Commentary: Do we have a consistent terminology for species diversity? The fallacy of true diversity.

There is no single best index that can be used to answer all questions about species diversity. Entropy-based diversity indices, including Hill's indices, cannot account for geographical and phylogenetic structure. While a single diversity index arises if we impose several constraints-most notably that gamma diversity be completely decomposed into alpha and beta diversity-there are many ecological questions regarding species diversity for which it is counterproductive, requiring decomposability. Non-decomposable components of gamma diversity may quantify important intrinsic ecological properties, such as resilience or nestedness.