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Shannon's entropy is a popular alpha diversity metric because it estimates both richness and evenness in a single equation. However, since its value is dependent on both those parameters, there is theoretically an infinite number of richness/evenness value combinations translating into the same index score. By decoupling both components measured by Shannon's entropy, two communities having identical indices can be differentiated by mapping richness and evenness coordinates on a scatter plot. In such graphs, confidence ellipses would allow testing significant differences between groups of samples. Multivariate statistical tests such as permutational multivariate analysis of variance (PERMANOVA) can be performed on distance matrices calculated from richness and evenness coordinates and detect statistically significant differences that would have remained unforeseen otherwise. Therefore, plotting richness and evenness on two-dimensional (2D) graphs gives a more thorough understanding of how alpha diversity differs between groups of samples.

Evenness-Richness Scatter Plots: a Visual and Insightful Representation of Shannon Entropy Measurements for Ecological Community Analysis