title: Why do lifespan variability trends for the young and old diverge? A perturbation analysis.
abstract: BACKGROUND
  Variation in lifespan has followed strikingly different trends for the young and old: while total 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 ages at death after survival to adult ages has followed a different trend than the variation at younger ages, and aim to explain the divergence in terms of the age pattern of historical mortality changes.
  
  
  METHODS
  Using simulations, we show that the empirical trends in lifespan variation are well characterized using the Siler model, which describes the mortality trajectory using functions representing early-life, later-life, and background mortality. We then obtain maximum likelihood estimates of the Siler parameters for Swedish females from 1900 to 2010. We express mortality in terms of a Markov chain model, and apply matrix calculus to compute the sensitivity of age-specific variance trends to the changes in Siler model parameters.
  
  
  RESULTS
  Our analysis quantifies the influence of changing demographic parameters on lifespan variability at all ages, highlighting the influence of declining childhood mortality on the reduction of lifespan variability, and the influence of subsequent improvements in adult survival 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.
authors: Department of Sociology and Center for Demography and Ecology, University of Wisconsin-Madison, USA.
authors: Michal
authors: M
authors: Engelman
authors: Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, Netherlands. Biology Department, Woods Hole Oceanographic Institution, USA.
authors: Hal
authors: H
authors: Caswell
authors: Hopkins Center for Population Aging and Health, Hopkins Population Center, and Department of Sociology, Johns Hopkins University, USA.
authors: Emily M
authors: EM
authors: Agree