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Theory of neutral clustering for growing populations.

The spatial distribution of most species in nature is nonuniform. We have shown recently [B. Houchmandzadeh, Phys. Rev. Lett. 101, 078103 (2008)] on an experimental ecological community of amoeba that the most basic facts of life--birth and death--are enough to cause considerable aggregation which cannot be smoothened by random movements of the organisms. This clustering, termed neutral and always present, is independent of external causes and social interaction. We develop here the theoretical groundwork of this phenomenon by explicitly computing the pair-correlation function and the variance to mean ratio of the above neutral model and its comparison to numerical simulations.