Many attempts to predict the biotic responses to climate change rely on the 'climate envelope' approach, in which the current distribution of a species is mapped in climate-space and then, if the position of that climate-space changes, the distribution of the species is predicted to shift accordingly. The flaw in this approach is that distributions of species also reflect the influence of interactions with other species, so predictions based on climate envelopes may be very misleading if the interactions between species are altered by climate change. An additional problem is that current distributions may be the result of sources and sinks, in which species appear to thrive in places where they really persist only because individuals disperse into them from elsewhere. Here we use microcosm experiments on simple but realistic assemblages to show how misleading the climate envelope approach can be. We show that dispersal and interactions, which are important elements of population dynamics, must be included in predictions of biotic responses to climate change.