  We investigate the traveling wave solutions of a three-species system
involving a single predator and a pair of strong-weak competing preys. Our
results show how the predation may affect this dynamics. More precisely, we
describe several situations where the environment is initially inhabited by the
predator and by either one of the two preys. When the weak competing prey is an
aboriginal species, we show that there exist traveling waves where the strong
prey invades the environment and either replaces its weak counterpart, or more
surprisingly the three species eventually co-exist. Furthermore, depending on
the parameters, we can also construct traveling waves where the weaker prey
actually invades the environment initially inhabited by its strong competitor
and the predator. Finally, our results on the existence of traveling waves are
sharp, in the sense that we find the minimal wave speed in all those
situations.
