Defining reliable demographic models is essential to understand the threats of ongoing environmental change. Yet, in the most remote and threatened areas, models are often based on the survey of a single population, assuming stationarity and independence in population responses. This is the case for the Emperor penguin Aptenodytes forsteri, a flagship Antarctic species that may be at high risk continent-wide before 2100. Here, using genome-wide data from the whole Antarctic continent, we reveal that this top-predator is organized as one single global population with a shared demography since the late Quaternary. We refute the view of the local population as a relevant demographic unit, and highlight that (i) robust extinction risk estimations are only possible by including dispersal rates and (ii) colony-scaled population size is rather indicative of local stochastic events, whereas the species' response to global environmental change is likely to follow a shared evolutionary trajectory.