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Summary A definitive list of invasive species traits remains elusive, perhaps due to inconsistent ways of identifying invasive species. Invasive species are typically identified using one or more of four demographic criteria (local abundance, geographic range, environmental range, spread rate), referred to here as the demographic dimensions of invasiveness. In 112 studies comparing invasive and non‐invasive plant traits, all 15 combinations of the four demographic dimensions were used to identify invasive species; 22% of studies identified invasive species solely by high abundance, while 25% ignored abundance. We used demographic data of 340 alien herbs classified as invasive or non‐invasive in Victoria, Australia, to test whether the demographic dimensions are independent and which dimensions influence invasive species listing in practice. Species' abundances, spread rates and range sizes were independent. Relative abundance best explained the invasiveness classification. However, invasive and non‐invasive species each spanned the full range of each demographic dimension, indicating that no dimension clearly separates invasive from non‐invasive species. Graminoids with longer minimum residence times were more frequently classified as invasive, as were forbs occurring near edges of native vegetation fragments. Synthesis . Conflating multiple forms of invasiveness, by not distinguishing invasive species that are identified using different demographic criteria, may obscure traits possessed by particular subsets of invasive species. Traits promoting high abundance likely differ from those enabling fast spread and broad ranges. Examining traits linked with the four demographic dimensions of invasiveness will highlight species at risk of becoming dominant, spreading quickly or occupying large ranges.