The wealth of species: ecological communities, complex systems and the legacy of Frank Preston

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Abstract
General statistical patterns in community ecology have attracted considerable recent debate. Difficulties in discriminating among mathematical models and the ecological mechanisms underlying them are likely related to a phenomenon first described by Frank Preston. He noted that the frequency distribution of abundances among species was uncannily similar to the Boltzmann distribution of kinetic energies among gas molecules and the Pareto distribution of incomes among wage earners. We provide additional examples to show that four different 'distributions of wealth' (species abundance distributions, species-area and species-time relations, and distance decay of compositional similarity) are not unique to ecology, but have analogues in other physical, geological, economic and cultural systems. Because these appear to be general statistical patterns characteristic of many complex dynamical systems they are likely not generated by uniquely ecological mechanistic processes.