A unified index to measure ecological diversity and species rarity

Abstract

Several indices have been created to measure diversity, and the most frequently used are the Shannon‐Wiener (H) and Simpson (D) indices along with the number of species (S) and evenness (E). Controversies about which index should be used are common in literature. However, a generalized entropy (Tsallis entropy) has the potential to solve part of these problems. Here we explore a family of diversity indices (S q ; where q is the Tsallis index) and evenness (E q ), based on Tsallis entropy that incorporates the most used indices. It approaches S when q=0, H when q→1 and gives D when q=2. In general, varying the value of the Tsallis index (q), S q varies from emphasis on species richness (q<1) to emphasis on dominance (q>1). Similarly, E q also works as a tool to investigate diversity. In particular, for a given community, its minimum value represents the maximum deviation from homogeneity (E q =1) for a particular q (herein named q*). It is remarkable that our analysis indicates that q* and its corresponding evenness, E q* , are negatively affected by S when using simulated data. They may represent an index related to species rarity. Furthermore, S q* (i.e. the value of S q for a specific q*) is positively affected by richness that is an important property of any diversity index. In general, our findings indicate that the indices H, D, S, S q* , E and E q* are only part of a whole set of possibilities. In addition, the ecological properties of E q* and S q* , proposed here for the first time, show promise in ecology.