Supporting information A in S1 File. Glossary of additional key terms. Supporting information B in S1 File. Table reporting contrasting arguments and approaches used to define how alien taxa are considered and should be managed in accordance with different conservation values/motivations. As multiple values/motivations exist and determine which entities we are interested in (see also Supporting information A), distinct conservation targets can be identified. Note that here, we only consider conservation values/motivations that are expressed regardless of any nature’s instrumental (utilitarian) value, i.e., regardless of nature’s contributions to human well-being (see “nature for itself” framing [9]). Also, note that such contrasting arguments and approaches are not necessarily mutually exclusive and have been occasionally combined to find a middle ground to achieve broader conservation goals [10–13]. Supporting information C in S1 File. Circumstances under which the prevention/mitigation of a decreasing change is considered as a positive change under EICAT+. In EICAT+, we also consider as positive impacts (i.e., increasing changes) cases in which an alien species prevents/mitigates decreasing changes, e.g., when the performance of a native individual, the size of a native population, or the occupancy of a native species would have decreased, or decreased to a greater extent, if the alien species had not been introduced. Although some of these positive impacts can be inferred, the prevention of a decreasing change should be assessed under EICAT+ only when there is convincing evidence that a certain biodiversity attribute (e.g., population size) would have decreased, or decreased to a greater extent, in the absence of the alien species. In the case of extinction prevention, for instance, it must be clear that (i) the population was locally heading toward extinction before the introduction of the alien; and (ii) the alien taxon prevented, through a specific impact mechanism, an extinction that would have occurred in its absence [41,42] (Fig 2b). Other cases where an alien species may prevent or mitigate decreasing changes are, for instance, those in which the abundance (i.e., a proxy for population size) of a native species declined in the uninvaded (i.e., control) plots but not, or to a lesser extent, in the plots invaded by the alien. Note that positive impacts associated with the prevention/mitigation of a decreasing change will generally be more difficult to study and identify than those associated with actual increasing changes, as the former require extensive data regarding the temporal trend of individual performance, population size, or area of occupancy. Supporting information D in S1 File. EICAT+ mechanisms and submechanisms by which an alien taxon can cause positive impacts on native biodiversity attributes and examples of positive impacts sourced from the literature and assessed under EICAT+ (ML+ = Minimal positive impact, MN+ = Minor positive impact, MO+ = Moderate positive impact, MR+ = Major positive impact, MV+ = Massive positive impact). Rationales behind the formulation of the mechanisms and submechanisms can be found in the main text and in Supporting information G, H, and J. Supporting information E in S1 File. Table reporting examples sourced from the literature and classified as information that cannot be classified under EICAT+, but that contain information about mechanisms and might set the stage for future studies. Although these studies described the existence of mechanisms by which alien taxa may cause positive impacts on native taxa, such literature is considered as nonrelevant, as it did not measure, or provide information on, biodiversity attributes used in EICAT+ (e.g., performance of individuals or population size). Rationales behind the formulation of the mechanisms and submechanisms can be found in the main text and in Supporting information G, H, and J. Supporting information F in S1 File. How to attribute a confidence score in EICAT+. Supporting information G in S1 File. Additional information around the rationale behind the formulation of the EICAT+ mechanisms and submechanisms. Supporting information H in S1 File. Additional information about how alien species can cause positive impacts on native biodiversity through overcompensation. Supporting information J in S1 File. Additional information about how alien species can cause positive impacts on native biodiversity through hybridization. Supporting information K in S1 File. References used in the Supporting information.

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