In predator–prey systems, especially in confined areas, the predator tends to capture all the prey and then starve, so the systems “crash.” But over large areas it is conceivable that a predator can completely wipe out its prey in one area and not go extinct, because it can simply move to another area where the prey still exist. Prey can then repopulate the area from which they had been depleted.
Imagine a series of interconnected cells where, with some restrictions, predator and prey can migrate between adjacent cells. Now, even though the system may be locally unstable and crash in individual cells, the entire system across all cells could be stable and persist indefinitely.
In the 1930s the Russian ecologist Gause conducted a very famous set of early experiments on competition among protozoa, but he also studied predation of Didinium on Paramecium. The populations he set up would commonly crash and go extinct, with the Didinium eating all the Paramecia and then finding themselves without food. If he made places for the Paramecium prey to hide, however, the systems could persist for many cycles.
In the 1960s Krebs noticed that populations of fenced mice, even those with a full half-acre within the fence, would crash and disappear after grossly overgrazing their habitat. But in areas where they were allowed to disperse, the populations would persist.
Huffaker also ran extensive experiments, again in the 1960s, with mites and oranges. A single population of mites on a single orange would crash and the whole population would disappear. Using multiple oranges with limited migration paths between them, however, allowed the system to persist for many generations.
And in the 1970s Lukinbill did similar work with protozoa in aquatic tubs— larger and larger tubs holding miniature predator–prey systems. He found that the larger the tub, the longer the system persisted.
The point to remember here is that the mere presence of spatial structure, in one form or another, can allow a let predator–prey system to persist. The basic reason is simply that species can go extinct in some areas while continually recolonizing other areas, always maintaining a population that blinks in and out locally, but persists globally.