Frailty in state-space models: application to actuarial senescence in the Dipper

Senescence, a decrease in life history traits with age, is a within-individual process. The lack of suitable methods to deal with individual heterogeneity has long impeded progress in exploring senescence in wild populations. Analyses of survival senescence are additionally complicated by the often neglected issue of imperfect detectability. To deal with both these issues, we developed state-space models to analyze capture-mark-recapture data while accounting for individual heterogeneity by incorporating random effects. We illustrated our approach by applying it to 29 years of data on breeding females in a Dipper (Cinclus cinclus) population. We highlighted patterns of age-related variation in annual survival by statistical comparisons of piecewise linear, quadratic, Gompertz, and Weibull survival models. The Gompertz model was ranked first in our set. It provided strong evidence for actuarial senescence with an onset of senescence estimated at about 2.3 years. The probability for this model to involve a frailty was 0.15, and the probability to involve an individual latent effect in detection was about 0.4. The estimated mean age at first reproduction was 1.2 years. The general case model described here in detail should encourage the reanalysis of actuarial senescence in cases where imperfect detection or individual heterogeneity is suspected.