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Dispersal strategies are one of the most important determinants of range dynamics and a surrogate for invasiveness. We tested three inter-related hypotheses derived from demographic and ecological models: (H1) short-distance dispersal strategies arise at native range margins due to their demographic advantage; (H2) in non-native areas a high diffusion rate is favoured at the advancing range front for niche filling; (H3) environmental deterioration can increase dispersal and lead to a ‘good–stay, bad–disperse’ strategy. Spatially and temporally explicit rates of spread and dispersal kernels of the European starling Sturnus vulgaris were generated for its native range (Britain) using ringing records from 1909 to 2008, and for a non-native area (South Africa) using ringing data and distributional records since its introduction in 1897. There was a marked spatial and temporal variation in the rate of spread within both native and non-native ranges. In the native range the rate of spread declined with increasing distance from the species’ European distribution (contradicting H1). In the non-native range the rate of spread increased with distance from the introduction locality (supporting H2). The annual rate of spread in the native range also increased significantly when environmental conditions were deteriorating as indicated by marked population declines and relatively low abundance (H3), providing clear evidence for flexible dispersal strategies based on a ‘good–stay, bad–disperse’ rule. Starlings’ dispersal kernel followed an inverse power law and showed strong anisotropy and significant divergence between native and invasive populations, suggesting a flexible strategy comprising a dynamic response to spatial and temporal environmental variation with implications for predicting dispersal and range dynamics arising from environmental change.