It is not clear which forms of plasticity in fitness-related traits are associated with invasive species. On one hand, it may be better to have a robust performance across environments. On the other, it may be beneficial to take advantage of limited favorable conditions. We chose to study a worldwide invasive species, Potamopyrgus antipodarum, and compare the plasticity of life-history traits of a sample of invasive genotypes to a sample of ancestral-range genotypes. We examined the responses to salinity in this freshwater snail because it varies spatially and temporally in the introduced range and contributes to variation in fitness in our system. We used a recently developed statistical method that quantifies aspects of differences in the shape among reaction norms. We found that the invasive lineages survived and reproduced with an increased probability at the higher salinities, and were superior to ancestral-range lineages in only two traits related to reproduction. Moreover, we found that in terms of traits related to growth, the invasive lineages have a performance optimum that is shifted to higher salinities than the ancestral-range lineages as well as having a narrower niche breadth. Contrary to the prediction of the general purpose genotype hypothesis, we found that invasive lineages tended to be opportunistic specialists.