Many Islands

Islands are surrounded by water, and this water is typically pretty inhospitable to the animals that live on islands. It is a sort of closed system, different from mainland ecosystems where plants and animals can easily migrate. So, special theories were needed to explain the number of species living and dying on islands at any given time (sidenote: the experiments necessary to test this theory, which involved fumigating entire small islands in the Florida Keys, could probably never be conducted today).

Perhaps the most ecologically important kernel in this theory is this: The number of species on an island is determined by how distant it is from other islands/the mainland (further away = fewer species), and the rate of extinction on islands is determined by the size of an island. So, on tiny, distant islands, there are fewer species, and they can go extinct rapidly, and on larger, closer islands, more species are present (since it is easier to get there) and extinction takes more time.

This difference in extinction rate is because large islands have larger and more varied habitat types, making it less likely that any given habitat or species will be wiped out by some chance event. For example, imagine a forest fire destroys all the forest on a distant, small island, plus all the forest creatures, forever and ever (or, until some other poor species blows onto this island, which is a low-probability event). Contrast this with a forest fire on a nearby, larger, more varied island with more forest habitat. In this scenario, the animals can run screaming and smoking to the next forest patch, and keep on eating, humping, and dying while new species from nearby colonize the burned patch. Circle of life.

This theory works pretty well for islands, and so, over time, ecologists started applying it to lots of other types of systems where an "island" of one habitat is surrounded by another, different habitat. Most often, this theory is applied to landscapes that have been altered severely by humans, like a patch of uncut tropical forest surrounded by a deforested area that has been converted to agriculture. This theory has also heavily informed conservation; we must preserve larger, more interconnected "islands", to stave off extinction and loss of species, so big reserves with corridors connecting them are the best strategy.