  This paper investigates the large time behaviour of a three species
reaction-diffusion system, modelling the spatial invasion of two predators
feeding on a single prey species. In addition to the competition for food, the
two predators exhibit competitive interactions and under some parameter
conditions ($\mu>0$), they can also be considered as two mutants. When
mutations occur in the predator populations, the spatial spread of invasion
takes place at a definite speed, identical for both mutants. When the two
predators are not coupled through mutation, the spreading behaviour exhibits a
more complex propagating pattern, including multiple layers with different
speeds. In addition, some parameter conditions reveal situations where a
nonlocal pulling phenomenon occurs and in particular where the spreading speed
is not linearly determined.
