.


How can the Gompertz-Makeham law be used?

By studying the historical dynamics of the mortality components in this law:

μ(x) = A + R e αx

Makeham component Gompertz component

The Strehler-Mildvan Correlation:

Inverse correlation between the Gompertz

parametersLimitation: Does not take into

account the Makeham parameter that leads to spurious correlation

Modeling mortality at different levels of Makeham parameter but

constant Gompertz parameters

1 – A=0.01 year-1

2 – A=0.004 year-1

3 – A=0 year-1

Coincidence of the spurious inverse correlation between the Gompertz parameters

and the Strehler-Mildvan correlation

Dotted line – spurious inverse correlation between the Gompertz parameters

Data points for the Strehler-Mildvan correlation were obtained from the data published by Strehler-Mildvan (Science, 1960)

Compensation Law of Mortality(late-life mortality

convergence) Relative differences in death

rates are decreasing with age, because the lower initial death rates are compensated by higher slope (actuarial aging rate)

Compensation Law of Mortality

Convergence of Mortality Rates with Age

1 – India, 1941-1950, males 2 – Turkey, 1950-1951,

males3 – Kenya, 1969, males 4 - Northern Ireland, 1950-

1952, males5 - England and Wales,

1930-1932, females 6 - Austria, 1959-1961,

females 7 - Norway, 1956-1960,

females

Source: Gavrilov, Gavrilova,“The Biology of Life Span”

1991

Compensation Law of Mortality (Parental Longevity Effects)

Mortality Kinetics for Progeny Born to Long-Lived (80+) vs Short-Lived Parents

Sons DaughtersAge40 50 60 70 80 90 100

Log(

Haz

ard

Rat

e)

0.001

0.01

0.1

1

short-lived parentslong-lived parents

Linear Regression Line

Age40 50 60 70 80 90 100

Log(

Haz

ard

Rat

e)

0.001

0.01

0.1

1



Compensation Law of Mortality in Laboratory

Drosophila1 – drosophila of the Old

Falmouth, New Falmouth, Sepia and Eagle Point strains (1,000 virgin females)

2 – drosophila of the Canton-S strain (1,200 males)

3 – drosophila of the Canton-S strain (1,200 females)

4 - drosophila of the Canton-S strain (2,400 virgin females)

Mortality force was calculated for 6-day age intervals.


1991

ImplicationsBe prepared to a paradox that higher

actuarial aging rates may be associated with higher life expectancy in compared populations (e.g., males vs females)

Be prepared to violation of the proportionality assumption used in hazard models (Cox proportional hazard models)

Relative effects of risk factors are age-dependent and tend to decrease with age

The Late-Life Mortality Deceleration (Mortality Leveling-off,

Mortality Plateaus)

The late-life mortality deceleration law states that death rates stop to increase exponentially at advanced ages and level-off to the late-life mortality plateau.

Mortality deceleration at advanced ages.

After age 95, the observed risk of death [red line] deviates from the value predicted by an early model, the Gompertz law [black line].

Mortality of Swedish women for the period of 1990-2000 from the Kannisto-Thatcher Database on Old Age Mortality

Source: Gavrilov, Gavrilova, “Why we fall apart. Engineering’s reliability theory explains human aging”. IEEE Spectrum. 2004.

Mortality Leveling-Off in House Fly

Musca domestica

Based on life table of 4,650 male house flies published by Rockstein & Lieberman, 1959

Age, days0 10 20 30 40

haza

rd ra

te, l

og s

cale

0.001

0.01

0.1

Non-Aging Mortality Kinetics in Later Life

Source: A. Economos. A non-Gompertzian paradigm for mortality kinetics of metazoan animals and failure kinetics of manufactured products. AGE, 1979, 2: 74-76.

Non-Aging Failure Kinetics of Industrial Materials in ‘Later Life’

(steel, relays, heat insulators)

Source: A. Economos. A non-

Gompertzian paradigm for mortality kinetics of metazoan animals and failure kinetics of manufactured products. AGE, 1979, 2: 74-76.

