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Understanding how and why some species or lineages become invasive is critically important for effectively predicting and mitigating biological invasions. Here, we address an important unanswered question in invasion biology: do key life‐history traits of invasive versus native lineages within a species differ in response to key environmental stressors? We focus on the environmental factor of population density, which is a fundamental characteristic of all populations, and investigate how changes in density affect native versus invasive Potamopyrgus antipodarum (New Zealand mudsnail). P. antipodarum has invaded 39 countries and detrimentally affects invaded environments. Previous studies of native and invasive populations and from laboratory experiments have demonstrated that growth and reproduction of P. antipodarum is sensitive to population density, though whether and how this sensitivity varies across native versus invasive lineages remains uncharacterized. We quantified individual growth rate and reproduction in P. antipodarum from multiple distinct native and invasive lineages across three different population density treatments. The growth of native but not invasive lineages decreased as density increased. There was no differential effect of density treatment on embryo production of invasive versus native snails, but a significantly higher proportion of snails were reproductive in high density compared to intermediate density for invasive lineages. In native lineages, there were no significant differences in the relative frequency of reproductive snails across density treatments. While the extent to which these results from our laboratory study can be extrapolated to the more complex natural world remain unclear, our findings are consistent with a scenario where differential sensitivity to population density could help explain why some lineages become successful invaders. Our findings also align with previous studies that show that invasive P. antipodarum lineages exhibit a relatively wide range of tolerance to environmental stressors. [ABSTRACT FROM AUTHOR]