Volume 30 - Article 48 | Pages 1367–1396

Why do lifespan variability trends for the young and old diverge? A perturbation analysis

By Michal Engelman, Hal Caswell, Emily Agree

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Date received:05 Apr 2013
Date published:01 May 2014
Word count:5537
Keywords:lifespan variability, mortality, perturbation analysis
Updated Items:On May 8, 2014 several references were updated on pages 1368, 1370, 1373, 1382, 1387, 1388, 1389 and on page 1390.


Background: Variation in lifespan has followed strikingly different trends for the young and old: while overall lifespan variability has decreased as life expectancy at birth has risen, the variability conditional on survival to older ages has increased. These diverging trends reflect changes in the underlying demographic parameters determining age-specific mortality.

Objective: We ask why the variation in the adult ages at death has followed a different trend than the variation at younger ages, and aim to explain the diverging patterns in terms of historical changes in the age schedule of mortality.

Methods: Using simulations, we show that the empirical trends in lifespan variation are well characterized using the Siler model, which describes the mortality hazard across the full lifespan using functions representing early-life, later-life, and background mortality. We then obtain maximum likelihood estimates of the Siler parameters over time. Finally, we express lifespan variation in terms of a Markov chain model, and apply matrix calculus perturbation analysis to compute the sensitivity of age-specific lifespan variance trends to the changing Siler model parameters.

Results: Our analysis produces a detailed quantification of the impact of changing demographic parameters on the pattern of lifespan variability at all ages, highlighting the impact of declining childhood mortality on the reduction of lifespan variability and the impact of improved survival in adulthood on the rising variability of lifespans at older ages.

Conclusions: These findings provide insight into the dynamic relationship between the age pattern of survival improvements and time trends in lifespan variability.

Author's Affiliation

Michal Engelman - University of Wisconsin–Madison, United States of America [Email]
Hal Caswell - Universiteit van Amsterdam, Netherlands [Email]
Emily Agree - Johns Hopkins University, United States of America [Email]

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» Lifetime reproduction and the second demographic transition: Stochasticity and individual variation
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» Demography and the statistics of lifetime economic transfers under individual stochasticity
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» A matrix approach to the statistics of longevity in heterogeneous frailty models
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» Reproductive value, the stable stage distribution, and the sensitivity of the population growth rate to changes in vital rates
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» Perturbation analysis of nonlinear matrix population models
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