Mortality Deceleration in Animal Species

Invertebrates: Nematodes, shrimps,

bdelloid rotifers, degenerate medusae (Economos, 1979)

Drosophila melanogaster (Economos, 1979; Curtsinger et al., 1992)

Housefly, blowfly (Gavrilov, 1980)

Medfly (Carey et al., 1992) Bruchid beetle (Tatar et al.,

1993) Fruit flies, parasitoid wasp

(Vaupel et al., 1998)

Mammals: Mice (Lindop, 1961;

Sacher, 1966; Economos, 1979)

Rats (Sacher, 1966) Horse, Sheep, Guinea

pig (Economos, 1979; 1980)

However no mortality deceleration is reported for

Rodents (Austad, 2001) Baboons (Bronikowski

et al., 2002)

Existing Explanations of Mortality Deceleration

Population Heterogeneity (Beard, 1959; Sacher, 1966). “… sub-populations with the higher injury levels die out more rapidly, resulting in progressive selection for vigour in the surviving populations” (Sacher, 1966)

Exhaustion of organism’s redundancy (reserves) at extremely old ages so that every random hit results in death (Gavrilov, Gavrilova, 1991; 2001)

Lower risks of death for older people due to less risky behavior (Greenwood, Irwin, 1939)

Evolutionary explanations (Mueller, Rose, 1996; Charlesworth, 2001)

Testing the “Limit-to-Lifespan” Hypothesis

Source: Gavrilov L.A., Gavrilova N.S. 1991. The Biology of Life Span

Implications There is no fixed upper limit to human longevity - there is no special fixed number, which separates possible and impossible values of lifespan.

This conclusion is important, because it challenges the common belief in existence of a fixed maximal human life span.

Latest Developments

Was the mortality deceleration law overblown?

A Study of the Extinct Birth Cohorts in the United States

More recent birth cohort mortality

Nelson-Aalen monthly estimates of hazard rates using Stata 11

What about other mammals?

Mortality data for mice: Data from the NIH Interventions Testing

Program, courtesy of Richard Miller (U of Michigan)

Argonne National Laboratory data, courtesy of Bruce Carnes (U of Oklahoma)

Mortality of mice (log scale) Miller data

Actuarial estimate of hazard rate with 10-day age intervals

males females

What are the explanations of mortality

laws?

Mortality and aging theories

What Should the Aging Theory Explain Why do most biological species

including humans deteriorate with age?

The Gompertz law of mortality

Mortality deceleration and leveling-off at advanced ages

Compensation law of mortality

Additional Empirical Observation:

Many age changes can be explained by cumulative effects of

cell loss over time Atherosclerotic inflammation -

exhaustion of progenitor cells responsible for arterial repair (Goldschmidt-Clermont, 2003; Libby, 2003; Rauscher et al., 2003).

Decline in cardiac function - failure of cardiac stem cells to replace dying myocytes (Capogrossi, 2004).

Incontinence - loss of striated muscle cells in rhabdosphincter (Strasser et al., 2000).

Like humans, nematode C. elegans experience muscle loss

Body wall muscle sarcomeres

Left - age 4 days. Right - age 18 days

Herndon et al. 2002. Stochastic and genetic factors influence tissue-specific decline in ageing C. elegans. Nature 419, 808 - 814.

“…many additional cell types (such as hypodermis and intestine) … exhibit age-related deterioration.”

What Is Reliability Theory? Reliability theory is a general

theory of systems failure developed by mathematicians:

Aging is a Very General Phenomenon!

Stages of Life in Machines and Humans

The so-called bathtub curve for technical systems

Bathtub curve for human mortality as seen in the U.S. population in 1999 has the same shape as the curve for failure rates of many machines.

Gavrilov, L., Gavrilova, N. Reliability theory of aging and longevity. In: Handbook of the Biology of Aging. Academic Press, 6th edition, 2006, pp.3-42.

The Concept of System’s Failure

In reliability theory failure is defined as the event when a required function is terminated.

Definition of aging and non-aging systems in reliability

theoryAging: increasing risk of failure

with the passage of time (age). No aging: 'old is as good as new'

(risk of failure is not increasing with age)

Increase in the calendar age of a system is irrelevant.

