Maximum penalized likelihood estimation in semiparametric capture-recapture models

We consider a semiparametric modeling approach for capture-recapture-recovery data where the temporal and/or individual variation of model parameters – usually the demographic parameters – is explained via covariates. Typically, in such analyses a fixed (or mixed) effects parametric model is specified for the relationship between the model parameters and the covariates of interest. In this paper, we specify the relationship via the use of penalized splines, to allow for considerably more flexible functional forms. Corresponding models can be fitted via numerical maximum penalized likelihood estimation, employing cross-validation to choose the smoothness parameters in a data-driven way. Our work builds on and extends the existing literature, providing a unified and general inferential framework for semiparametric capture-recapture models. The approach is applied to two real datasets, corresponding to grey herons (Ardea Cinerea), where the covariate corresponds to environmental conditions (a time-varying global covariate), and Soay sheep (Ovis Aries), where the covariate corresponds to weight (a time-varying individual-specific covariate). The proposed semiparametric approach is compared to a standard parametric (logistic) regression and new interesting underlying dynamics are observed in both cases.