Metapopulation

A metapopulation consists of a group of spatially separated populations of the same species which interact at some level. The term metapopulation was coined by Richard Levins in 1969 to describe a model of population dynamics of insect pests in agricultural fields, but the idea has been most broadly applied to species in naturally or artificially fragmented habitats.

A metapopulation is generally considered to consist to several distinct populations together with areas of suitable habitat which are currently unoccupied. Each population cycles in relative independence of the other populations and eventually goes extinct as a consequence of demographic stochasticity (fluctuations in population size due to random demographic events); the smaller the population, the more prone it is to extinction.

Although individual populations have finite life-spans, the population as a whole is often stable because immigrants from one population (which may, for example, be experiencing a population boom) are likely to re-colonize habitat which has been left open by the extinction of another population. They may also immigrate into another small population and so rescue it from extinction (called the rescue effect).

The development of metapopulation theory, in conjunction with the development of source-sink dynamics emphasis the importance of connectivity between seemingly isolated populations. Although no one population may be able to guarantee the long-term survival of a given species, the combined effect of many populations may be able to do this.

The most important contributer to metapopulation theory is the Finnish biologist Ilkka Hanski of the University of Helsinki.

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 step, each occupied patch can become unoccupied with an extinction probability e. Additionally, 1-N of the patches are unoccupied. Each of these may become populated by colonization. Let c be a constant rate of propagule generation for each of the N occupied patches. This give a probability of cN for each unoccupied patch to be colonized. So for each time step, the change in the proportion of occupied patches, dN, is

dN = (1 - N)cN - eN.

This takes on a sigmoid shape similar to the logistic model. The equilibrium value of N can be calculated by setting dN to be equal to zero. Solving for N gives either N = 0 or

N = 1 - e / c

This result, that N is always less than one, implies that some fraction of a species habitat will always be unoccupied.

See also

• Landscape ecology
• Conservation biology

References

• Levins, R. (1969) "Some demographic and genetic consequences of environmental heterogeneity for biological control." Bulletin of the Entomology Society of America, 71, 237-240
• Hanski, I. Metapopulation Ecology Oxford University Press. 1999. ISBN 0198540655