Ecological Succession — Patch Occupancy

Tilman competition-colonization tradeoff: coexistence via successional niches

Species Parameters

p₁ (pioneer)
p₂ (mid)
p₃ (climax)
Empty
Patch occupancy model (Tilman 1994):

dp₁/dt = c₁p₁(1−p₁) − e₁p₁
dp₂/dt = c₂p₂(1−p₁−p₂) − e₂p₂ − c₁p₁p₂
dp₃/dt = c₃p₃(1−p₁−p₂−p₃) − e₃p₃ − (c₁p₁+c₂p₂)p₃

Coexistence: Species 1 (pioneer) colonizes fastest but suffers higher extinction. Species 3 (climax) colonizes slowly but persists — survives on patches not yet invaded.
Species 1 (pioneer)
Species 2 (mid-successional)
Species 3 (climax)
Empty patch