The Species Abundances Distribution in a new perspective
  Studies on distribution, abundance and diversity of species revealed fascinating universalities in macroecology. Many of these patterns, like the species-area and range-abundance relationship or the year-to-year fluctuations in population sizes are expressed as power-law distributions, and indicate thus scale-invariance. The species abundance distribution (SAD) apparently shows this scale-free nature only for rare species, and its mathematical form is much debated. In the present work we propose a new mathematical expression for SAD which describes reasonable well most of the presently available large-scale experimental data and the results of the neutral models. This distribution function leads to an interesting relation between the total number of individuals, total number of species and the size of the most abundant species of the meta-community. This novel scaling relation is confirmed by computer simulations on neutral models. 
M. Ravasz, A. Balog, V. Marko and Z. Neda