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Ecologists have had limited success in understanding which introduced species may become invasive. An evolutionary model is used to investigate which traits are associated with invasiveness. Translocation experiments were simulated in which species were moved into similar but evolutionarily younger communities. The main findings were that species that had previously been the most abundant in their original communities have significantly higher rates of establishment than did species that had previously occurred at low abundance in their original community. However, if establishment did occur, previously abundant and previously low-abundant species were equally likely to become dominant and were equally likely to exclude other species from their new community. There was a suggestion that the species that were most likely to establish and exclude others were ‘genetically’ different. When species that had evolved in different simulations (but with identical environmental conditions) were transplanted into communities that had also evolved in different simulations of the same conditions, the outcomes were difficult to predict. Observed rates of establishment and subsequent competitive dominance were observed to be species- and community combination–specific. This evolutionary study represents a novel in silico attempt to tackle invasiveness in an experimental framework and may provide a new methodology for tackling these issues.