The goal of this US-Hungarian collaborative work is to evaluate the importance of environmental constraints to the structure of arid and semiarid grasslands. For analyzing biodiversity, we use techniques based upon information statistics developed by Hungarian ecologists, while simulation models developed by U.S. ecologists are used to evaluate short- and long-term responses of vegetation to current and expected climatic conditions. Changes of diversity and spatial patterns of vegetation were studied along aridity gradients in both countries across a range of scales from 0.05m to 50m. In both cases, the diversity of species combinations and the strength of spatial associations decreased and the characteristic scale of maximum diversity of species combinations increased with increasing aridity. The spatial variation of estimated characteristics was higher at the arid end of the gradients.