Species abundance distributions, meaning counts of individuals apportioned among species, are fundamental patterns in ecology. Numerous distribution models have been proposed, and most suffer from poor fit to data, complex formulation, excessive parameterisation, or unrealistic modelling of processes. I discuss three that meet all the basic criteria, are easily distinguished, and stem from simple and distinct population dynamics. The log series can be produced by assuming taxonomically and temporally fixed turnover rates. A model derived from scaled odds ratios assumes highly variable dynamics, and one derived from exponential variates assumes taxonomically variable but temporally fixed rates. Mathematical derivations are elementary. Maximum likelihood fits to published empirical data suggest that the two new distributions are more common in nature. Saturated models are rarely better. Ecological communities may be assembled by processes that are easily discerned, instead of being as mysterious as many have thought.

The gzipped Ecological Register data file (Ecological_Register_data.txt.gz) is a full set of published species inventories of trees and terrestrial animals downloaded from the Ecological Register website on 23 October 2022. The additional files include metadata pertaining to the references used to document the inventories (Ecological_Register_references.txt.gz) and to the species inventories themselves (Ecological_Register_samples.txt.gz) .The gzipped and tarred richness R library (richness.tar.gz) was used to prepare the data and analyses in the associated paper. The blank cells in the files represent cases where no data were entered into the relevant fields, and will be interpreted as NAs when uploaded by an R script. There are no hidden values.

The R programming environment is required to open the richness library and the scripts.