A mathematical measure that combines species richness and evenness to quantify biological diversity in an ecosystem or information entropy in other systems.

Shannon Diversity Index

The Shannon Diversity Index (H'), also known as the Shannon-Wiener Index, is a fundamental metric in ecological diversity and information theory that quantifies both the variety and distribution of elements within a system.

Mathematical Foundation

The index is calculated using the formula: H' = -∑(pi * ln(pi))

Where:

H' is the diversity index
pi is the proportion of individuals belonging to species i
ln is the natural logarithm
∑ represents the sum across all species

Applications in Ecology

Primary Uses

Measuring species diversity in ecosystems
Comparing biodiversity across different habitats
Monitoring ecological changes over time
Assessing ecosystem health and stability

The index increases when both:

The number of unique species increases (species richness)
The evenness of species distribution improves (species evenness)

Information Theory Connection

Originally developed by Claude Shannon for communication theory, the index measures information entropy in various contexts:

Digital communication systems
Language patterns
Genetic sequences
Social network analysis

Advantages and Limitations

Strengths

Considers both abundance and evenness
Widely accepted in scientific literature
Allows meaningful comparisons between different ecosystems
Sensitive to rare species

Limitations

Requires accurate species identification
Cannot distinguish between different community compositions with same H' value
sampling bias can affect results
Assumes all species are equally different from each other

Related Measures

The Shannon Diversity Index is often used alongside other diversity metrics:

Applications Beyond Ecology

The versatility of the index has led to its adoption in:

Economics (market concentration)
Linguistics (language diversity)
Social sciences (cultural diversity)
genetic diversity studies

Historical Context

The index emerged from Claude Shannon's work on information theory in 1948 and was later adapted for ecological studies by E.H. Simpson and others. Its mathematical properties make it particularly useful for quantifying uncertainty and diversity across multiple disciplines.