From a participatory governance perspective, managing changes in ecosystems requires involvement of stakeholders. However, when the impacts of such changes are unclear or unknown, problem perceptions are latent and stakeholders cannot be identified. To elicit perceptions of an ecosystem change despite unknown impacts, we employed Q methodology regarding landscape values. From these perceptions we derived stakeholder stances on the ecosystem change constituted by the invasive alien plant Coralita (Antigonon leptopus) on the Caribbean Netherlands islands of St. Eustatius and Saba. Ecologists view Coralita as a clear threat, but the exact impacts of the plant are unknown and therefore locals do not have manifest problem perceptions. Nevertheless, we derived three perspectives on the value of nature per island, which in turn yielded insights into stakeholders’ views on Coralita management. Our approach can be applied for other management questions regarding changes in ecosystems when the impacts on humans are unclear and hence problem perceptions latent.