Evidence for species range shifts in response to climatic change is common in the Pleistocene and earlier fossil record. However, little work has been done to model how such shifts in species range limits would change compositions of species assemblages over different spatial scales. Here I present a simple model that explores the role of biogeography in constraining changes in the compositions of species assemblages under the null hypothesis of random range shifts. The model predicts that localities where most species are far away from the edges of their ranges (e.g., localities at the center of a biogeographic province) would show relatively stable diversity patterns even during episodes of climatic change. Only localities with many range endpoints (such as those near the edges of biogeographic provinces) would show large fluctuations in species composition (and richness) in response to changes in the ambient climatic conditions. I test the predictions of the model using (1) simulations and (2) the Pleistocene bivalve fauna of California. The simulations as well as the empirical data from the Pleistocene terraces are consistent with the model predictions. These results show that attempts to quantify temporal trends in local and regional diversity and assemblage compositions need to take biogeographic structure into account.