  Does a high dispersal rate provide a competitive advantage when risking
competitive exclusion? To this day, the theoretical literature cannot answer
this question in full generality. The present paper focuses on the simplest
mathematical model with two populations differing only in dispersal ability and
whose one-dimensional territories are spatially segregated. Although the motion
of the border between the two territories remains elusive in general, all cases
investigated in the literature concur: either the border does not move at all
because of some environmental heterogeneity or the fast diffuser chases the
slow diffuser. Counterintuitively, it is better to randomly explore the hostile
enemy territory, even if it means highly probable death of some individuals,
than to "stay united". This directly contradicts a celebrated result on the
intermediate competition case, emphasizing the importance of the competition
intensity. Overall, the larger picture remains unclear and the optimal strategy
regarding dispersal remains ambiguous. Several open problems worthy of a
special attention are raised.
