  In this paper, we investigate so-called forced wave solutions of a three
components reaction-diffusion system from population dynamics. Our system
involves three species that are respectively two competing preys and one
predator; moreover, the competition between both preys is strong, i.e. in the
absence of the predator, one prey is driven to extinction and the other
survives. Furthermore, our problem includes a spatio-temporal heterogeneity in
a moving variable that typically stands as a model for climate shift. In this
context, forced waves are special stationary solutions which are expected to
describe the large-time behavior of solutions, and in particular to provide
criteria on the climate shift speed to allow survival of either of the three
species. We will consider several types of forced waves to deal with various
situations depending on which species are indigenous and which species are
aboriginal.
