The Relation between Evenness and Diversity
AbstractContrary to common belief, decomposition of diversity into independent richness and evenness components is mathematically impossible. However, richness can be decomposed into independent diversity and evenness or inequality components. The evenness or inequality component derived in this way is connected to most of the common measures of evenness and inequality in ecology and economics. This perspective justifies the derivation of measures of relative evenness, which give the amount of evenness relative to the maximum and minimum possible for a given richness. Pielou’s  evenness measure J is shown to be such a measure.
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Jost, L. The Relation between Evenness and Diversity. Diversity 2010, 2, 207-232.
Jost L. The Relation between Evenness and Diversity. Diversity. 2010; 2(2):207-232.Chicago/Turabian Style
Jost, Lou. 2010. "The Relation between Evenness and Diversity." Diversity 2, no. 2: 207-232.