Calculating Gamma Diversity
Suppose species diversity is equated with the effective number of species in a dataset. Then gamma diversity can be calculated by first taking the weighted mean of species proportional abundances in the dataset, and then taking the inverse of this mean. 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 .
Large values of q lead to smaller gamma diversity than small values of q, because increasing q increases the weight given to those species with the highest proportional abundance, and fewer equally-abundant species are hence needed to obtain this proportional abundance.
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