Aging and non-aging systems

Perfect clocks having an ideal marker of their increasing age (time readings) are not aging

Progressively failing clocks are aging (although their 'biomarkers' of age at the clock face may stop at 'forever young' date)

Mortality in Aging and Non-aging Systems

Age0 2 4 6 8 10 12

Ris

k of

dea

th

1

2

3

Age0 2 4 6 8 10 12

Ris

k of

Dea

th

0

1

2

3

non-aging system aging system

Example: radioactive decay

According to Reliability Theory:Aging is NOT just growing oldInsteadAging is a degradation to failure: becoming sick, frail and dead

'Healthy aging' is an oxymoron like a healthy dying or a healthy disease

More accurate terms instead of 'healthy aging' would be a delayed aging, postponed aging, slow aging, or negligible aging (senescence)

The Concept of Reliability Structure

The arrangement of components that are important for system reliability is called reliability structure and is graphically represented by a schema of logical connectivity

Two major types of system’s logical connectivity

Components connected in series

Components connected in parallel

Fails when the first component fails

Fails when all

components fail

Combination of two types – Series-parallel system

Ps = p1 p2 p3 … pn = pn

Qs = q1 q2 q3 … qn = qn

Series-parallel Structure of Human Body

• Vital organs are connected in series

• Cells in vital organs are connected in parallel

Redundancy Creates Both Damage Tolerance and Damage Accumulation

(Aging)

System with redundancy accumulates damage (aging)

System without redundancy dies after the first random damage (no aging)

Reliability Model of a Simple Parallel

SystemFailure rate of the

system:

Elements fail randomly and independently with a constant failure rate, k

n – initial number of elements

nknxn-1 early-life period approximation, when 1-e-kx kx k late-life period approximation, when 1-e-kx 1

( )x = dS( )xS( )x dx

= nk e kx( )1 e kx n 1

1 ( )1 e kx n

Failure Rate as a Function of Age in Systems with Different Redundancy

Levels

Failure of elements is random

Standard Reliability Models Explain

Mortality deceleration and leveling-off at advanced ages

Compensation law of mortality

Standard Reliability Models Do Not Explain

The Gompertz law of mortality observed in biological systems

Instead they produce Weibull (power) law of mortality growth with age

An Insight Came To Us While Working With Dilapidated

Mainframe Computer The complex

unpredictable behavior of this computer could only be described by resorting to such 'human' concepts as character, personality, and change of mood.

Reliability structure of (a) technical devices and (b) biological

systems Low redundancy

Low damage load

High redundancy

High damage load

X - defect

Models of systems with distributed redundancy

Organism can be presented as a system constructed of m series-connected blocks with binomially distributed elements within block (Gavrilov, Gavrilova, 1991, 2001)

Model of organism with initial damage load

Failure rate of a system with binomially distributed redundancy (approximation for initial period of life):

x0 = 0 - ideal system, Weibull law of mortality x0 >> 0 - highly damaged system, Gompertz law of

mortality

( )x Cmn( )qk n 1 qqk

x + n 1

= ( )x0 x + n 1

where - the initial virtual age of the systemx0 =1 qqk

The initial virtual age of a system defines the law of system’s mortality:

Binomial law of mortality

People age more like machines built with lots of faulty parts than like ones built with

pristine parts. As the number

of bad components, the initial damage load, increases [bottom to top], machine failure rates begin to mimic human death rates.

Statement of the HIDL hypothesis:

(Idea of High Initial Damage Load )

"Adult organisms already have an exceptionally high load of initial damage, which is comparable with the amount of subsequent aging-related deterioration, accumulated during the rest of the entire adult life."

Source: Gavrilov, L.A. & Gavrilova, N.S. 1991. The Biology of Life Span: A Quantitative Approach. Harwood Academic Publisher, New York.

Why should we expect high initial damage load in biological systems?

General argument:-- biological systems are formed by self-assembly without helpful external quality control.

Specific arguments:

• Most cell divisions responsible for DNA copy-errors occur in early development leading to clonal expansion of mutations• Loss of telomeres is also particularly high in early-life• Cell cycle checkpoints are disabled in early development

Practical implications from the HIDL hypothesis:

"Even a small progress in optimizing the early-developmental processes can potentially result in a remarkable prevention of many diseases in later life, postponement of aging-related morbidity and mortality, and significant extension of healthy lifespan."

