Our ability to predict consequences of climate change is severely impaired by the lack of knowledge on the ability of species to adapt to changing environmental conditions. We used distribution data for 140 mammal species in Europe, together with data on climate, land cover and topography, to derive a statistical description of their realized climate niche. We then compared climate niche overlap of pairs of species, selected on the basis of phylogenetic information. In contrast to expectations, related species were not similar in their climate niche. Rather, even species pairs that had a common ancestor less than 1Ma already display very high climate niche distances. We interpret our finding as a strong interspecific competitive constraint on the realized niche, rather than a rapid evolution of the fundamental niche. If correct, our results imply a very limited usefulness of climate niche models for the prediction of future mammal distributions.