Reproductive pair correlations and the clustering of organisms

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Abstract
Clustering of organisms can be a consequence of social behaviour, or of the response of individuals to chemical and physical cues1. Environmental variability can also cause clustering: for example, marine turbulence transports plankton2,3,4,5,6,7,8 and produces chlorophyll concentration patterns in the upper ocean9,10,11. Even in a homogeneous environment, nonlinear interactions between species12,13,14 can result in spontaneous pattern formation. Here we show that a population of independent, random-walking organisms (‘brownian bugs’), reproducing by binary division and dying at constant rates, spontaneously aggregates. Using an individual-based model, we show that clusters form out of spatially homogeneous initial conditions without environmental variability, predator–prey interactions, kinesis or taxis. The clustering mechanism is reproductively driven—birth must always be adjacent to a living organism. This clustering can overwhelm diffusion and create non-poissonian correlations between pairs (parent and offspring) or organisms, leading to the emergence of patterns.

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