Confidence in Life Tables

Abstract

Confidence limits of age–specific mortality and fecundity rates are rarely provided. However, this information is important for judging the reliability of life tables, especially those based on small studbooks. The occurrence of a single death within an age class is a Bernoulli process, i.e. an individual is either dead or living at the end of the age class, with the mortality rate as the probability of dying. Simulation experiments using random sampling introduce the effect of sample size on the confidence limits of mortality rates. Variances of mortality rates can be calculated from binomial theory. Fecundity rates are often assumed to follow the Poisson distribution. The variance is estimated accordingly. Variances, confidence limits and coefficients of variation are estimated for both mortality and fecundity in young and older age classes. Bootstrap is applied to measure variance (and associated statistics) in both mortality and fecundity rates in female snow leopards. The results of χ2 tests show that theoretical and bootstrap variances do not differ for mortality (except for the oldest age class). However, these variances do differ for fecundity, indicating that the Poisson distribution is not the correct assumption. Reliability of life tables can be improved by increasing sample sizes through pooling older age classes and applying wider age classes (at the cost of detail). Smoothing techniques to reduce gaps and peaks in life tables and application of the Gompertz(–Makeham), Weibull and Siler parametric models to fit mortality curves, are illustrated with real studbook data.