Fig. 6. Phase portraits of Eqs. (14) from Supplementary Note 1 illustrating a sudden transition are shown for six distinct values of f₁, the influx rate of iron(II).

For f₁ = 73 (a), there is a single stable equilibrium (green dot) describing a world dominated by APB. For values of f₁ = 65 (b), 62 (c), 51 (d), and 47 (e), there is a second stable equilibrium (green dot) describing the dominance of cyanobacteria, and in addition, there is an unstable equilibrium (red dot). The unstable equilibrium moves as the value of f₁ changes. For f₁ = 40 (f), the only stable equilibrium is the one where cyanobacteria dominate. Parameter values are f₂ = 10, c = 1, a = 10, b = 1, u₁ = u₂ = 1, and α₁ = α₂ = 1. The GOE is triggered by a saddle-node bifurcation and is sudden.