Fig. 1 in Unveiling global species abundance distributions

Fig. 1 | Conceptual scheme illustrating the Poisson sampling of a community with species abundances described by a gamma or a log-normal distribution. Two types of gSAD—gamma (left) and log-normal distribution (right) are shown at the top.Each distribution represents the probability f of a species having a given abundance λ, with the gamma distribution having parameters k (shape) and θ (scale) and the log-normal distribution having parameters μ (mean) and σ (standard deviation), and Γ() representing the gamma function.In the middle, sampling of the gSAD with the probability of each species having a given number of individuals sampled described by a Poisson distribution is illustrated. The mean abundance of each species sampled is randomly taken from the SAD.We exemplify two samples of different sizes, where different symbols denote individuals of different species. The bottom graphs show that: if the global abundances have a log-normal distribution, the mixture distribution of abundances in the sample is a Poisson log-normal; if the global abundances follow a gamma distribution the resulting mixture distribution is a negative binomial but in the limit k→0, we obtain the Fisher log-series.Published as part of Callaghan, Corey T., Borda-de-Água, Luís, van Klink, Roel, Rozzi, Roberto & Pereira, Henrique M., 2023, Unveiling global species abundance distributions, pp. 1-13 in Nature Ecology & Evolution CLXVI (CLXVI) on page 3, DOI: 10.1038/s41559-023-02173-y, http://zenodo.org/record/831979