Abstract
We study two competitive species living in patch environment under shifting ranges induced by climate change. We introduce the non-local dispersal strategy due to normal long-distance interaction of species and study the spatial dynamical behavior of the species responding to climate change. Some spatial spreading results are established in this paper in terms of the shifting speed of environment. Particularly, we prove that the model system admits a forced wave when the shifting speed belongs to a certain interval, which indicates that the competition exclusion takes place as the shifting ranges is beneficial to one species while is harmful to the another species. In addition, we obtain some gap formations when the shifting speed outside that interval, which suggest that both species will eventually disappear as a result of fast climate change.
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