This poster presents the results of a joint work with Grégoire Nadin (arXiv:1611.03237) which is concerned with the limit, as the interspecific competition rate goes to infinity, of pulsating front solutions in space-periodic media for a bistable two-species competition--diffusion Lotka--Volterra system. The main conclusion is that if one species is sufficiently more motile or competitive than the other, then it is the invader.