Trophic Cascade — Keystone Species

3-level Lotka-Volterra food web: Plants → Herbivores → Predators

P: — | H: — | Pred: —

Trophic cascades: removing a keystone predator releases herbivore populations, which then overgraze and crash the plants. The 3-level Lotka-Volterra system: dP/dt = rP(1−P/K) − αPH, dH/dt = eαPH − mH − βHX, dX/dt = eβHX − dX. Yellow = predator, red = herbivore, green = plant. The phase portrait shows the attractor; removing the predator collapses the system to a new equilibrium with low plant biomass.