Species abundance distributions (SADs) follow one of ecologyÕs oldest and most universal laws -every community shows a hollow curve or hyperbolic shape on a histogram with many rare species and just a few common species. Here, we review theoretical, empirical and statistical developments in the study of SADs. Several key points emerge. (i) Literally dozens of models have been proposed to explain the hollow curve. Unfortunately, very few models are ever rejected, primarily because few theories make any predictions beyond the hollow-curve SAD itself. (ii) Interesting work has been performed both empirically and theoretically, which goes beyond the hollow-curve prediction to provide a rich variety of information about how SADs behave. These include the study of SADs along environmental gradients and theories that integrate SADs with other biodiversity patterns. Central to this body of work is an effort to move beyond treating the SAD in isolation and to integrate the SAD into its ecological context to enable making many predictions. (iii) Moving forward will entail understanding how sampling and scale affect SADs and developing statistical tools for describing and comparing SADs. We are optimistic that SADs can provide significant insights into basic and applied ecological science.

Analyses of statistical distributions of body mass, population density, and size and shape of geographic range offer insights into the empirical patterns and causal mechanisms that characterize the allocation of food and space among the diverse species in continental biotas. These analyses also provide evidence of the processes that couple ecological phenomena that occur on disparate spatial and temporal scales-from the activities of individual organisms within local populations to the dynamics of continent-wide speciation, colonization, and extinction events.

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We describe a general framework for testing neutral theory. We summarize similarities and differences between ten different versions of neutral theory. Two central predictions of neutral theory are that species abundance distributions will follow a zero-sum multinomial distribution and that community composition will change over space due to dispersal limitation. We review all published empirical tests of neutral theory. With the exception of one type of test, all tests fail to support neutral theory. We identify and perform several new tests. Specifically, we develop a set of best practices for testing the fit of the zero-sum multinomial (ZSM) vs. a lognormal null hypothesis and apply this to a data set, concluding that the lognormal outperforms neutral theory on robust tests. We explore whether a priori parameterization of neutral theory is possible, and we conclude that it is not. We show that non-curve-fitting predictions readily derived from neutral theory are easily falsifiable. In toto, there is a current overwhelming weight of evidence against neutral theory. We suggest some next steps for neutral theory.