The Biology of Life Span: A Quantitative Approach Leonid A. Gavrilov, Ph.D. Natalia S. Gavrilova, Ph.D. Center on Aging NORC and The University of Chicago Chicago, Illinois, USA

Our brief self-introduction We met as students at Moscow State University (Chemistry department), Russia, and found a common interest in understanding the mechanisms of human aging, with a hope to find ways for extending healthy life. We were inspired by scientific approach of Nobel laureate Nikolay Semyonov, while studying as students at his chemical kinetics department. We loved the idea that you can find out the mechanisms of chemical reactions by clever quantitative analysis of a process kinetics (change over time). We decided to apply this approach to study aging and mortality by quantitative analysis of mortality kinetics (survival curves). Now this approach is a part of bioinformatics in aging research.

In our studies we followed advice of Russian geneticist Nikolay Timofeev-Ressovsky: "If you understand the problem, you write an article. If you do not understand the problem, you write a book.“ [in order to come to understanding of a problem by writing a book] As a result of our studies we wrote a book: The Biology of Life Span: A Quantitative Approach

Empirical Laws of Mortality Biological mortality laws and reliability theory of aging

The Gompertz-Makeham Law μ(x) = A + R e αx A – Makeham term or background mortality R 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). Source: Gavrilov, Gavrilova, “The Biology of Life Span” 1991

Gompertz-Makeham Law of Mortality in Italian Women Based on the official Italian period life table for Source: Gavrilov, Gavrilova, “The Biology of Life Span” 1991

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, , males 2 – Turkey, , males 3 – Kenya, 1969, males 4 - Northern Ireland, , males 5 - England and Wales, , females 6 - Austria, , females 7 - Norway, , females Source: Gavrilov, Gavrilova, “The Biology of Life Span” 1991

Compensation Law of Mortality The Association Between Income and mortality of men in the United States, Source: JAMA. 2016;315(16): doi: /jama

Compensation Law of Mortality in Laboratory Drosophila 1 – 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. Source: Gavrilov, Gavrilova, “The Biology of Life Span” 1991

Implications  Be 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 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

Mortality Leveling-Off in House Fly Musca domestica Based on life table of 4,650 male house flies published by Rockstein & Lieberman, 1959

Testing the “Limit-to-Lifespan” Hypothesis Source: Gavrilov L.A., Gavrilova N.S 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.

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 et al., 2012; Libby, 2003; Rauscher et al., 2003). Loss of neurons in substantia nigra – may lead to Parkinson’s disease (Rodrigues et al., 2015) 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 Stochastic and genetic factors influence tissue- specific decline in ageing C. elegans. Nature 419, “…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:

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, 6 th 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 theory Aging: 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 non-aging system aging system Example: radioactive decay

According to Reliability Theory: Aging is NOT just growing old Instead Aging is a degradation to failure: becoming sick, frail and dead 'Healthy aging' is an oxymoron like ‘healthy dying’ or ‘healthy disease’ More accurate terms instead of 'healthy aging' would be ‘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 P s = p 1 p 2 p 3 … p n = p n Q s = q 1 q 2 q 3 … q n = q n

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 System Failure rate of the system: Elements fail randomly and independently with a constant failure rate, k n – initial number of elements  nk n x n-1 early-life period approximation, when 1-e -kx  kx  k late-life period approximation, when 1-e -kx  1

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): x 0 = 0 - ideal system, Weibull law of mortality x 0 >> 0 - highly damaged system, Gompertz law of mortality where - the initial virtual age of the system 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 The Biology of Life Span: A Quantitative Approach. Harwood Academic Publisher, New York.

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 The Biology of Life Span: A Quantitative Approach. Harwood Academic Publisher, New York.

Life Expectancy and Month of Birth Data source: Social Security Death Master File

Latest Developments Was the mortality deceleration law overblown? A Study of the Extinct Birth Cohorts in the United States

U.S. birth cohort mortality Nelson-Aalen monthly estimates of hazard rates using Stata 11 Data from the Social Security Death Index

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 malesfemales

Testing biological theories of aging with human data Natalia S. Gavrilova, Ph.D. Center on Aging NORC and The University of Chicago Chicago, Illinois, USA

New Vision of Aging-Related Diseases

Hypothesis: Ovarian aging (decline in egg quality) may have long-term effects on offspring quality, health and longevity. Down syndrome is just a tip of the iceberg of numerous less visible defects. Testable prediction: Odds of longevity decrease with maternal age Negative impact of maternal aging on offspring longevity

Within-Family Approach Allows researchers to eliminate between-family variation including the differences in genetic background and childhood living conditions

Computerized genealogies is a promising source of information about potential predictors of exceptional longevity: life- course events, early-life conditions and family history of longevity

Within-family study of longevity Cases - 1,081 centenarians survived to age 100 and born in USA in Controls – 6,413 their shorter-lived brothers and sisters (5,778 survived to age 50) Method: Conditional logistic regression Advantage: Allows to eliminate between- family variation

Age validation is a key moment in human longevity studies Death date was validated using the U.S. Social Security Death Index Birth date was validated through linkage of centenarian records to early U.S. censuses (when centenarians were children)

