Metapopulation Persistence, explained.
A metapopulation is a set of local populations linked by dispersal, allowing regional persistence despite local extinctions.
Why it happens
The Levins mean-field equation dp/dt = cp(1−p)−ep balances colonisation and extinction of occupied patches. Positive equilibrium occupancy is 1−e/c when c exceeds e.
A metapopulation is a set of local populations linked by dispersal, allowing regional persistence despite local extinctions.
Read the result
The curve shows mean-field occupied fraction rather than a literal integer number of patches. Compare colonisation with local extinction before reading a positive equilibrium.
A worked example
Regional persistence despite local extinction
Leave colonisation at 0.5 and local extinction at 0.2.
Advance the model and compare occupancy with the positive equilibrium of 0.6.
Raise local extinction above colonisation and observe the loss of a positive equilibrium under the same mean-field rule.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
The Levins mean-field equation dp/dt = cp(1−p)−ep balances colonisation and extinction of occupied patches. Positive equilibrium occupancy is 1−e/c when c exceeds e.
Where this idea is useful
A practical use
Ask whether protecting connectivity changes regional persistence as well as local habitat survival.
A common misconception
“Every local extinction implies the entire regional species disappears.”
Dispersal can recolonise empty patches when regional colonisation is sufficient, although finite spatial systems can have additional risks.
What this explanation leaves out
- Patches are homogeneous and occupancy is continuous. Spatial structure, finite chance, habitat quality and actual dispersal distances are omitted.
Does the model identify which real habitat corridor to protect?
No. All patches are treated equally; spatial distance, quality and actual dispersal mechanisms are absent.
What maintains recolonisation after a local population is lost?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.