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Description: 1. Non-native plant species can dominate communities by competitively excluding native species. However, quantifying the competitive impact of non-native species is difficult because they may simply be abundant where native species are not due to different environmental requirements, meaning that the effects of environmental and competitive variation are confounded. 2. Joint-species distribution models (JSDMs) can potentially untangle the environmental and competitive drivers of community composition. Extending JSDMs to include abundance data would allow them to be used to answer questions of community composition and species dominance. We describe a modelling approach that incorporates abundance data within a JSDM framework to identify non-native species having strong competitive impacts. 3. We applied this approach to Australian grassy-woodland communities and manipulated grazing along a fertility gradient. The JSDM identified two of 72 non-native species (Avena fatua and Bromus diandrus) as having strong competitive impacts at high fertility sites, particularly after grazing exclusion. Competitive impact was well explained by traits associated with the ability to compete for light. 4. Synthesis. JSDMs hold promise for identifying problematic plant invaders, quantifying their impact, and determining where on the landscape impacts are greatest. Our study demonstrates how a carefully formulated JSDM can extract accurate information about the key interactions driving variation in community composition from observational data alone. We provide a thorough treatment of the modelling procedure and reproducible code examples to encourage further adoption.