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A recent analysis by Moulton & Cropper (2019) of a global dataset on alien bird population introductions claims to find no evidence that establishment success is a function of the size of the founding population. Here, we re-analyse Moulton & Cropper’s data and show that this conclusion is based on flawed statistical methods—their data in fact confirm a strong positive relationship between founding population size and establishment success. We also refute several non-statistical arguments against the likelihood of such an effect presented by Moulton & Cropper. We conclude that a core tenet of population biology—that small populations are more prone to extinction—applies to alien populations beyond their native geographic range limits as much as to native populations within them.