262    ◾    Bioinformatics

7.2.5.1  Alpha Diversity Indices

7.2.5.1.1  Shannon’s Diversity Index

The Shannon’s Index also called Shannon–Wiener Index is the most commonly used mea-

sure for alpha diversity of an individual sample. It is defined as:

H

p

p

i

S

i

i

∑

( )

=

×

=

ln

1

(7.11)

where pi is the probability of finding species/taxon i in the sample and S is the number of

taxa in the sample or richness.

The values of Shannon diversity usually fall between 1.5 and 3.5. The higher the value

of H, the higher the diversity of taxa in a sample. The lower the value of H, the lower the

diversity. A sample with a single taxon will have H = 0 (not diverse sample).

7.2.5.1.2  Pielou’s Evenness

The evenness of taxa in a sample refers to how similar the abundances of the different taxa

in the sample are and it is obtained by dividing Shannon–Wiener Index by the natural

logarithm of the number of unique taxa in the sample as follows:

H

S( )

=

Evenness

ln

(7.12)

The evenness value ranges from 0 to 1, where 1 indicates complete evenness or the taxo-

nomic groups in the sample have similar abundances.

7.2.5.1.3  Faith’s Phylogenetic Diversity Index

Faith’s phylogenetic diversity (PD) index is a qualitative measure of community richness.

It is based on phylogeny and is defined as the phylogenetic diversity of a set of sequences

being equal to the sum of the lengths of all the branches on the tree. A higher PD indicates

more richness or diversity in the sample.

7.2.5.2  Beta Diversity

Beta diversity quantifies the difference among biological communities in different samples.

It is defined as the ratio between regional (gamma) and local (alpha) diversities. Most of the

beta diversity metrics are based on dissimilarity measures such as Jaccard distance, Bray–

Curtis distance, and weighted and unweighted UniFrac distance. Let a be the number of

species/taxa found in both samples, b is the number of species/taxa in the first sample but

not in the second sample, and c is the number of species/taxa in the second sample but not

in the first sample. The beta diversity metrics are computed as follows.

7.2.5.2.1  Jaccard Diversity Distance

b

c

a b

c

β

=

+

+ +



^



^×100

jac

(7.13)