A general sampling formula for community structure data

1. The development of neutral community theory has shown that the assumption of species neutrality, although implausible on the level of individual species, can lead to reasonable predictions on the community level. While Hubbell's neutral model and several of its variants have been analysed in quite some detail, the comparison of theoretical predictions with empirical abundance data is often hindered by technical problems. Only for a few models the exact solution of the stationary abundance distribution is known and sufficiently simple to be applied to data. For other models, approximate solutions have been proposed, but their accuracy is questionable. 2. Here, we argue that many of these technical problems can be overcome by replacing the assumption of constant community size (the zero-sum constraint) by the assumption of independent species abundances. 3. We present a general sampling formula for community abundance data under this assumption. We show that for the few models for which an exact solution with zero-sum constraint is known, our independent species approach leads to very similar parameter estimates as the zero-sum models, for six frequently studied tropical forest community samples. 4. We show that our general sampling formula can be easily confronted to a much wider range of datasets (very large datasets, relative abundance data, presence-absence data, and sets of multiple samples) for a large class of models, including non-neutral ones. We provide an R package, called SADISA (Species Abundance Distributions under the Independent Species Assumption), to facilitate the use of the sampling formula.