Estimating and comparing biodiversity with a single universal metric

The development of a unique index to represent the real diversity of a community is still a challenge. The difficulties to find a single, reliable, diversity metric is mostly due to the fact that the indices allowing an estimation of the number of species actually present in a sample do not provide information on how species abundances are distributed within a community. Although some diversity measures attempted to weigh richness in relation to the total abundance, the homogeneity (evenness) of individuals within species is not integrated into them. The most common diversity indices have been "summarized" by Hill in 1973 in a single equation and, subsequently, different indicators have been proposed to estimate the "absolute" and the “effective” number of species present in a study area in an attempt to find a unified treatment of all standard diversity indices and to compare the true diversity among community. However, the choice of one of the effective number of species indices depends on what aspects of diversity of the study sites the research aims to investigate and could bias the study and mislead the interpretation of the comparative results. Moreover, effective Hill numbers account for only the observed, and not the expected (i.e. the absolute) diversity of the studied community. To compare and interpret the effective number of species with one single metric and analyze the diversity data with techniques that do not depend on a traditional non-parametric index, we developed an absolute measure of diversity based on the effective number of species and derived from the Hill numbers of order 0, 1, and 2. We tested the new index against previously-proposed absolute diversity estimators and the first three Hill numbers taken alone. We simulated the new index's behavior with different gradients of richness, abundance and evenness and we, finally, empirically tested it on tree communities of three biomes (boreal, temperate and tropical forests) of the United States and on a coral reef community of Cuba. This new index proved to be the first reliable and comparable measure, which combines both the absolute richness and the evenness of a community related to the most used traditional indices in a unique, simple and comprehensive numerical value that would represent the absolute effective diversity (AED) of any biological community.