The sampled relative abundances of species of a taxonomic group, whether birds, trees, or moths, in a natural community at a particular place vary in a way that suggests a consistent underlying pattern, referred to as the species abundance distribution (SAD). Preston  conjectured that the numbers of species, plotted as a histogram of logarithmic abundance classes called octaves, seemed to fit a lognormal distribution; that is, the histograms look like normal distributions, although truncated on the left-hand, or low-species-abundance, end. Although other specific curves for the SAD have been proposed in the literature, Preston’s lognormal distribution is widely cited in textbooks and has stimulated attempts at explanation. An important aspect of Preston’s lognormal distribution is the ‘veil line’, a vertical line drawn exactly at the point of the left-hand truncation in the distribution, to the left of which would be species missing from the sample.
Dewdney rejects the lognormal conjecture. Instead, starting with the long-recognized fact that the number of species sampled from a community, when plotted as histograms against population abundance, resembles an inverted J, he presents a mathematical description of an alternative that he calls the ‘J distribution’, a hyperbolic density function truncated at both ends. When multiplied by species richness, R, it becomes the SAD of the sample.
Additional publication details
Book review: A new view on the species abundance distribution Stochastic communities: A mathematical theory of biodiversity