Ecological Neutral Theory: Hubbell Forest
Zero-sum dynamics · Immigration · Speciation · Log-series SAD
Species richness: — | Shannon H: —
Neutral Theory (Hubbell 2001): All individuals are ecologically equivalent — fitness differences are zero. Community dynamics driven purely by demographic stochasticity, immigration, and speciation.
Fundamental Biodiversity Number: θ = 2J_M·ν (metacommunity size × speciation rate). The predicted species abundance distribution (SAD) is the Ewens sampling formula:
P(n₁,...,n_S) ∝ θ^S / [θ]_J · ∏ (nᵢ-1)! / J
Log-series approximation: For small immigration m, the local SAD approaches the Fisher log-series: φ(n) = α·xⁿ/n where x = 1−m and α ≈ θ. The green histogram (SAD) should follow this.
Zero-sum: When an individual dies, exactly one replaces it — from the local community (prob 1-m) or the metacommunity (prob m). The metacommunity has log-series abundance with parameter θ.