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A model of spatial population dynamics was developed in which small and large local populations are distinguished. In the model, emigration from small populations is assumed to be inconsequential, but the dynamics of currently small populations are affected by immigration from large ones. If immigration substantially increases the likelihood that a small population will grow large, two alternative stable states are possible in the model corresponding to regional commonness and regional extinction (or regional rarity, if dispersal from s afe sites or from outside the region is allowed for). Analysis of the model showed that even a small number of large local populations may play a crucial role in the regional dynamics of some species. The process of regional extinction, when it occurs, may show as an unexpected crash in the time trajectory.
Ilkka Hanski (1985) studied this question.