The European rabbit (Oryctolagus cuniculus) is a notorious economic and environmental pest species in its invasive range. To better understand the population and range dynamics of this species, 41 yr of abundance data have been collected from 116 unique sites across a broad range of climatic and environmental conditions in Australia. We analyzed this time series of abundance data to determine whether interannual variation in climatic conditions can be used to map historic, contemporary, and potential future fluctuations in rabbit abundance from regional to continental scales. We constructed a hierarchical Bayesian regression model of relative abundance that corrected for observation error and seasonal biases. The corrected abundances were regressed against environmental and disease variables in order to project high spatiotemporal resolution, continent-wide rabbit abundances. We show that rabbit abundance in Australia is highly variable in space and time, being driven primarily by internnual variation in temperature and precipitation in concert with the prevalence of a non-pathogenic virus. Moreover, we show that internnual variation in local spatial abundances can be mapped effectively at a continental scale using highly resolved spatiotemporal predictors, allowing “hot spots” of persistently high rabbit abundance to be identified. Importantly, cross-validated model performance was fair to excellent within and across distinct climate zones. Long-term monitoring data for invasive species can be used to map fine-scale spatiotemporal fluctuations in abundance patterns when accurately accounting for inherent sampling biases. Our analysis provides ecologists and pest managers with a clearer understanding of the determinants of rabbit abundance in Australia, offering an important new approach for predicting spatial abundance patterns of invasive species at the near-term temporal scales that are directly relevant to resource management.