Source: Gavrilov, L.A. & Gavrilova, N.S. 1991. The Biology of Life Span: A Quantitative Approach. Harwood Academic Publisher, New York.

Month of BirthJan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

life

expe

ctan

cy a

t age

80,

yea

rs

7.6

7.7

7.8

7.9

1885 Birth Cohort1891 Birth Cohort

Life Expectancy and Month of Birth

Data source: Social Security Death Master File

Evolution of Species Reliability

• Reliability theory of aging is perfectly compatible with the idea of biological evolution.

• Moreover, reliability theory helps evolutionary theories to explain how the age of onset of diseases caused by deleterious mutations could be postponed to later ages during the evolution.

Evolution in the Direction of Low Mortality at Young

Ages

This could be easily achieved by simple increase in the initial redundancy levels (e.g., initial cell numbers).

Log

risk

of d

eath

Age

Evolution of species reliability

• Fruit flies from the very beginning of their lives have very unreliable design compared to humans.

• High late-life mortality of fruit flies compared to humans suggests that fruit flies are made of less reliable components (presumably cells), which have higher failure rates compared to human cells.

Reliability of Birds vs Mammals

• Birds should be very prudent in redundancy of their body structures (because it comes with a heavy cost of additional weight).

Result: high mortality at younger ages.

• Flight adaptation should force birds to evolve in a direction of high reliability of their components (cells).

Result: low rate of elements’ (cells’) damage resulting in low mortality at older ages

Effect of extrinsic mortality on the evolution of senescence in

guppies.Reznick et al. 2004. Nature 431, 1095 -

1099 Reliability-theory perspective:

Predators ensure selection for better performance and lower initial damage load.

Hence life span would increase in high predator localities.

Solid line – high predator locality

Dotted line –low predator locality

Conclusions (I) Redundancy is a key notion for

understanding aging and the systemic nature of aging in particular. Systems, which are redundant in numbers of irreplaceable elements, do deteriorate (i.e., age) over time, even if they are built of non-aging elements.

An apparent aging rate or expression of aging (measured as age differences in failure rates, including death rates) is higher for systems with higher redundancy levels.

Conclusions (II) Redundancy exhaustion over the life course explains the

observed ‘compensation law of mortality’ (mortality convergence at later life) as well as the observed late-life mortality deceleration, leveling-off, and mortality plateaus.

Living organisms seem to be formed with a high load of initial damage, and therefore their lifespans and aging patterns may be sensitive to early-life conditions that determine this initial damage load during early development. The idea of early-life programming of aging and longevity may have important practical implications for developing early-life interventions promoting health and longevity.

Testing Biological Theories of Aging with

Demographic and Genealogical Data

What are the data and the predictions of the evolutionary

theory onLinks between human longevity and

fertility

Lifespan heritability in humans

Quality of offspring conceived to older parents

Founding Fathers• Beeton, M., Yule, G.U., Pearson,

K. 1900. Data for the problem of evolution in man. V. On the correlation between duration of life and the number of offspring. Proc. R. Soc. London, 67: 159-179.

• Data used: English Quaker records and Whitney Family of Connectucut records for females and American Whitney family and Burke’s ‘Landed Gentry’ for males.

Findings and Conclusions by Beeton et al., 1900

They tested predictions of the Darwinian evolutionary theory that the fittest individuals should leave more offspring.

Findings: Slightly positive relationship between postreproductive lifespan (50+) of both mothers and fathers and the number of offspring.

Conclusion: “fertility is correlated with longevity even after the fecund period is passed” and “selective mortality reduces the numbers of the offspring of the less fit relatively to the fitter.”

Other Studies, Which Found Positive Correlation Between Reproduction and

Postreproductive Longevity

• Bettie Freeman (1935): Weak positive correlations between the duration of postreproductive life in women and the number of offspring borne. Human Biology, 7: 392-418.

