Can climate change lead to gap formation?

Consider a situation where spatial heterogeneity leads to a cline, a gradual transition in dominance of two competing species. We first prove, in the context of a simplified competition–diffusion model, that there exists a stationary solution showing that the two species coexist in a transition zone. What happens then if, owing to climate change, the environmental profile moves with constant speed in space? We show here that, when the speed with which the environmental condition shifts exceeds the Fisher invasion speed of the advancing species, an expanding gap will form. We raise the question of whether such a phenomenon has been or can be observed.