MacArthur-Wilson Niche Theory
Each species has a Gaussian utilization function u_i(r) centered on its optimal resource. The competition coefficient α_ij = ∫u_i u_j dr measures niche overlap.
Competitive exclusion principle (Gause 1934): two species sharing a single resource cannot stably coexist. With many resources, coexistence requires niche differentiation — niche width σ must be small enough that overlap α_ij ≪ 1.
Neutral theory (Hubbell 2001): small immigration m prevents extinction and maintains diversity even without niche differences. The Unified Neutral Theory predicts log-normal species abundance distributions.
MacArthur consumer-resource
competitive exclusion
neutral theory