Individual-based models are increasingly used by marine ecologists to predict species responses to environmental change on a mechanistic basis. Dynamic Energy Budget (DEB) models allow the simulation of physiological processes (maintenance, growth, reproduction) in response to variability in environmental drivers. High levels of computational capacity and remote-sensing technologies provide an opportunity to apply existing DEB models across global spatial scales. To do so, however, we must first test the assumption of stationarity, i.e., that parameter values estimated for populations in one location/time are valid for populations elsewhere. Using a validated DEB model parameterized for the cosmopolitan intertidal mussel Mytilus galloprovincialis, we ran growth simulations for native, Mediterranean Sea, populations and non-native, South African populations. The model performed well for native populations, but overestimated growth for non-native ones. Overestimations suggest that: (1) unaccounted variables may keep the physiological performance of non-native M. galloprovincialis in check, and/or (2) phenotypic plasticity or local adaptation could modulate responses under different environmental conditions. The study shows that stationary mechanistic models that aim to describe dynamics in complex physiological processes should be treated carefully when implemented across large spatial scales. Instead, we suggest placing the necessary effort into identifying the nuances that result in non-stationarity and explicitly accounting for them in geographic-scale mechanistic models.