1. Measure of diversity

2. 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.

3. 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

4. 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

5. 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 = ; Σ is the sum of pi ln pi =
Shannon index H = -( ) = 1.736
Simpson index D = 1/( ) = 5.59

6. STRUCTURE