Impact scores of invasive plants are biased by disregard of environmental co-variation and non-linearity.
Prioritisation of high-impact species is becoming increasingly important for management of introduced species ('neobiota') because of their growing number of which, however, only a small fraction has substantial impacts. Impact scores for prioritising species may be affected by the type of effect model used. Recent studies have shown that environmental co-variation and non-linearity may be significant for effect models of biological invasions. Here, we test for differences in impact scores between simple and complex effect models of three invasive plant species (Heracleum mantegazzianum, Lupinus polyphyllus, Rosa rugosa). We investigated the effects of cover percentages of the invasive plants on species richness of invaded communities using both simple linear effect models ('basic models') and more complex linear or non-linear models including environmental co-factors ('full models'). Then, we calculated impact scores for each invasive species as the average reduction of species richness predicted by basic and full effect models. All three non-native species had negative effects on species richness, but the full effect models also indicated significant influence of habitat types. Heracleum mantegazzianum had uniform linear effects in all habitats, while effects of Lupinus polyphyllus interacted strongly with habitat type, and Rosa rugosa showed a marked non-linear relationship. Impact scores were overestimated by basic effect models for Heracleum mantegazzianum and Rosa rugosa due to disregard of habitat effects and non-linearity, respectively. In contrast, impact of Lupinus polyphyllus was underestimated by the basic model that did not account for the strong interaction of invader cover and habitat type. We conclude that simple linear models will often yield inaccurate impact scores of non-native species. Hence, effect models should consider environmental co-variation and, if necessary, non-linearity of the effects of biological invasions on native ecosystems.