Measure of diversity

Diversity Indices A diversity index measure species diversity in a given community. Based on the species richness (the number of species present) and species abundance (the number of individuals per species). There are two types of indices, information statistic indices (Shannon), and dominance indices (Simpson). Richness is a number of different species in a given community.

Shannon diversity index Shannon index is an information statistics. The assumption is that all species are presented in a sample and that they are randomly sampled. p is the proportion (n/N) n is one particular species found in a population N ln is a natural logarithm Σ is the sum s is the number of species

Simpson diversity index The Simpson index is a dominance index because it gives more weight to common or dominant species. p is the proportion (n/N) n is one particular species found in a population N ln is a natural logarithm Σ is the sum s is the number of species

Richness, Shannon and Simpson indices examples Species Operational Taxonomic Unit (OTU) n/N pi pi2 ln pi pi ln pi Alistipes onderdonkii 1200 1200/9100 0.132 0.017 -2.025 -0.267 Barnesiella intestinihominis 2100 2100/9100 0.231 0.053 -1.465 -0.338 Blautia coccoides 500 500/9100 0.055 0.003 -2.900 -0.160 Eubacterium biforme 2500 2500/9100 0.245 0.060 -1.406 -0.345 Lactobacillus johnsonii 200 200/9100 0.022 0.0004 -3.817 -0.084 Turicibacter sanguinis 1700 1700/9100 0.187 0.035 -1.677 -0.314 Salmonella Typhimurium 900 900/9100 0.099 0.010 -2.313 -0.229 Total (N) 9100 Richness (number of species [s] = 7 ; Total number of OTUs (N) = 9100 Σ is the sum of pi2 (n/N)2 = 0.179 ; Σ is the sum of pi ln pi = -1.736 Shannon index H = -(-0.267 + -0.338 + -0.084 + -0.314 + -0.229 ) = 1.736 Simpson index D = 1/(0.017 + 0.053 + 0.060 + 0.0004 + 0.035 + 0.010) = 5.59

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