Clustering in neutral ecology

The “neutral ecology” model assumes that all organisms in the same trophic level have the same death, duplication, migration and mutation rates and are subjected to a zero sum rule. We show by exact analytical methods that under the assumption of this model, organisms tend to aggregate and form clusters. At dimensions less than or equal to 2, cluster size grows in average and one specie will dominate the whole ecosystem if enough time is allocated. At dimension $d=3\mathrm{}$ (or higher), an equilibrium is reached and cluster sizes are distributed as a power law.