**Fig. 1.** Phase diagrams in state space for the ecosystem’s natural dynamics without any harvesting (C = H = 0). Dynamics are characterized by dx/dt > 0 (< 0) below (above) the green line, and dw/dt > 0 (< 0) left (right) of the red line. Blue lines indicate saddlepaths. The upper diagram displays the case of independent species (γx = γw = 0). In the middle diagram interspecies competition is weaker than intra-species competition (γx = γw = 0.25), and in the lower diagram, interspecies competition is stronger than intra-species competition (γx = γw = 1.25). Parameter values for all diagrams: ρx = ρw = 0.5, κx = κw = 1.