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. 2020 Sep 21;11:4743. doi: 10.1038/s41467-020-18529-y

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© The Author(s) 2020

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 1 — a The species abundance distribution (SAD) describes the fluctuations of abundance across species in a community. b The Abundance Fluctuation Distribution (AFD) describes the distribution of abundances of a species across communities. I consider cross-sectional data from 9 data sets (colored symbols, see Methods). A Gamma distribution (solid black line) closely matches the AFD, here reported for the most abundant species (see Methods). The Gamma distribution describes the AFD of both abundant and rare species (Supplementary Note 1 and Supplementary Fig. 2). c The mean and variance of the abundance distribution are not independent across species, a relationship known as Taylor’s Law. The variance is, in fact, proportional to the square of the mean (solid line), implying that the coefficient of variation of the abundance fluctuations is constant across species (Supplementary Fig. 7). Taylor’s Law (together with a Gamma AFD) implies that a single parameter per species (the average abundance) recapitulates the distribution of fluctuations. d The Mean Abundance Distribution (MAD), defined as the distribution of mean abundance (obtained by averaging over communities) across species, is Lognormally distributed (black line, Supplementary Note 7).