Metapopulation - The Levins Model

The Levins Model

Levins' original model applied to a metapopulation distributed over many patches of suitable habitat with significantly less interaction between patches than within a patch. Population dynamics within a patch were simplified to the point where only presence and absence were considered. Each patch in his model is either populated or not.

Let N be the fraction of patches occupied at a given time. During a time dt, each occupied patch can become unoccupied with an extinction probability edt. Additionally, 1 − N of the patches are unoccupied. Assuming a constant rate c of propagule generation from each of the N occupied patches, during a time dt, each unoccupied patch can become occupied with a colonization probability cNdt . Accordingly, the time rate of change of occupied patches, dN/dt, is

This equation is mathematically equivalent to the logistic model, with a carrying capacity K given by

and growth rate r

At equilibrium, therefore, some fraction of the species's habitat will always be unoccupied.