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Bioclimate envelope models (BEMs) have often been criticized as being too simplistic due to e.g. not incorporating effects of biotic interactions or evolutionary adaptation. However, BEMs are widely applied and have proven to be often useful. Here we investigate, under which conditions evolution of dispersal, local adaptation or interspecific competition may be of minor importance for forecasting future range shifts. Therefore we use individual-based simulations of metapopulations under climate change living in spatial temperature gradients. Scenarios incorporate single-species systems or systems with competing species, respectively. Dispersal rate is evolving and adaptation to local conditions may also evolve in some scenarios. Results show that in single-species scenarios excluding evolutionary adaptation, species either follow optimal habitat conditions or go extinct if habitat connectivity is too low. These simulations are in close accordance to predictions from BEMs. Including evolutionary adaptation qualitatively changes these results. In the absence of competing species the species either completely invades the world or goes extinct. With competitors, results strongly depend on habitat fragmentation. For highly connected habitats the range border may shift as predicted by BEMs, for intermediate connectivity it will lag behind, while species will go extinct if fragmentation is too high. Our results indicate that (simple) BEMs may work well if habitats are well connected and species will not encounter many difficulties in dispersing to new sites. Selection in this case may promote evolution of even higher dispersal activities. We thus show that the presence of biotic interactions may be ignored for predictions of range shifts when high dispersal can be expected.