• Capture–recapture;
  • Cross-validation;
  • Little Penguins Eudyptula minor;
  • Open population;
  • P-splines

In capture–recapture models, survival and capture probabilities can be modelled as functions of time-varying covariates, such as temperature or rainfall. The Cormack–Jolly–Seber (CJS) model allows for flexible modelling of these covariates; however, the functional relationship may not be linear. We extend the CJS model by semi-parametrically modelling capture and survival probabilities using a frequentist approach via P-splines techniques. We investigate the performance of the estimators by conducting simulation studies. We also apply and compare these models with known semi-parametric Bayesian approaches on simulated and real data sets.