Prey (Rabbits)
500
Predators (Foxes)
50
When more food causes extinction
In 1971, ecologist Michael Rosenzweig discovered something deeply counterintuitive: adding more food to an ecosystem can destabilize it and cause extinctions.
This defies common sense. Shouldn't more food mean more prey, which means more predators, leading to a larger but stable ecosystem? Instead, the mathematics shows that enrichment beyond a critical threshold causes the system to oscillate wildly—and potentially collapse.
Stable equilibrium. Populations find a balance and stay there.
Hopf bifurcation! Stable cycles emerge—boom and bust.
Oscillations become extreme. Predator extinction likely.
1. More food → More prey: The prey population grows larger.
2. More prey → More predators: Predators thrive and reproduce rapidly.
3. Too many predators → Prey crash: Predators eat prey faster than they reproduce.
4. Prey crash → Predator crash: With no food, predators starve.
5. Extreme cycles: These boom-bust cycles grow more violent with more enrichment.
The key insight comes from the Lotka-Volterra equations with a type II functional response (predators get "full" and can't eat faster). At low carrying capacity, the system finds equilibrium. But beyond a critical K value, a Hopf bifurcation occurs—the equilibrium becomes unstable and limit cycles emerge.
The paradox has been confirmed in laboratory experiments, particularly with microorganisms and small invertebrates. In the field, it's harder to observe directly because natural ecosystems have evolved stabilizing mechanisms:
These mechanisms explain why ecosystems don't constantly collapse—evolution has built in stabilizers. But when humans artificially enrich systems (fertilizer runoff, for example), these safeguards can be overwhelmed.