  Recent studies of cluster distribution in various ecosystems revealed Pareto
statistics for the size of spatial colonies. These results were supported by
cellular automata simulations that yield robust criticality for endogenous
pattern formation based on positive feedback. We show that this self-organized
criticality is a manifestation of the law of proportionate effect, first
discovered in the context of business firm size. Mapping the stochastic model
to a Markov birth-death process, the transition rates are shown to scale
linearly with cluster size. This mapping provides a connection between patch
statistics and the dynamics of the ecosystem; the "first passage time" for
different colonies emerges as a powerful tool that discriminates between
endogenous and exogenous clustering mechanisms. Imminent catastrophic shifts
(like desertification) manifest themselves in a drastic change of the stability
properties of spatial colonies, as the chance of a cluster to disappear depends
logarithmically, rather than linearly, on its size.
