We turn now to considering the balance between colonization and extinction on the spatial scale of continents, oceanic islands, and the distances between them. In doing so, we move from a single species occupying many patches to many species in a single large patch. The influential theory for this situation is 'island biogeography theory', and Island Biogeography covers it in detail. In brief, the theory predicts that the number ofspecies on an island depends on a dynamic balance between colonization of the island by species from the mainland and extinction of species already on the island. The mainland serves as a permanent pool of a fixed number of colonist species, and the island is permanently suitable for all of them, but each species colonizes the island only when not currently present there. As a result, as the number of species occupying the island increases, the rate of colonization per unit time decreases. If all species were equal in their colonization ability, then the colonization rate would decrease linearly with the number of species on the island. Since species usually differ in colonization ability, however, as we discussed above, the poorer colonizers take longer to arrive, and the better colonizers are likely already present when they do. Thus, we expect the decrease in the colonization rate to be more gradual at higher island species richness, and the rate should be a convex decreasing function of species richness on the island. The exact value of the colonization rate function at any richness depends on the specifics of a given situation, including the identities of the species in the colonist pool and the isolation of the island from the mainland. The intersection of the colonization function with the extinction function (an increasing function of island richness (see Island Biogeography)) determines the richness at which colonization and extinction balance. This is the island's equilibrial or long-term species richness.
Empirical tests of the general theory have upheld its essential points. The classic model, however, does not detail interaction between colonizing species (such as facilitation of colonization by earlier colonists, for example (see. Succession) and also excludes any effects on species richness of evolution on either the mainland or the island. Despite these omissions, the model provides a valuable conceptual framework for understanding the role of colonization in determining diversity and community composition over large spatial scales, and also provides a starting point for understanding spatial systems other than oceanic islands. For instance, the theory can apply to habitat islands such as mountaintops or lakes, as long as a permanent 'mainland' habitat exists to provide colonists. 'Island biogeography theory', where colonization occurs between pairs of very unequal habitat patches, and metapopulation theory, where colonization takes place between many equal patches, are two special cases of colonization-extinction interactions in patchy habitats. These two classical theories are thus useful tools for understanding the dynamics of the many patchy natural systems on regional to continental spatial scales. Metacommunity theory (see Metacommunities) is a contemporary synthesis of these and other conceptual approaches to spatially structured communities.
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