• Bideau A. (1986): Duration of life in women after age 45 was longer for those women who borne 12 or more children. Population 41: 59-72.

Telephone inventor Alexander Graham Bell (1918): “The longer lived parents were the most fertile.”

Studies that Found no Relationship Between Postreproductive Longevity and

ReproductionHenry L. 1956. Travaux et

Documents.Gauter, E. and Henry L. 1958.

Travaux et Documents, 26.Knodel, J. 1988. Demographic

Behavior in the Past. Le Bourg et al., 1993. Experimental

Gerontology, 28: 217-232.

Study that Found a Trade-Off Between Reproductive Success and

Postreproductive Longevity

Westendorp RGJ, Kirkwood TBL. 1998. Human longevity at the cost of reproductive success. Nature 396: 743-746.

Extensive media coverage including BBC and over 100 citations in scientific literature as an established scientific fact. Previous studies were not quoted and discussed in this article.

Point estimates of progeny number for married aristocratic women from different birth cohorts as a function of age at

death. The estimates of progeny number are adjusted for trends over

calendar time using multiple regression.

Source: Westendorp, Kirkwood, Human longevity at the cost of reproductive success. Nature, 1998, 396, pp 743-746

“… it is not a matter of reduced fertility, but a case of 'to have or have not'.“

Table 1 Relationship between age at death and number of children for married aristocratic women Age at death Proportion childless Number of children (years) mean for all women mean for women having children <20 0.66 0.45 1.32 21-30 0.39 1.35 2.21 31-40 0.26 2.05 2.77 41-50 0.31 2.01 2.91 51-60 0.28 2.4 3.33 61-70 0.33 2.36 3.52 71-80 0.31 2.64 3.83 81-90 0.45 2.08 3.78 >90 0.49 1.80 3.53

Source: Toon Ligtenberg & Henk Brand. Longevity — does family

size matter? Nature, 1998, 396, pp 743-746

Number of progeny and age at first childbirth dependent on the age at death of married aristocratic women

Source: Westendorp, R. G. J., Kirkwood, T. B. L. Human longevity at the cost of reproductive success. Nature, 1998, 396, pp 743-746

Do longevous women have impaired fertility ?Why is this question so important and interesting?

Scientific Significance This is a testable prediction of some evolutionary theories of aging - disposable soma theory of aging (Kirkwood)

"The disposable soma theory on the evolution of ageing states that longevity requires investments in somatic maintenance that reduce the resources available for reproduction“ (Westendorp, Kirkwood, Nature, 1998).

Do longevous women have impaired fertility ?

• Practical Importance. Do we really wish to live a long life at the cost of infertility?: “the next generations of Homo sapiens will have even longer life spans

but at the cost of impaired fertility” Rudi Westendorp “Are we becoming less disposable? EMBO Reports,

2004, 5: 2-6.

"... increasing longevity through genetic manipulation of the mechanisms of aging raises deep biological and moral questions. These questions should give us pause before we embark on the enterprise of extending our lives“ Walter Glennon "Extending the Human Life Span", Journal of Medicine and Philosophy, 2002, Vol. 27, No. 3, pp. 339-354.

Educational Significance Do we teach our students right? Impaired fertility of longevous women is often

presented in scientific literature and mass media as already established fact (Brandt et al., 2005; Fessler et al., 2005; Schrempf et al., 2005; Tavecchia et al., 2005; Kirkwood, 2002; Westendorp, 2002, 2004; Glennon, 2002; Perls et al., 2002, etc.).

This "fact" is now included in teaching curriculums in biology, ecology and anthropology world-wide (USA, UK, Denmark).

Is it a fact or artifact ?

General Methodological Principle:Before making strong conclusions, consider all

other possible explanations, including potential flaws in data quality and analysis

Previous analysis by Westendorp and Kirkwood was made on the assumption of data completeness:Number of children born = Number of children recorded

Potential concerns: data incompleteness, under-reporting of short-lived children, women (because of patrilineal structure of genealogical records), persons who did not marry or did not have children.Number of children born >> Number of children recorded

Test for Data CompletenessDirect Test: Cross-checking of the initial dataset with other data sources We examined 335 claims of childlessness in the dataset used

by Westendorp and Kirkwood. When we cross-checked these claims with other professional sources of data, we found that at least 107 allegedly childless women (32%) did have children!

