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A diversity index is a quantitative measure that reflects how many different types (such as species) there are in a dataset, and simultaneously takes into account how evenly the basic entities (such as individuals) are distributed among those types. The value of a diversity index increases both when the number of types increases and when evenness increases. For a given number of types, the value of a diversity index is maximized when all types are equally abundant. 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 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). ==True diversity== 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. When , the above equation is undefined. However, the mathematical limit as approaches 1 is well defined and the corresponding diversity is calculated with the following equation: : which is the exponential of the Shannon entropy calculated with natural logarithms (see below). The value of is often referred to as the order of the diversity. It defines the sensitivity of the diversity value to rare vs. abundant species by modifying how the weighted mean of the species proportional abundances is calculated. With some values of the parameter , the value of assumes familiar kinds of weighted mean as special cases. In particular, corresponds to the weighted harmonic mean, to the weighted geometric mean and to the weighted arithmetic mean. As approaches infinity, the weighted generalized mean with exponent approaches the maximum value, which is the proportional abundance of the most abundant species in the dataset. Generally, increasing the value of increases the effective weight given to the most abundant species. This leads to obtaining a larger value and a smaller true diversity () value with increasing . When , the weighted geometric mean of the values is used, and each species is exactly weighted by its proportional abundance (in the weighted geometric mean, the weights are the exponents). When , the weight given to abundant species is exaggerated, and when , the weight given to rare species is. At , the species weights exactly cancel out the species proportional abundances, such that the weighted mean of the values equals even when all species are not equally abundant. At , the effective number of species, , hence equals the actual number of species . In the context of diversity, is generally limited to non-negative values. This is because negative values of would give rare species so much more weight than abundant ones that would exceed .〔〔 The general equation of diversity is often written in the form〔〔 : and the term inside the parentheses is called the basic sum. Some popular diversity indices correspond to the basic sum as calculated with different values of .〔 ==Richness== (詳細はウィキペディア（Wikipedia）』 ■ウィキペディアで「diversity index」の詳細全文を読む スポンサード リンク
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