1. Testing Evolutionary Theories of Aging and Longevity
Dr. Natalia S. Gavrilova, Ph.D.
Dr. Leonid A. Gavrilov, Ph.D.
Center on Aging
NORC and The University of Chicago
Chicago, Illinois, USA

2. What are the data and the predictions of evolutionary theories of aging on
Variability of age-related outcomes
Old-age mortality trajectories
Trade-offs between longevity and fertility

3. Part 1 Testing Predictions of Programmed vs. Stochastic Aging
Opponents of programmed aging often argue that there is a too high variation in timing of aging-related outcomes, compared to much smaller variation in timing of programmed developmental outcomes (such as age of sexual maturation).
In other words, aging just does not have an expected clock-wise accuracy, which is anticipated for programmed events.

4. Part 1 Testing Predictions of Programmed vs. Stochastic Aging
To test the validity of this argument we compared relative variability (coefficient of variation) for parameters that are known to be determined by the developmental program (age at sexual maturity) with variability of characteristic related to aging (age at menopause).
We used information on the ages at sexual maturation (menarche) and menopause from the nationally representative survey of the adult population of the United States (MIDUS) as well as published data for 14 countries.

5. Why use relative variability, coefficient of variation?
"The fact that elephants, for instance, may have a standard deviation of 50 mm for some linear dimension and shrews a standard deviation of 0.5 mm for the same dimension does not necessarily mean that the elephants are more variable, in the essential zoological sense, than the shrews. The elephants are a hundred times the size of the shrews in any case, and we should expect the absolute variation also to be a hundred times as great without any essential difference in functional variability. The solution of this problem is very simple: it is necessary only to relate the measure of absolute variation to a measure of absolute size. The best measures to use for this purpose are the standard deviation and the mean, and since their quotient is always a very small number it is convenient to multiply it by 100. The resulting figure is a coefficient of variation, or of variability"
Simpson GG, Roe A, Lewontin RG. Quantitative Zoology: Revised Edition. New York: Dover Publications, Inc.; 2003.

6. Our results using the MIDUS study

7. National survey conducted in 1994/95 Americans aged 25-74
core national sample (N=3,485)
city oversamples (N=957)
Additional samples: twins, siblings
Subsample used in this study: women having natural menopause (no surgeries affecting the age at menopause) aged 60-74 7

8. A 30-40 minute telephone survey A 114 page mail survey
Number of respondents: 4, Number of respondents: 3,690 8

9. MIDUS SAMPLE POPULATION DISTRIBUTIONS (%)
Women Aged (n=2,087)
AGE
25-54
68.8
55-64
19.8
65-74
11.4
RACE/ETHNICITY
White
86.9
African-American
7.7
Other
8.9
RELATIONSHIP STATUS
Married
54.2
Other intimate relationship
4.7
a Estimates are weighted to account for differential probabilities of selection and differential non-response.
b Excludes those respondents who reported their race as black/African-American (n=6).
The estimated distributions of key demographic variables closely match those from the 2000 Census and from other national surveys. Men are more likely to be married than women. The distribution of self-rated health is similar for men and women and mirrors that seen in other current population-based studies of aging. 9

10. DISTRIBUTION OF AGE AT MENARCHE IN THE MIDUS SAMPLE
a Estimates are weighted to account for differential probabilities of selection and differential non-response.
b Excludes those respondents who reported their race as black/African-American (n=6).
The estimated distributions of key demographic variables closely match those from the 2000 Census and from other national surveys. Men are more likely to be married than women. The distribution of self-rated health is similar for men and women and mirrors that seen in other current population-based studies of aging. 10

11. DISTRIBUTION OF AGE AT MENOPAUSE IN THE MIDUS SAMPLE
a Estimates are weighted to account for differential probabilities of selection and differential non-response.
b Excludes those respondents who reported their race as black/African-American (n=6).
The estimated distributions of key demographic variables closely match those from the 2000 Census and from other national surveys. Men are more likely to be married than women. The distribution of self-rated health is similar for men and women and mirrors that seen in other current population-based studies of aging. 11