At least 32% of childlessness claims proved to be wrong ("false negative claims") !

Some illustrative examples:

Henrietta Kerr (1653 1741) was apparently childless in the dataset used by Westendorp and Kirkwood and lived 88 years. Our cross-checking revealed that she did have at least one child, Sir William Scott (2nd Baronet of Thirlstane, died on October 8, 1725).

Charlotte Primrose (1776 1864) was also considered childless in the initial dataset and lived 88 years. Our cross-checking of the data revealed that in fact she had as many as five children: Charlotte (1803 1886), Henry (1806 1889), Charles (1807 1882), Arabella (1809-1884), and William (1815 1881).

Wilhelmina Louise von Anhalt-Bernburg (1799 1882), apparently childless, lived 83 years. In reality, however, she had at least two children, Alexander (1820 1896) and Georg (1826 1902).

Point estimates of progeny number for married aristocratic women from different birth cohorts as a function of age at death.

The estimates of progeny number are adjusted for trends over calendar time using multiple regression.


Antoinette de Bourbon(1493-1583)

Lived almost 90 yearsShe was claimed to have only one child in the

dataset used by Westendorp and Kirkwood: Marie (1515-1560), who became a mother of famous Queen of Scotland, Mary Stuart.

Our data cross-checking revealed that in fact Antoinette had 12 children!

• Marie 1515-1560 • Francois Ier 1519-1563 • Louise 1521-1542 • Renee 1522-1602 • Charles 1524-1574 • Claude 1526-1573 • Louis 1527-1579 • Philippe 1529-1529 • Pierre 1529 • Antoinette 1531-1561 • Francois 1534-1563• Rene 1536-1566

Characteristics of Our Data Sample for ‘Reproduction-Longevity’ Studies• 3,723 married women

born in 1500-1875 and belonging to the upper European nobility.

• Women with two or more marriages (5%) were excluded from the analysis in order to facilitate the interpretation of results (continuity of exposure to childbearing).

•Every case of childlessness has been checked using at least two different genealogical sources.

Typical Mistakes in Biological Studies of

Human Longevity• Using lifespan data for non-extinct

birth cohorts (“cemetery effect”)• Failure to control for birth cohort –

spurious correlations may be found if variables have temporal dynamics

• Failure to take into account social events and factors – e.g., failure to control for age at marriage in longevity-reproduction studies

Tim e

Fertility

Longevity

Childlessness is better outcome than number of children for testing

evolutionary theories of aging on human data

Applicable even for population practicing birth control (few couple are voluntarily childless)

Lifespan is not affected by physiological load of multiple pregnancies

Lifespan is not affected by economic hardship experienced by large families

Source: Gavrilova et al. Does exceptional human longevity come with high cost of infertility? Testing the evolutionary theories of aging. Annals of the New York Academy of Sciences, 2004, 1019: 513-517.

Source: Gavrilova, Gavrilov. Human longevity and reproduction: An evolutionary perspective. In: Grandmotherhood - The Evolutionary Significance of the Second Half of Female Life. Rutgers University Press, 2005, 59-80.

Short Conclusion:

Exceptional human longevity is NOT associated with infertility or childlessness

More Detailed ConclusionsWe have found that previously reported high rate of

childlessness among long-lived women is an artifact of data incompleteness, caused by under-reporting of children. After data cleaning, cross-checking and supplementation the association between exceptional longevity and childlessness has disappeared.

Thus, it is important now to revise a highly publicized scientific concept of heavy reproductive costs for human longevity. and to make corrections in related teaching curriculums for students.

More Detailed Conclusions (2)It is also important to disavow the doubts and

concerns over further extension of human lifespan, that were recently cast in biomedical ethics because of gullible acceptance of the idea of harmful side effects of lifespan extension, including infertility (Glannon, 2002).

There is little doubt that the number of children can affect human longevity through complications of pregnancies and childbearing, as well as through changes in socioeconomic status, etc. However, the concept of heavy infertility cost of human longevity is not supported by data, when these data are carefully reanalyzed.

