Aim: Linking local population dynamics and species distributions is crucial to predicting the impacts of climate change. Although many studies focus on the mean fitness of populations, theory shows that species distributions can be shaped by demographic stochasticity or population resilience. Here, we examine how mean fitness (measured by invasion rate), demographic stochasticity and resilience (measured by the ability to recover from disturbance) constrain populations at the edges compared with the climatic centre. Location: Europe: Spain, France, Germany, Finland and Sweden. Period: Forest inventory data used for fitting the models cover the period from 1985 to 2013. Major taxa: Dominant European tree species; angiosperms and gymnosperms. Methods: We developed dynamic population models covering the entire life cycle of 25 European tree species with climatically dependent recruitment models fitted to forest inventory data. We then ran simulations using integral projection and individual-based models to test how invasion rates, risk of stochastic extinction and ability to recover from stochastic disturbances differ between the centre and edges of the climatic niches of species. Results: Results varied among species, but in general, demographic constraints were stronger at warm edges and for species in harsher climates. Conversely, recovery was more limiting at cold edges. In addition, we found that for several species, constraints at the edges were attributable to demographic stochasticity and capacity for recovery rather than mean fitness. Main conclusions: Our results highlight that mean fitness is not the only mechanism at play at the edges; demographic stochasticity and population capacity to recover also matter for European tree species. To understand how climate change will drive species range shifts, future studies will need to analyse the interplay between population mean growth rate and stochastic demographic processes in addition to disturbances.