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Concept
Species diversity
Summary
Species diversity is the number of different species that are represented in a given community (a dataset). The effective number of species refers to the number of equally abundant species needed to obtain the same mean proportional species abundance as that observed in the dataset of interest (where all species may not be equally abundant). Meanings of species diversity may include species richness, taxonomic or phylogenetic diversity, and/or species evenness. Species richness is a simple count of species. Taxonomic or phylogenetic diversity is the genetic relationship between different groups of species. Species evenness quantifies how equal the abundances of the species are.
Species diversity in a dataset can be calculated by first taking the weighted average of species proportional abundances in the dataset, and then taking the inverse of this. The equation is:
The denominator equals mean proportional species abundance in the dataset as calculated with the weighted generalized mean with exponent q - 1. In the equation, S is the total number of species (species richness) in the dataset, and the proportional abundance of the ith species is . The proportional abundances themselves are used as weights.
The equation is often written in the equivalent form:
The value of q determines which mean is used. q = 0 corresponds to the weighted harmonic mean, which is 1/S because the values cancel out, with the result that 0D is equal to the number of species or species richness, S. q = 1 is undefined, except that the limit as q approaches 1 is well defined:
which is the exponential of the Shannon entropy.
q = 2 corresponds to the arithmetic mean. As q approaches infinity, the generalized mean approaches the maximum value. In practice, q modifies species weighting, such that increasing q increases the weight given to the most abundant species, and fewer equally abundant species are hence needed to reach mean proportional abundance. Consequently, large values of q lead to smaller species diversity than small values of q for the same dataset.
Official source
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