Fig 4. Plot of the phase diagram of the solutions of the nonlinear model.

The stability diagram as a function of K_γ is computed using the exact solution (11) of the nonlinear dynamical system for the same 9 empirical mutualistic networks used in Fig 3. The tipping line is plotted according to the nonlinear model which predicts that the tipping point is given for $k_{\text{core}}^{\text{max}}=K_{\gamma }$. All the networks lie in the region $k_{\text{core}}^{\text{max}}>K_{\gamma }$ and thus they are stable, as they should.