# Statistics - Shannon Wiener Diversity Index

In the literature, the terms species richness and species diversity are sometimes used interchangeably. We suggest that at the very least, authors should define what they mean by either term. Of the many species diversity indices used in the literature, the Shannon Index is perhaps most commonly used. On some occasions it is called the Shannon-Wiener Index and on other occasions it is called the Shannon-Weaver Index. We suggest an explanation for this dual use of terms and in so doing we offer a tribute to the late Claude Shannon (who passed away on 24 February 2001).

Shannon-Wiener Index is defined and given by the following function:

${ H = \sum[(p_i) \times ln(p_i)] }$

Where −

• ${p_i}$ = proportion of total sample represented by species ${i}$. Divide no. of individuals of species i by total number of samples.

• ${S}$ = number of species, = species richness

• ${H_{max} = ln(S)}$ = Maximum diversity possible

• ${E}$ = Evenness = ${\frac{H}{H_{max}}}$

### Example

Problem Statement:

The samples of 5 species are 60,10,25,1,4. Calculate the Shannon diversity index and Evenness for these sample values.

Sample Values (S) = 60,10,25,1,4 number of species (N) = 5

First, let us calculate the sum of the given values.

sum = (60+10+25+1+4) = 100

Species ${(i)}$No. in sample${p_i}$${ln(p_i)}$${p_i \times ln(p_i)}$
Big bluestem600.60-0.51-0.31
Partridge pea100.10-2.30-0.23
Sumac250.25-1.39-0.35
Sedge10.01-4.61-0.05
Lespedeza40.04-3.22-0.13
S = 5Sum = 100  Sum = -1.07

${H = 1.07 \\[7pt] H_{max} = ln(S) = ln(5) = 1.61 \\[7pt] E = \frac{1.07}{1.61} = 0.66 \\[7pt] Shannon\ diversity\ index(H) = 1.07 \\[7pt] Evenness =0.66 }$
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