Semivarying coefficient models for capture–recapture data: Colony size estimation for the little penguin Eudyptula minor

• We propose a new capture–recapture model to estimate wildlife population sizes.
• Seasonality that changes yearly is accommodated by a time-varying coefficient model.
• Simulations were conducted to examine the model performance.
• The model is fitted to 25 years of real data collected on little penguins.
• Our results revealed key structures relating to environmental and biological changes.

To accommodate seasonal effects that change from year to year into models for the size of an open population we consider a time-varying coefficient model. We fit this model to a capture–recapture data set collected on the little penguin Eudyptula minor in south-eastern Australia over a 25 year period using Jolly–Seber type estimators and nonparametric P-spline techniques. The time-varying coefficient model identified strong changes in the seasonal pattern across the years which we further examined using functional data analysis techniques. To evaluate the methodology we also conducted several simulation studies that incorporate seasonal variation.