The structure of species abundance at a site may provide a better characterization of the environment than the list of named species. A diversity index is an attempt to give a 1-dimensional description of this structure. Hill (1973) has defined a family of functions of the species relative abundances, which contains the Simpson and Information diversity index and the total species count as special cases. Sample estimators of these indices will generally be biased. Alternatively the species count, standardized for differences in the sizes of the samples or collections to be compared, provides a family of diversity measures for which unbiased estimators exist. Members of both families can be graded according to their sensitivity to the commonest species in the community. Diversity measures which are based primarily on the pattern of abundance of those species with medium abundance and give undue emphasis to neither the very common or rare species are most consistent over years at the same site and give greatest discrimination between sites. Different diversity indices may give inconsistent orderings of a group of communities. A partial ordering on intrinsic diversity can be defined for which all measures give consistent results. Adopting a parametric distribution to describe the species frequencies allows efficient standardization for differences in sample size. If the log-series provides a good fit to all the communities under comparison, the ordering on intrinsic diversity is complete and given by the parameter .alpha.. Comparison is made between the species abundance distribution observed from a transect sample of forest trees when abundance is measured by the total number of individuals representing the species and by a measure of total biomass. The separation of diversity into 2 components representing species richness and evenness apparently is seldom justified on available data.