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Are ecological communities symmetric? Frequency dependence and the statistical mechanics of relative species abundance.
Hubbell, Stephen1, Banavar, Jaynath2, Maritan, Amos3, 1 University of Georgia, Athens, Georgia2 Pennsylvania State University, University Park, Pennsylvania3 International School for Advanced Studies (S.I.S.S.A.), Trieste, Italy
ABSTRACT- A simple generalization of Hubbell's stochastic neutral theory of relative species abundance (RSA) leads to an analytical solution for the distribution of RSA that incorporates symmetric density- and frequency-dependence (rare species advantage). The predicted RSA distribution is a modified Fisher's logseries with an interior mode and a shape controlled by the functional relationship between species abundance and the ratio of the birth rate to the death rate (b/d). The ratio b/d > 1 for species with abundances below a value near the modal abundance, and b/d 1 for species with abundances above the mode. Our combined theory shows that two independent symmetric mechanisms, frequency dependence and dispersal limitation, are both sufficient to explain the skewed RSA distributions observed in large samples from natural ecological communities. Excellent fits of the theory to data on RSA are obtained. We also demonstrate a remarkable mathematical concilience with physics in that these distributions are closely related to classic problems in statistical mechanics, including the Boltzman, Fermi-Dirac, and Bose-Einstein equations. In ecology, our combined results provide a very promising theoretical foundation for reconciling the niche assembly and dispersal assembly perspectives.
Key words: relative species abundance, frequency dependence