12. Variation for characteristics of human aging and development
Mean age (SD) years
Coefficient of variation
Source
Age at onset of menarche
12.9 (1.6)
12.4%
MIDUS data
Age at onset of menopause
49.7 (5.2)
10.5%
Age at death
78.7 (16.1)
20.5%
USA, women, Human mortality database

13. Variation of age at onset of menarche and age at death (in 2005)
Country
Mean age (SD) for onset of menarche CV %
Mean age (SD) at death
France
12.84 (1.40)
10.9
83.3 (13.8)
16.6
Italy
12.54 (1.46)
11.6
83.3 (13.1)
15.7
Sweden
13.59 (1.41)
10.4
82.3 (12.9) UK
12.89 (1.54)
12.0
80.2 (14.0)
17.5
USA
12.9 (1.60)
12.4
78.7 (16.1)
20.5

14. Mean age (standard deviation, SD) at natural menopause
Population
Mean age (SD) at menopause, years
Source
South Korean women
46.9 (4.9)
Hong et al., MATURITAS, 2007
Viennese women aged 47 to 68
49.2 (3.6)
Kirchengast et al., International Journal of Anthropology , 1999
Mexico: Puebla
Mexico city
46.7 (4.77)
46.5 (5.00)
Sievert, Hautaniemi, Human Biology, 2003
Black women in South Africa: rural
urban
49.5 (4.7)
48.9 (4.2)
Walker et al., International Journal of Obstetrics & Gynaecology, 2005

15. Mean Values and Standard Deviations for Human Developmental Characteristics
a Estimates are weighted to account for differential probabilities of selection and differential non-response.
b Excludes those respondents who reported their race as black/African-American (n=6).
The estimated distributions of key demographic variables closely match those from the 2000 Census and from other national surveys. Men are more likely to be married than women. The distribution of self-rated health is similar for men and women and mirrors that seen in other current population-based studies of aging.
Comparison of mean ages at menarche (1), menopause (2), and death (3) as well as their standard deviations for studied human populations. Source: Gavrilova N.S., Gavrilov L.A., Severin, F.F. and Skulachev, V.P. Testing predictions of the programmed and stochastic theories of aging: Comparison of variation in age at death, menopause, and sexual maturation. Biochemistry (Moscow), 2012, 77(7), 15

16. Conclusions
Relative variability, coefficients of variation, for ages at onset of menarche and ages at death for contemporary populations are of the same order of magnitude
Theories of programmed aging are fruitful in suggesting new testable predictions.
"Although any claim that humans are programmed to age and die would be highly speculative, we believe that as a hypothesis it suggests fruitful avenues for biological and even medical research." Longo VD, Mitteldorf J, Skulachev VP. Programmed and altruistic ageing. Nature Review Genetics Nov;6(11):

17. To read more about this part of our study see:
Gavrilova NS, Gavrilov LA, Severin FF, Skulachev VP. Testing predictions of the programmed and stochastic theories of aging: comparison of variation in age at death, menopause, and sexual maturation. Biochemistry (Moscow) Jul;77(7):

18. Part 2 Testing the Prediction of Late-Life Mortality Plateau
Many evolutionary biologists believe that aging can be readily understood in terms of the declining force of selection pressure with age.
At extremely old postreproductive ages when the force of natural selection reaches a zero plateau, some evolutionary biologists (i.e. Michael Rose) believe that the mortality plateau should also be observed (no further increase in mortality rates with age).
To test the validity of this argument we analyzed mortality data for humans, rats and mice.

19. Some evolutionary theories predict late-life mortality plateau
Source: Presentation by Michael Rose

20. When the force of natural selection reaches a zero plateau, the mortality plateau is also expected

21. Problems with Hazard Rate Estimation At Extremely Old Ages
Mortality deceleration in humans may be an artifact of mixing different birth cohorts with different mortality (heterogeneity effect)
Standard assumptions of hazard rate estimates may be invalid when risk of death is extremely high
Ages of very old people may be highly exaggerated

22. Monthly Estimates of Mortality are More Accurate Simulation assuming Gompertz law for hazard rate
Stata package uses the Nelson-Aalen estimate of hazard rate:
H(x) is a cumulative hazard function, dx is the number of deaths occurring at time x and nx is the number at risk at time x before the occurrence of the deaths. This method is equivalent to calculation of probabilities of death:

