We study a reaction diffusion system that models the dynamics of two species that display
inter-species competition and intra-species cooperation. We find that there are between
three and six different equilibrium states and a variety of possible travelling wave
solutions that can connect them. After examining the travelling waves that are generated
in three different ecologically-relevant initial value problems, we construct asymptotic
solutions in the limit λ ≪ 1 (fast diffusion, slow reaction for the
second species relative to the first).