Niche Overlap & Competitive Exclusion

Overlap α₁₂ 0.50 Overlap α₂₁ 0.50 K₁/K₂ ratio 1.00 Niche width σ 0.18

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Lotka-Volterra: dN₁/dt = r₁N₁(1−(N₁+α₁₂N₂)/K₁), dN₂/dt = r₂N₂(1−(N₂+α₂₁N₁)/K₂). Coexistence: α₁₂α₂₁ < 1 and α₁₂ < K₁/K₂ < 1/α₂₁. Exclusion if overlap is too high. α = ∫p₁(x)p₂(x)dx (Gaussian niche overlap).