Estimating age-specific survival when age is unknown: Open population capture-recapture models with age structure and heterogeneity

When studying senescence in wildlife populations, we are often limited by the sparseness of the available information on the ages of the individuals under study. Additionally, heterogeneity between individuals can be substantial. Ignoring this heterogeneity can lead to biased estimates of the population parameters of interest and can mask senescence. This article demonstrates the use of a recently developed capture-recapture model for extracting age-dependent estimates of survival probabilities for individuals of unknown age and extends the model by allowing for heterogeneity in survival and capture probabilities using finite mixtures. Using simulation, we show that the estimates of age-dependent survival probabilities when age is unknown can be biased when heterogeneity in capture probabilities is not modelled, in contrast to the case of time-dependent survival probabilities when the estimates are robust to similar violations of model assumptions. The methods are demonstrated using a long-term data set of female brushtail possums (Trichosurus vulpecula Kerr) for which age-specific models for survival probabilities indicating senescence are strongly favoured. We found no evidence of heterogeneity in survival but strong evidence of heterogeneity in capture probabilities. These models have a wide range of applications for estimating age dependence in survival when the age is unknown as they can be applied to any capture-recapture data set, as long as it is collected over a period which is longer, and preferably considerably so, than the life span of the species studied.