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Recent studies of cluster distribution in various ecosystems revealed Paretostatistics for the size of spatial colonies. These results were supported bycellular automata simulations that yield robust criticality for endogenouspattern formation based on positive feedback. We show that this self-organizedcriticality is a manifestation of the law of proportionate effect, firstdiscovered in the context of business firm size. Mapping the stochastic modelto a Markov birth-death process, the transition rates are shown to scalelinearly with cluster size. This mapping provides a connection between patchstatistics and the dynamics of the ecosystem; the "first passage time" fordifferent colonies emerges as a powerful tool that discriminates betweenendogenous and exogenous clustering mechanisms. Imminent catastrophic shifts(like desertification) manifest themselves in a drastic change of the stabilityproperties of spatial colonies, as the chance of a cluster to disappear dependslogarithmically, rather than linearly, on its size.

From companies to colonies: The origin of Pareto-like distributions in ecosystems