Metapopulation Rescue Effect — Levins Patch Model
Colonization, extinction, and the rescue effect in fragmented landscapes
The Levins metapopulation model describes a collection of habitat patches, each occupied or empty, connected by dispersal. The fraction of occupied patches p evolves as dp/dt = cp(1−p) − ep, giving equilibrium p* = 1 − e/c. The rescue effect (Brown & Kodric-Brown 1977) occurs when immigration from occupied patches reduces the local extinction probability — patches with more occupied neighbors have lower effective extinction rates. This creates positive feedback: high connectivity stabilizes the metapopulation above the extinction threshold. The simulation shows each patch as a circle; green=occupied, gray=empty. Link width shows connectivity. The rescue effect is visible when removing connectivity causes cascading extinctions even with c/e > 1.