Levins Metapopulation: Rescue & Extinction

Patch colonization-extinction dynamics — rescue effect

Colonization rate c 0.30 Extinction rate e 0.15

Num patches n 100 Rescue strength δ 0.10

Initial fraction p₀ 0.50

Levins Model: dp/dt = cp(1−p) − ep Equilibrium: p* = 1 − e/c (if c > e)
Rescue effect: immigration reduces local extinction rate: e_eff = e − δ·p
Modified equilibrium: p* = 1 − e/(c+δ) — rescue allows persistence when e > c.