||Decisions on biodiversity management and conservation are increasingly based on indicators. These imply, explicitly or implicitly, a number of criteria such as nativeness, rarity, endangeredness and (economic) value. We investigated to which degree such criteria matter to members of the general public and conducted a survey in eight sites across Europe (n = 2378). We explored the relationships between perceived desirability of a species' population increase and six species-related attributes, including previous population change, rarity, vulnerability, harmfulness, value, attractiveness, and nativeness. For all three species types investigated, previous population change, followed by perceived harmfulness and value, had the strongest relationship with desirability of future increase. Perceived nativeness played only a minor role in informing a species' desirability. A strong relationship between previous change and desirability of future increase could also be found in a number of additional species and six different habitat types, suggesting that previous change is a key criterion that the general public draws on to inform their attitudes towards biodiversity management. We compare the roles of such criteria for the general public to those used in the scientific and political discourse, and draw conclusions for the use of indicators in the conservation debate, arguing that biodiversity management that is strongly focused on nativeness might fall short of the interests of the citizenship, whereas other criteria, such as population trends, harmfulness and role and value of a species in the ecosystem strongly resonate with the views of the general public.