Abstract The success of invasive plant species can be evaluated using different dimensions, such as, range size, abundance and impact. These different dimensions do not always covary but are rarely separated, suggesting an urgency to disentangle the functional mechanisms behind them. A dataset of leaf traits and four dimensions of invasion success (i.e. range size, local abundance, impact on native plant abundance and impact on native plant diversity) were compiled for 395 non‐native plant species in the US and Europe. Associations among dimensions of invasion success and between leaf traits and dimensions were analysed with general linear models (LMs) and supplemented by phylogenetic generalized least square (PGLS) models, which control for the phylogenetic relatedness across species. The pair‐wise associations between most pairs of invasion dimensions were weak or neutral. The only exception was the association between impact on native plant abundance and impact on native plant diversity, which was strongly positive. Traits of species that have large range sizes were associated with a high metabolic rate; whereas, traits of species that were abundant or had a strong impact at the local scale were associated with low metabolic rate. In addition, traits of species with a large range size or having strong impacts on native plant abundance were associated with acquisitive strategies; whereas, traits of species with a high local abundance or strong impacts on native plant diversity were associated with conservative strategies. Synthesis. Different dimensions of invasion success were associated with different functional traits. Invasion success at the regional scale was related to traits that promote rapid colonization; whereas, invasion success at the local scale was related to traits that are potentially less preferred by herbivores. Some locally successful invaders even possessed traits that facilitate a high stress tolerance and conservative strategy, which were similar to locally abundant native species. Therefore, an ambiguous definition of ‘invasion success’ in mechanism‐related studies may produce inconsistent or even controversial conclusions, highlighting the importance of separately studying different dimensions of invasion success.
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