# Shannon Diversity Index: Definition & Example

The Shannon Diversity Index (sometimes called the Shannon-Wiener Index) is a way to measure the diversity of species in a community.

Denoted as H, this index is calculated as:

H = -Σpi * ln(pi)

where:

• Σ: A Greek symbol that means “sum”
• ln: Natural log
• pi: The proportion of the entire community made up of species i

The higher the value of H, the higher the diversity of species in a particular community. The lower the value of H, the lower the diversity. A value of H = 0 indicates a community that only has one species.

The Shannon Equitability Index is a way to measure the evenness of species in a community. The term “evenness” simply refers to how similar the abundances of different species are in the community.

Denoted as EH, this index is calculated as:

EH = H / ln(S)

where:

• H: The Shannon Diversity Index
• S: The total number of unique species

This value ranges from 0 to 1 where 1 indicates complete evenness.

The following step-by-step example shows how to calculate the Shannon Diversity Index and the Shannon Equitability Index for a given community.

### Step 1: Collect the Data

Suppose a biologist wants to measure the diversity of species in a local forest. She collects the following data: ### Step 2: Calculate the Proportions

Next, the biologist can calculate the proportion of the community made up of each species.

For example, there are a total of 105 individuals and 40 are classified as species A. Thus, species A makes up 40 /105 =  0.38 of the total community.

She can perform a similar calculation for each species: ### Step 3: Calculate the Natural Log of the Proportions

Next, she can calculate the natural log of each proportion: ### Step 4: Multiply the Proportions by the Natural Log of the Proportions

Next, she can multiply the proportions by the natural log of the proportions: ### Step 5: Calculate the Shannon Diversity Index

Lastly, she can use the following formula to calculate the Shannon Diversity Index:

H = -Σpi * ln(pi)

For this example, she can take the sum of the last column and multiply by negative one: The Shannon Diversity Index for this community is 1.49.

She can also use the following formula to calculate the Shannon Equitability Index:

EH = H / ln(S)

For this example, there are S = 5 total species, so see can calculate this index to be:

EH = 1.49 / ln(5) = 0.92.