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The Gini coefficient is defined as (Gini, 1912):
S is the number of species in the sample
xi is the abundance of the ith species ranked from least to most abundant, i = 1 to S and
m is the mean abundance of a species - the mean of the xi values.
The Gini coefficient is a measure of inequality developed by the Italian statistician Corrado Gini and published in his 1912 paper "Variabilità e mutabilità". It is usually used to measure income inequality, but can be used to measure any form of uneven distribution. The Gini coefficient is a number between 0 and 1, where 0 corresponds with perfect inequality and 1 corresponds with perfect equality (where each species has the same abundance).
If every species has the same abundance then the species rank curve would be a straight line at 45 degrees (see below); because of inequalities in abundance the actual curve lies below this line (see below). The Gini coefficient is ratio of the areas below these curves.