23. Social Security Administration’s Death Master File (SSA’s DMF) Helps to Alleviate the First Two Problems
Allows to study mortality in large, more homogeneous single-year or even single-month birth cohorts
Allows to estimate mortality in one-month age intervals narrowing the interval of hazard rates estimation

24. What Is SSA’s DMF ?
As a result of a court case under the Freedom of Information Act, SSA is required to release its death information to the public. SSA’s DMF contains the complete and official SSA database extract, as well as updates to the full file of persons reported to SSA as being deceased.
SSA DMF is no longer a publicly available data resource (now is available from Ancestry.com for fee)
We used DMF full file obtained from the National Technical Information Service (NTIS). Last deaths occurred in September 2011.

25. SSA DMF birth cohort mortality
Nelson-Aalen monthly estimates of hazard rates using Stata 11

26. Conclusions from our earlier study of SSA DMF
Mortality deceleration at advanced ages among DMF cohorts is more expressed for data of lower quality
Mortality data beyond ages years have unacceptably poor quality (as shown using female-to-male ratio test). The study by other authors also showed that beyond age 110 years the age of individuals in DMF cohorts can be validated for less than 30% cases (Young et al., 2010)
Source: Gavrilov, Gavrilova, North American Actuarial Journal, 2011, 15(3):

27. Selection of competing mortality models using DMF data
Data with reasonably good quality were used: non-Southern states and years age interval
Gompertz and logistic (Kannisto) models were compared
Nonlinear regression model for parameter estimates (Stata 11)
Model goodness-of-fit was estimated using AIC and BIC

28. Fitting mortality with Kannisto and Gompertz models
Kannisto model

29. Akaike information criterion (AIC) to compare Kannisto and Gompertz models, men, by birth cohort (non-Southern states)
Conclusion: In all ten cases Gompertz model demonstrates better fit than Kannisto model for men in age interval years

30. Akaike information criterion (AIC) to compare Kannisto and Gompertz models, women, by birth cohort (non-Southern states)
Conclusion: In all ten cases Gompertz model demonstrates better fit than Kannisto model for men in age interval years

31. The second studied dataset: U. S
The second studied dataset: U.S. cohort death rates taken from the Human Mortality Database

32. Selection of competing mortality models using HMD data
Data with reasonably good quality were used: years age interval
Gompertz and logistic (Kannisto) models were compared
Nonlinear weighted regression model for parameter estimates (Stata 11)
Age-specific exposure values were used as weights (Muller at al., Biometrika, 1997)
Model goodness-of-fit was estimated using AIC and BIC

33. Fitting mortality with Kannisto and Gompertz models, HMD U.S. data

34. Fitting mortality with Kannisto and Gompertz models, HMD U.S. data

35. Akaike information criterion (AIC) to compare Kannisto and Gompertz models, men, by birth cohort (HMD U.S. data)
Conclusion: In all ten cases Gompertz model demonstrates better fit than Kannisto model for men in age interval years

36. Akaike information criterion (AIC) to compare Kannisto and Gompertz models, women, by birth cohort (HMD U.S. data)
Conclusion: In all ten cases Gompertz model demonstrates better fit than Kannisto model for men in age interval years

37. Compare DMF and HMD data Females, 1898 birth cohort
Hypothesis about two-stage Gompertz model is not supported by real data

38. 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)

39. Mortality of mice (log scale) Data by Richard Miller
males
females
Actuarial estimate of hazard rate with 10-day age intervals

40. Better fit (lower BIC) is highlighted in red
Bayesian information criterion (BIC) to compare the Gompertz and Kannisto models, mice data
Dataset
Miller data
Controls
Exp., no life extension
Carnes data
Early controls
Late controls
Sex M F
Cohort size at age one year
1281
1104
2181
1911
364
431
487
510
Gompertz
-597.5
-496.4
-660.4
-580.6
-585.0
-566.3
-639.5
-549.6
Kannisto
-565.6
-495.4
-571.3
-577.2
-556.3
-558.4
-638.7
-548.0
Better fit (lower BIC) is highlighted in red
Conclusion: In all cases Gompertz model demonstrates better fit than Kannisto model for mortality of mice after one year of age

