Mathematical convergences of biodiversity indices

Various indices are used in the scientific literature to describe biodiversity changes. Nevertheless, the appropriateness of an index rather than another to transcribe trends in biodiversity of plankton communities is not clearly established. So, starting from the definitions of the diversity indices of Simpson, Gleason-Margalef, Menhinick, Brillouin, Shannon, Patten, Pielou and Hurlbert, the aim of this work is to state, under the assumption that the total number of individual is great, a mathematical convergence between the indices of Brillouin, Shannon, Simpson's reciprocal, Hurlbert on the one hand and between the indices of Pielou and Patten on the other hand. More particularly, it will be also established that these last two indices are complementary provided that the total number of individual is greater than the number of species. Gleason-Margalef's and Menhinick's indices will be considered as independents. Thus, such a convergence will lead to propose a classification of these indices into three great groups reducing their number from eight to four. This theoretical result will be then applied on phytoplankton and zooplankton communities of two neighbouring bays differently affected by anthropogenic inputs in NW Mediterranean Sea (Toulon area, France) throughout three consecutive annual cycles. A strong statistical correlation between the indices belonging to the same group seems to confirm the validity of our classification. (C) 2013 Elsevier Ltd. All rights reserved.