Perturbation Analysis of Measures of Lifespan Variability

Alyson A. van Raalte, Max Planck Institute for Demographic Research
Hal Caswell, Woods Hole Oceanographic Institution

A number of measures have been used in recent years to calculate lifespan variation, each with different underlying properties. Although these measures are assumed to be interchangeable, little research has been conducted to show under which conditions this assumption is appropriate, or how to compare their responses to the underlying mortality schedule. We compare seven commonly used measures of lifespan variation. We derive the sensitivity and elasticity of each measure by applying Markov chain theory and matrix calculus. Using empirical data we compare the underlying sensitivities to mortality change under different mortality regimes in order to test under which conditions the measures might differ in their conclusions about the magnitude of lifespan variation. Finally we demonstrate how integrating these sensitivities can be used as a method of age decomposition. The result is an easily computable method for calculating the properties of this important class of longevity measures.