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.

Read more about this topic:  Metapopulation

Famous quotes containing the word model:

    I had a wonderful job. I worked for a big model agency in Manhattan.... When I got on the subway to go to work, it was like traveling into another world. Oh, the shops were beautiful, we had Bergdorf’s, Bendel’s, Bonwit’s, DePinna. The women wore hats and gloves. Another world. At home, it was cooking, cleaning, taking care of the kids, going to PTA, Girl Scouts. But when I got into the office, everything was different, I was different.
    Estelle Shuster (b. c. 1923)