Fig. 7. Phase space showing 5-yr period mean environmental benefits (Be) as a function of percent external phosphorus load reduction (LR), which is inversely related to production benefits (Bp), for two simulated gradual mussel invasions that differed in the magnitude of mussel excretory effect (final MCF = 1.25 in both cases).

Note: For both simulations, the model simulated the first 30 yrs without mussels, a gradual mussel invasion from yrs 30–40, and then constant mussel effects until yr 50. In each case, the system began at LR = 0 and management increased with time until the “no mussel” social–ecological equilibrium (labeled “O”) was nearly achieved at yr 30. Subsequent decreases in environmental quality because of gradual mussel invasions shifted the system toward new attractors (labeled “X” in bold) identical to those identified in the simulations where MEF and MCF were held constant at post-invasion values (Fig. 4). For the case where the final MEF = 2.00 and MCF = 1.25, the system did not achieve equilibrium after 50 yrs, hence the gap between the end of the red dotted line and the attractor from Fig. 4.