Ecological Fold Bifurcation — Regime Shifts

Fold bifurcations (saddle-node) create catastrophic regime shifts with hysteresis in ecosystems. Scheffer's shallow lake model has two alternative stable states: clear water with macrophytes vs. turbid water dominated by phytoplankton. The vegetation state V follows dV/dt = rV(1 − V/K) − harvV/(h + V) · T − P·V, where P is nutrient loading and T is turbidity. Hysteresis means the threshold to switch from clear→turbid differs from turbid→clear — recovery requires reducing nutrients far below the collapse point. Early warning signals (rising variance, slower return after perturbations) appear near the tipping point. The bifurcation diagram shows stable (solid) and unstable (dashed) equilibria as functions of P.