Bayesian inference on age‐specific survival for censored and truncated data

Abstract

1. Traditional estimation of age-specific survival and mortality rates in vertebrates is limited to individuals with known age. Although this subject has been studied extensively using effective capture-recapture and capture-recovery models, inference remains challenging because of large numbers of incomplete records (i.e. unknown age of many individuals) and because of the inadequate duration of the studies. 2. Here, we present a hierarchical model for capture-recapture/recovery (CRR) data sets with large proportions of unknown times of birth and death. The model uses a Bayesian framework to draw inference on population-level age-specific demographic rates using parametric survival functions and applies this information to reconstruct times of birth and death for individuals with unknown age. 3. We simulated a set of CRR data sets with varying study span and proportions of individuals with known age, and varying recapture and recovery probabilities. We used these data sets to compare our method to a traditional CRR model, which requires knowledge of individual ages. Subsequently, we applied our method to a subset of a long-term CRR data set on Soay sheep. 4. Our results show that this method performs better than the common CRR model when sample sizes are low. Still, our model is sensitive to the choice of priors with low recapture probability and short studies. In such cases, priors that overestimate survival perform better than those that underestimate it. Also, the model was able to estimate accurately ages at death for Soay sheep, with an average error of 0.94 years and to identify differences in mortality rate between sexes. 5. Although many of the problems in the estimation of age-specific survival can be reduced through more efficient sampling schemes, most ecological data sets are still sparse and with a large proportion of missing records. Thus, improved sampling needs still to be combined with statistical models capable of overcoming the unavoidable limitations of any fieldwork. We show that our approach provides reliable estimates of parameters and unknown times of birth and death even with the most incomplete data sets while being flexible enough to accommodate multiple recapture probabilities and covariates.