In this paper, we explore the radial basis function network-based state-dependent autoregressive (RBF-AR) model by modelling and forecasting an ecological time series: the famous Canadian lynx data. The interpretability of the state-dependent coefficients of the RBF-AR model is studied. It is found that the RBF-AR model can account for the phenomena of phase and density dependencies in the Canadian lynx cycle. The post-sample forecasting performance of one-step and two-step ahead predictors of the RBF-AR model is compared with that of other competitive time-series models including various parametric and non-parametric models. The results show the usefulness of the RBF-AR model in this ecological time-series modelling.