Four remarkable situations when distinct species concepts are applied. Each species concept groups a set of organisms, as members of a species taxon, as illustrated by a colored circle (purple for the phylogenetic species, green for the recombining or biological species, blue for the morphological species, pink for the barcode-based species). The overlap between groups is indicated by red dashes. A. In prokaryotes, the groups defined by the various species concepts are largely not nested. A unified species concept would be a poor descriptor of biodiversity: inter-approach pluralism is an issue for species definition. So is intra-approach pluralism, as indicated by smaller circles corresponding to the incongruent groups proposed by different markers, for a given species concept. B. Exploratory use of DNA barcoding to define groups of specimens belonging to a same species. On a histogram of p-distances frequencies, the identification of a barcode gap provides a threshold over which two specimens cannot belong to the same species. The monophyly of specimens falling in a same group can also be assessed. C. The ideal case: all the species concepts identify the same sets of organisms. Intra- and inter-approach pluralisms are not a problem. A unified species concept is a good descriptor of biodiversity D. Type I grey zone: the species concepts produce a series of nested groups. Ranking these groups is an issue. E. Type II grey zone: the species concepts produce partially non-nested groups. Inter- and intra-approach pluralism can be problematic. For cases D & E, pragmatic descriptors would be more accurate and informative about biodiversity than a unified species concept.