1. Department of Physics, 104 Davey Laboratory,
2. Center for Infectious Disease Dynamics, Department of Biology, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
3. Department of Ecology and Evolutionary Biology, The University of California, Los Angeles, California 90095, USA
4. The Smithsonian Tropical Research Institute, Unit 0948, APO AA 34002, Panama
5. Dipartimento di Fisica 'G. Galilei', Università di Padova CNISM and INFN, via Marzolo 8, 35131 Padova, Italy

Correspondence to: Jayanth R. Banavar¹Amos Maritan⁵ Correspondence and requests for materials should be addressed to J.R.B. (Email: banavar@psu.edu) or A.M. (Email: maritan@pd.infn.it).

Abstract

A formidable many-body problem in ecology is to understand the complex of factors controlling patterns of relative species abundance (RSA) in communities of interacting species. Unlike many problems in physics, the nature of the interactions in ecological communities is not completely known. Although most contemporary theories in ecology start with the basic premise that species interact, here we show that a theory in which all interspecific interactions are turned off leads to analytical results that are in agreement with RSA data from tropical forests and coral reefs. The assumption of non-interacting species leads to a sampling theory for the RSA that yields a simple approximation at large scales to the exact theory. Our results show that one can make significant theoretical progress in ecology by assuming that the effective interactions among species are weak in the stationary states in species-rich communities such as tropical forests and coral reefs.

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