AbstractThe abundance–impact curve is helpful for understanding and managing the impacts of non‐native species. Abundance–impact curves can have a wide range of shapes (e.g., linear, threshold, sigmoid), each with its own implications for scientific understanding and management. Sometimes, the abundance–impact curve has been viewed as a property of the species, with a single curve for a species. I argue that the abundance–impact curve is determined jointly by a non‐native species and the ecosystem it invades, so that a species may have multiple abundance–impact curves. Models of the impacts of the invasive mussel Dreissena show how a single species can have multiple, noninterchangeable abundance–impact curves. To the extent that ecosystem characteristics determine the abundance–impact curve, abundance–impact curves based on horizontal designs (space‐for‐time substitution) may be misleading and should be used with great caution, it at all. It is important for scientists and managers to correctly specify the abundance–impact curve when considering the impacts of non‐native species. Diverting attention from the invading species to the invaded ecosystem, and especially to the interaction between species and ecosystem, could improve our understanding of how non‐native species affect ecosystems and reduce uncertainty around the effects of management of populations of non‐native species.