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Species richness and species abundance unevenness are two major synthetic descriptors of the internal organization within ecological communities. Yet, while the former is a simple concept in essence, the unevenness of species abundance distribution is less so, being partly linked (negatively) to species richness as a general trend while, yet, more or less deviating from this average trend according to idiosyncratic specificities of each community (a bit similar to the size among individuals of a same species, which depend on age but more or less deviates due to inter-individual differences in growth rate which singularizes each individual). I argue that for abundance unevenness it is therefore relevant to consider and quantify separately these two aspects – the overall trend on the one hand and the idiosyncratic deviation from this trend on the other hand. In particular, comparing abundance unevenness levels between communities differing in species richness requires considering separately what has to be directly assigned to the difference in species richness and what can be relevantly attributed to some genuine, idiosyncratic difference in the hierarchical structuring of abundances between the compared communities. The appropriate formalism arising from this approach is detailed for practical implementation, thereby allowing for a deeper understanding of the ins and outs of the functional organization within ecological communities.