Indices used to quantify the diversity of simulated bacterial communities and their associated community profilesa

Richness (S) S
Shannon index (H′) $$mathtex$$\(H{^\prime}\ {=}\ {{\sum}_{i\ {=}\ 1}^{S}}\ p_{i}\ \mathrm{ln}(p_{i})\)$$mathtex$$
Shannon effective no. of species (eH) $$mathtex$$\(e^{H{^\prime}}\ {=}\ \mathrm{exp}(H{^\prime})\)$$mathtex$$
Simpson index (1/D) $$mathtex$$\(1/D\ {=}\ 1/\ {{\sum}_{i\ {=}\ 1}^{S}}\ p_{i}^{2}\)$$mathtex$$
Berger-Parker index (1/d) $$mathtex$$\(1/d\ {=}\ 1/\mathrm{max}(p_{i})\)$$mathtex$$
Shannon evenness (J′) $$mathtex$$\(J{^\prime}\ {=}\ \frac{H{^\prime}}{\mathrm{ln}(S)}\)$$mathtex$$
Simpson evenness (E1/D) $$mathtex$$\(E_{1/D}\ {=}\ \frac{1/D}{S}\)$$mathtex$$
Smith and Wilson evenness (Evar) $$mathtex$$\(E_{\mathrm{var}}\ {=}\ 1\ {-}\ \frac{2}{{\pi}}\ \mathrm{arctan}\ \left\{\ {{\sum}_{i\ {=}\ 1}^{S}}\left(\mathrm{ln}(p_{i})\ {-}\ {{\sum}_{j\ {=}\ 1}^{S}}\ \mathrm{ln}(p_{j})/S\right)^{2}\left/S\right\}\right.\)$$mathtex$$
  • a S is the number of species in the community or the number of biomarkers present; pi is the relative abundance of species or biomarker i. For further information, see Jost (21), Magurran (29), and Smith and Wilson (37).