Calculation of Diversity
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 defines which kind of mean is used. q = 0 corresponds to the harmonic mean, and gives values equal to species richness because the values cancel out. q = 1 corresponds to the geometric mean and q = 2 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. If all species are equally abundant in the dataset, changing the value of q has no effect, but species diversity at any value of q equals species richness.
Negative values of q are not used, because then the effective number of species (diversity) would exceed the actual number of species (richness). As q approaches negative infinity, the generalized mean approaches the minimum value. In many real datasets, the least abundant species is represented by a single individual, and then the effective number of species would equal the number of individuals in the dataset.
The same equation can be used to calculate the diversity in relation to any classification, not only species. If the individuals are classified into genera or functional types, represents the proportional abundance of the ith genus or functional type, and qD equals genus diversity or functional type diversity, respectively.
Read more about this topic: Species Diversity
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