An undersirable property of Hill's diversity indexN 2

Summary A desirable property of a diversity index is that it be a convex function of the proportions of different species that constitute a community.N₂, a diversity index belonging to the Hill's series of diversity indices and which is equivalent to the reciprocal of Simpson's diversity index violates this requirement when the proportion of one of the species is close to 1. Recommendations ofN₂ as the best possible index of diversity therefore need to be examined judiciously.