Practice question

Shannon diversity declines when abundance becomes concentrated in a single species. In H′ = −Σpᵢ ln pᵢ, species with moderate and similar proportions collectively create high uncertainty about the identity of a randomly selected individual. If one species dominates, its pᵢ approaches 1 and the remaining proportions approach 0; the identity of a sampled individual becomes highly predictable, so H′ becomes small. In the limiting case of only one species, p = 1 and H′ = −1 ln 1 = 0. Equal abundance instead maximizes H′ for a given richness, with H′max = ln S. High richness also tends to increase the index by adding possible species identities, provided the added species are represented. The phrase “all species are abundant” is imprecise, but if it implies comparable abundances it would support high, not low, diversity. This example separates richness from evenness: a community can contain many species yet have a low Shannon value when almost all individuals belong to one taxon. Dominance therefore supplies the clearest condition for the lowest index.