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Hub AI
Diversity index AI simulator
(@Diversity index_simulator)
Hub AI
Diversity index AI simulator
(@Diversity index_simulator)
Diversity index
A diversity index is a method of measuring how many different types (e.g. species) there are in a dataset (e.g. a community). Diversity indices are statistical representations of different aspects of biodiversity (e.g. richness, evenness, and dominance), which are useful simplifications for comparing different communities or sites.
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 organisms (e.g. 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.
Diversity indices described in this article include:
Some more sophisticated indices also account for the phylogenetic relatedness among the types. These are called phylo-divergence indices, and are not yet described in this article.
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 Mq−1 of the proportional abundances of the types in the dataset, and then taking the reciprocal of this. The equation is:
![{\displaystyle {}^{q}\!D={1 \over M_{q-1}}={1 \over {\sqrt[{q-1}]{\sum _{i=1}^{R}p_{i}p_{i}^{q-1}}}}=\left({\sum _{i=1}^{R}p_{i}^{q}}\right)^{1/(1-q)}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/daf7e22f4730ed7b47ebb145d7a495dfd5ef9177)
The denominator Mq−1 equals the average proportional abundance of the types in the dataset as calculated with the weighted generalized mean with exponent q − 1. In the equation, R is richness (the total number of types in the dataset), and the proportional abundance of the ith type is pi. The proportional abundances themselves are used as the nominal weights. The numbers are called Hill numbers of order q or effective number of species.
Diversity index
A diversity index is a method of measuring how many different types (e.g. species) there are in a dataset (e.g. a community). Diversity indices are statistical representations of different aspects of biodiversity (e.g. richness, evenness, and dominance), which are useful simplifications for comparing different communities or sites.
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 organisms (e.g. 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.
Diversity indices described in this article include:
Some more sophisticated indices also account for the phylogenetic relatedness among the types. These are called phylo-divergence indices, and are not yet described in this article.
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 Mq−1 of the proportional abundances of the types in the dataset, and then taking the reciprocal of this. The equation is:
The denominator Mq−1 equals the average proportional abundance of the types in the dataset as calculated with the weighted generalized mean with exponent q − 1. In the equation, R is richness (the total number of types in the dataset), and the proportional abundance of the ith type is pi. The proportional abundances themselves are used as the nominal weights. The numbers are called Hill numbers of order q or effective number of species.