A typical image of ‘centenarian’ family in 1900 census

Maternal age and chances to live to 100 for siblings survived to age 50 Conditional (fixed-effects) logistic regression N=5,778. Controlled for month of birth, paternal age and gender. Paternal and maternal lifespan >50 years Maternal ageOdds ratio95% CIP-value < Reference

People Born to Young Mothers Have Twice Higher Chances to Live to 100 Within-family study of 2,153 centenarians and their siblings survived to age 50. Family size <9 children. p=0.020 p=0.013 p=0.043 Source: Gavrilov, Gavrilova, Gerontology, 2015

Being born to Young Mother Helps Laboratory Mice to Live Longer Source: Tarin et al., Delayed Motherhood Decreases Life Expectancy of Mouse Offspring. Biology of Reproduction : Similar results on mice obtained by Carnes et al., 2012 (for female offspring)

Possible explanations  Quality of oocytes declines with age (Kalmbach et al., 2015).  These findings are also consistent with the 'best eggs are used first' hypothesis suggesting that earlier formed oocytes are of better quality, and go to fertilization cycles earlier in maternal life (Keefe et al., 2005). Note: Our original findings were independently confirmed in the study of Canadian centenarians (Jarry et al., Vienna Yearbook of Population Research, 2013)

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, Evolution in Age-structured Populations). This should result in higher heritability estimates for lifespan of offspring born to longer-lived parents.

Linearity Principle of Inheritance in Quantitative Genetics Dependence between parental traits and offspring traits is linear

Dataset on European Aristocracy Over 16,000 persons belonging to the European aristocracy 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 Offspring data for adult lifespan (30+ years) are smoothed by 5-year running average. Extinct birth cohorts (born in ) European aristocratic families. 6,443 cases

Daughter's Lifespan (Mean Deviation from Cohort Life Expectancy) as a Function of Maternal Lifespan Offspring data for adult lifespan (30+ years) are smoothed by 5-year running average. Extinct birth cohorts (born in ) European aristocratic families. 5,779 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., Danish twins Ljungquist et al., 1998<0.33Swedish twins Bocquet-Appel, Jacobi, French village Mayer, New England families Cournil et al., French village Mitchell et al., Old Order Amish

Another Prediction of the Mutation Accumulation Theory of Aging (Medawar, 1946) The theory predicts that the observed pattern of familial transmission of human lifespan is caused by higher equilibrium frequency of late-acting deleterious mutations at older ages (Medawar 1952). Therefore, children born to long-lived parents should experience survival advantage mostly in their old ages (because they have less late-acting deleterious mutations).

The alternative hypotheses Reliability theory of aging predicts that children born to long living parents will experience survival advantage mostly in their younger adult ages, because of higher redundancy in functional elements (cells) not yet exhausted over time (Gavrilov and Gavrilova 2006). Finally, the third hypothesis suggests the life-long sustained mortality advantage for persons having protection of familial longevity (Perls et al. 2002).

Parental Longevity Effects Mortality Kinetics for Progeny Born to Long-Lived (80+) vs Short-Lived Parents SSonsDaughters Data on European aristocracy

American centenarians born in

Database on Exceptional Longevity About 4,000 records of centenarians born in the United States. Age of centenarians was validated using the Social Security Death Master File linkage (82% validated) About 4,000 records of shorter-lived controls (died at 65 years) Both centenarians and controls have information about lifespan of parents Both centenarians and controls have information about siblings, children, souses, siblings-in-law and grandparents

Data used in the study Shorter-lived persons (65 years) Longer-lived persons (100+) MenWomenMenWomen Identified cases Identified relatives of cases Parents Siblings

Hypotheses If prediction of the mutation accumulation theory is correct then familial longevity should be a significant predictor of mortality at advanced ages If parental longevity is of no importance for survival after age 100 years then it should not affect mortality of centenarians

Parental longevity does not affect survival after age 100 VariableHazard Ratio95% CIP-value Paternal lifespan , Maternal lifespan , Sex (0- men, 1-women) , 0.914<0.001 Second analysis: Paternal lifespan , Maternal lifespan , Sex (0- men, 1-women) ,

Survival of siblings with different levels of familial longevity I - siblings of shorter-lived persons (died at age 65) II - siblings of centenarians

Mortality of men with different levels of familial longevity

Mortality of women with different levels of familial longevity

Conclusions  Familial longevity improves survival mostly at younger adult rather than older ages  Parental longevity has no significant effect on survival of centenarians  These findings support predictions of reliability theory of aging, but do not support predictions of the mutation accumulation theory of aging, as well as the hypothesis of life-long sustained mortality advantage.

Fertility and Longevity How are they related?

Founding Fathers Beeton, M., Yule, G.U., Pearson, K 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: 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 post-reproductive 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.”

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).

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 200 citations in the 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

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 (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 ( ), and William (1815­-1881).

Antoinette de Bourbon ( ) 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

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

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.

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: Childlessness and lifespan in aristocratic women 31 case Our results were based on carefully checked data (genealogies for European aristocratic families)

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,

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

What we would like to do next: To increase our understanding of the biology that controls human lifespan by developing and analyzing large-scale high- quality human pedigrees using bioinformatics approaches. When we learned about creation of Calico, it sounded to us as a dream coming true. We would be delighted to collaborate, or to become a part of your team!