41. Laboratory rats
Data sources: Dunning, Curtis (1946); Weisner, Sheard (1935), Schlettwein-Gsell (1970)

42. Mortality of Wistar rats
males
females
Actuarial estimate of hazard rate with 50-day age intervals
Data source: Weisner, Sheard, 1935

43. Better fit (lower BIC) is highlighted in red
Bayesian information criterion (BIC) to compare Gompertz and Kannisto models, rat data
Line
Wistar (1935)
Wistar (1970)
Copenhagen
Fisher
Backcrosses
Sex M F
Cohort size
1372
1407
2035
1328
1474
1076
2030
585
672
Gompertz
-34.3
-10.9
-53.7
-11.8
-46.3
-17.0
-13.5
-18.4
-38.6
Kannisto
7.5
5.6
1.6
2.3
-3.7
6.9
9.4
2.48
-2.75
Better fit (lower BIC) is highlighted in red
Conclusion: In all cases Gompertz model demonstrates better fit than Kannisto model for mortality of laboratory rats

44. Simulation study of the Gompertz mortality Kernel smoothing of hazard rates

45. Recent developments
“none of the age-specific mortality relationships in our nonhuman primate analyses demonstrated the type of leveling off that has been shown in human and fly data sets”
Bronikowski et al., Science, 2011
"

46. Conclusions for Part 2 of our Study
We found that mortality rates increase exponentially with age (the Gompertz law), and no expected late-life mortality plateaus are observed in humans, mice, and rats.
Late-life mortality deceleration and mortality plateau observed in some earlier studies may be related to problems with data quality and biased estimates of hazard rates at extreme old ages
It seems unreasonable to explain aging (Gompertz law of mortality) by declining force of natural selection, because aging continues at the same pace at extremely old postreproductive ages when the force of natural selection already reaches a zero plateau

47. To read more about this part of our study see:
Gavrilov L.A., Gavrilova N.S. Mortality measurement at advanced ages: A study of the Social Security Administration Death Master File. North American Actuarial Journal, 2011, 15(3):

48. Part 3 Testing the Prediction of a Trade-off between Longevity and Fertility
One of the predictions of the disposable soma theory and the antagonistic pleiotropy theory is that exceptional longevity should come with the price of impaired fertility (longevity-fertility trade-off ).
This prediction seems to be confirmed by a high profile study published by Nature, which claimed that almost half of long lived women were childless.
Here we re-evaluate this study with more complete data

49. Study that Found a Trade-Off Between Reproductive Success and Postreproductive Longevity
Westendorp RGJ, Kirkwood TBL Human longevity at the cost of reproductive success. Nature 396:
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.

50. 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

51. “… it is not a matter of reduced fertility, but a case of 'to have or have not'.“
Source: Toon Ligtenberg & Henk Brand. Longevity — does family size matter? Nature, 1998, 396, pp

52. 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

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

54. Do longevous women have impaired fertility
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).

55. 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

56. 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 ?

57. 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

58. Test for Data Completeness
Direct 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 (1653­1741) 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 (1776­1864) 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 (1803­1886), Henry (1806­1889), Charles (1807­1882), Arabella ( ), and William (1815­1881).
Wilhelmina Louise von Anhalt-Bernburg (1799­1882), apparently childless, lived 83 years. In reality, however, she had at least two children, Alexander (1820­1896) and Georg (1826­1902).

59. 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, R. G. J., Kirkwood, T. B. L. Human longevity at the cost of reproductive success. Nature, 1998, 396, pp

60. Antoinette de Bourbon (1493-1583)
Lived almost 90 years
She was claimed to have only one child in the dataset used by Westendorp and Kirkwood: Marie ( ), who became a mother of famous Queen of Scotland, Mary Stuart.
Our data cross-checking revealed that in fact Antoinette had 12 children!
Marie
Francois Ier
Louise
Renee
Charles
Claude
Louis
Philippe
Pierre 1529
Antoinette
Francois
Rene

61. Characteristics of Our Data Sample for ‘Reproduction-Longevity’ Studies
3,723 married women born in 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.

62. 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

64. 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:

65. 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,

66. Short Conclusion:
Exceptional human longevity is NOT associated with infertility or childlessness

67. More Detailed Conclusions
We 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.

68. 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.

69. Acknowledgments This 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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