Heritability of Longevity

Mutation Accumulation Theory of Aging

(Medawar, 1946)

• From the evolutionary perspective, aging is an inevitable result of the declining force of natural selection with age.

• So, over successive generations, late-acting deleterious mutations will accumulate, leading to an increase in mortality rates late in life.

Predictions of the Mutation Accumulation Theory of Aging

• Mutation accumulation theory predicts that those deleterious mutations that are expressed in later life should have higher frequencies (because mutation-selection balance is shifted to higher equilibrium frequencies due to smaller selection pressure).

• Therefore, ‘expressed’ genetic variability should increase with age (Charlesworth, 1994. Evolution in Age-structured Populations).

• This should result in higher heritability estimates for lifespan of offspring born to longer-lived parents.

Parental Lifespan0 20 40 60 80

Offs

prin

g Li

fesp

an0

10

20

30

40

Linearity Principle of Inheritance in Quantitative Genetics

• Dependence between parental traits and offspring traits is linear

The Best Possible Source on Familial Longevity Genealogies of European Royal and Noble Families

Charles IX d’Anguleme (1550-1574)

Henry VIII Tudor (1491-1547)

Marie-Antoinette von Habsburg-Lothringen

(1765-1793)

Characteristic of our Dataset• Over 16,000 persons

belonging to the European aristocracy

• 1800-1880 extinct birth cohorts

• Adult persons aged 30+

• Data extracted from the professional genealogical data sources including Genealogisches Handbook des Adels, Almanac de Gotha, Burke Peerage and Baronetage.

Daughter's Lifespan(Mean Deviation from Cohort Life Expectancy)

as a Function of Paternal Lifespan

Paternal Lifespan, years40 50 60 70 80 90 100

Dau

ghte

r's L

ifesp

an (d

evia

tion)

, yea

rs

-2

2

4

6

0

• Offspring data for adult lifespan (30+ years) are smoothed by 5-year running average.

• Extinct birth cohorts (born in 1800-1880)

• European aristocratic families. 6,443 cases

“The Heritability of Life-Spans Is Small”C.E. Finch, R.E. Tanzi, Science, 1997, p.407

“… long life runs in families”A. Cournil, T.B.L. Kirkwood, Trends in Genetics, 2001, p.233

Paradox of low heritability of lifespan vs high familial clustering of longevity

Heritability Estimates of Human Lifespan

Author(s) Heritability estimate

Population

McGue et al., 1993 0.22 Danish twins

Ljungquist et al., 1998 <0.33 Swedish twins

Bocquet-Appel, Jacobi, 1990

0.10-0.30 French village

Mayer, 1991 0.10-0.33 New England families

Cournil et al., 2000 0.27 French village

Mitchell et al., 2001 0.25 Old Order Amish

Compensation Law of Mortality

Convergence of Mortality Rates with Age

1 – India, 1941-1950, males 2 – Turkey, 1950-1951,

males3 – Kenya, 1969, males 4 - Northern Ireland, 1950-

1952, males5 - England and Wales,

1930-1932, females 6 - Austria, 1959-1961,

females 7 - Norway, 1956-1960,

females


1991

Compensation Law of Mortality (Parental Longevity Effects)

Mortality Kinetics for Progeny Born to Long-Lived (80+) vs Short-Lived Parents

Sons DaughtersAge40 50 60 70 80 90 100

Log(

Haz

ard

Rat

e)

0.001

0.01

0.1

1



Age40 50 60 70 80 90 100

Log(

Haz

ard

Rat

e)

0.001

0.01

0.1

1



AcknowledgmentsThis study was made possible

thanks to: generous support from the

National Institute on Aging (R01 AG028620) Stimulating working environment at the Center on Aging, NORC/University of Chicago

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Spontaneous mutant frequencies with age in heart and small

intestine

0

5

10

15

20

25

30

35

40

0 5 10 15 20 25 30 35Age (months)

Mut

ant f

requ

ency

(x10-5

)

Small IntestineHeart

Source: Presentation of Jan Vijg at the IABG Congress, Cambridge, 2003