As discussed in Chapter 1, conservation biologists introduced the concept of minimum viable population size (Soule 1980), although this approach has been replaced by various population-viability analyses. The MVP size was intended to estimate the minimum number of individuals necessary for a population to have a specific probability of surviving for a fixed period of time. When applied to metapopulations the analogous concept would be defined as the minimum number of local populations necessary for the long-term persistence of the metapopulation. Gurney and Nisbet (1978) and Nisbet and Gurney (1982) developed a stochastic version of the Levins model with a finite number of habitat patches and local populations. In the analysis of their results they defined long-term persistence of the metapopulation, TM, as at least 100 times the expected time of local extinction, TL.
If P is the fraction of occupied patches at equilibrium, and H is the total number of habitat patches, Gurney and Nisbet (1978) found that the product of 4H must be greater than 3:
For example, if there are 50 habitat patches, this equation says that colonization and extinction rates must be such that P > 0.42 for a metapopulation to persist more than 100 times Tl. This relationship does not take into account the size and quality of the habitat patches, but does demonstrate that long-term metapopulation persistence benefits from a large number of habitat patches.
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