• climate change;
  • competition;
  • geographic range shift;
  • lattice map model;
  • local adaptation;
  • species interactions

Local adaptation and species interactions have been shown to affect geographic ranges; therefore, we need models of climate impact that include both factors. To identify possible dynamics of species when including these factors, we ran simulations of two competing species using an individual-based, coupled map–lattice model using a linear climatic gradient that varies across latitude and is warmed over time. Reproductive success is governed by an individual's adaptation to local climate as well as its location relative to global constraints. In exploratory experiments varying the strength of adaptation and competition, competition reduces genetic diversity and slows range change, although the two species can coexist in the absence of climate change and shift in the absence of competitors. We also found that one species can drive the other to extinction, sometimes long after climate change ends. Weak selection on local adaptation and poor dispersal ability also caused surfing of cooler-adapted phenotypes from the expanding margin backwards, causing loss of warmer-adapted phenotypes. Finally, geographic ranges can become disjointed, losing centrally-adapted genotypes. These initial results suggest that the interplay between local adaptation and interspecific competition can significantly influence species’ responses to climate change, in a way that demands future research.