The effects of climate change on biodiversity should depend in part on climate displacement rate (climate-change velocity) and its interaction with species’ capacity to migrate. We estimated Late Quaternary glacial-interglacial climate-change velocity by integrating macroclimatic shifts since the Last Glacial Maximum with topoclimatic gradients. Globally, areas with high velocities were associated with marked absences of small-ranged amphibians, mammals and birds. The association between endemism and velocity was weakest in the highly vagile birds and strongest...