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Many species dynamics in space
Natural ecosystems often harbor individuals of many species, spread out in space. We describe two very different dynamical behaviors ("phases") that can be found in such systems, depending on the interactions between the species. In one phase, population sizes undergone huge fluctuations, spanning many orders of magnitude, that persist indefinitely in time. In the other phase, every location in space assumes one of many stable states, where each state is characterized by the combination of species present in that location. These different states may then expand in space, resulting in a self-replication mechanism that competes over space. This leads to selection over ecosystem states, in analogy with Darwinian selection.