Hill numbers everywhere. Does it make ecological sense?

A supposed weakness of most diversity measures is their non-linearity with respect to species addition. Even for a community where all species have equal abundance, each added species usually leads to a smaller increment in the diversity measure than the species added before it. A recent proposal to solve this problem was to transform classical diversity measures to ‘effective numbers of species’ or ‘Hill numbers.’ For any community with diversity D, the effective number of species N is the number of equally abundant species that is needed to get a diversity value equal to D. The conversion of classical diversity measures to Hill numbers makes them linear with respect to species addition such that, given two equally large and completely distinct communities, each with diversity D, if these communities are pooled, the diversity of the pooled communities is 2D. According to this proposal, Hill numbers have been widely adopted in ecological literature as the ultimate solution for diversity analysis regardless of the scientific question at hand. In contrast, we believe that assuming a non-linear response of diversity measures to species addition is more suitable for many ecological questions. Building on this idea, we have introduced a typification of diversity measures based on how quickly diversity increases as species are added.