A diversity index is a quantitative measure that reflects how many different types (such as species) there are in a dataset (a community), and that can simultaneously take into account the phylogenetic relations among the individuals distributed among those types, such as richness, divergence or evenness. These indices are statistical representations of biodiversity in different aspects (richness, evenness, and dominance). Effective number of species or Hill numbers When diversity indices are used in ecology, the types of interest are usually species, but they can also be other categories, such as genera, families, functional types, or haplotypes. The entities of interest are usually individual plants or animals, and the measure of abundance can be, for example, number of individuals, biomass or coverage. In demography, the entities of interest can be people, and the types of interest various demographic groups. In information science, the entities can be characters and the types of the different letters of the alphabet. The most commonly used diversity indices are simple transformations of the effective number of types (also known as 'true diversity'), but each diversity index can also be interpreted in its own right as a measure corresponding to some real phenomenon (but a different one for each diversity index). Many indices only account for categorical diversity between subjects or entities. Such indices, however do not account for the total variation (diversity) that can be held between subjects or entities which occurs only when both categorical and qualitative diversity are calculated. True diversity, or the effective number of types, refers to the number of equally abundant types needed for the average proportional abundance of the types to equal that observed in the dataset of interest (where all types may not be equally abundant). The true diversity in a dataset is calculated by first taking the weighted generalized mean of the proportional abundances of the types in the dataset, and then taking the reciprocal of this. The equation is: The denominator equals the average proportional abundance of the types in the dataset as calculated with the weighted generalized mean with exponent . In the equation, is richness (the total number of types in the dataset), and the proportional abundance of the th type is . The proportional abundances themselves are used as the nominal weights. The numbers are called Hill numbers of order q or effective number of species. When , the above equation is undefined. However,