Fig. 4. Phase diagrams for the ecosystem's dynamics under open access and profit-maximizing harvesting for different levels of relative importance of ecosystem services, α. Dynamics are characterized by dx/dt > 0 (< 0) left (right) of the green line, and dw/dt > 0 (< 0) below (above) the red line. Blue lines indicate saddlepaths. In both diagrams, A is an unstable equilibrium. In the left diagram, relative importance of ecosystem services is low (α = 0.25) and D is an (almost) globally stable equilibrium, whereas B and C are only saddlepoint-stable. In the right diagram, relative importance of ecosystem services is high (α = 0.75) and D is only saddlepoint-stable while B and C are locally stable, the corresponding basins of attraction consisting of the areas northeast (B) and southwest (C) of the saddlepath. Parameter values for both diagrams: ρx = ρw = 0.5, κx = κw = 1, γx = γw = 0, νx = νw = 1, σ = 0.4, n = 1.


Fig. 4