MacArthur-Wilson Island Biogeography

S = cA^z (species-area law) — immigration rate λ(S), extinction rate μ(S) at equilibrium Ŝ

SAR exponent z 0.25

SAR constant c 5.0

Total species pool P 100

Immigration rate I₀ 0.20

Extinction rate E₀ 0.05

Number of islands 8

MacArthur-Wilson (1967): Equilibrium species richness Ŝ where immigration rate λ(S) equals extinction μ(S). λ(S) = I₀(P−S)/P (declines as island fills), μ(S) = E₀·S (increases with diversity). Ŝ = P·I₀/(I₀+E₀). Species-Area Law: S = cA^z, empirical z ≈ 0.2–0.35. Larger islands: lower extinction → higher Ŝ. Closer to mainland: higher immigration → higher Ŝ. SLOSS debate: one large vs several small reserves — turnover and area both matter.