Two species competing for shared resources. Gause's law: coexistence requires interspecific competition to be weaker than intraspecific competition
0.80
0.70
200
180
Lotka–Volterra competition: dN₁/dt = r₁N₁(1−(N₁+α₁₂N₂)/K₁), dN₂/dt = r₂N₂(1−(N₂+α₂₁N₁)/K₂).
Stable coexistence when α₁₂ < K₁/K₂ AND α₂₁ < K₂/K₁ (isoclines cross with stable node between them).
Competitive exclusion when one species wins (α₁₂ > K₁/K₂ OR α₂₁ > K₂/K₁).
Priority effects (bistability) when BOTH α₁₂ > K₁/K₂ AND α₂₁ > K₂/K₁ — whoever is more abundant wins.