Reproductive pair correlations and the clustering of organisms

Clustering of organisms can be a consequence of social behaviour, or of the response of individuals to chemical and physical cues(1). Environmental va riability can also cause clustering: for example, marine turbulence transpo rts plankton(2-8) and produces chlorophyll concentration patterns in the up per ocean(9-11). Even in a homogeneous environment, nonlinear interactions between species(12-14) 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, sponta neously 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 m echanism is reproductively driven-birth must always be adjacent to a living organism. This clustering can overwhelm diffusion and create non-poissonia n correlations between pairs (parent and offspring) or organisms, leading t o the emergence of patterns.