Shannon Diversity Index Calculator
Measure biodiversity using Shannon’s index.
Formula first
Overview
The Shannon Diversity Index quantifies the biological complexity of a community by considering both the number of species present and their relative abundance. It calculates the entropy or uncertainty involved in predicting the species of a random individual, where higher values reflect greater diversity and evenness.
Symbols
Variables
H = Shannon Index, p = Proportion, n = Individuals in Species, N = Total Individuals
Apply it well
When To Use
When to use: This index is ideal when comparing communities where rare species are present, as it is sensitive to both richness and evenness. It is best applied to large, random samples where all species in the community are likely to be represented.
Why it matters: Measuring diversity helps ecologists assess the impact of environmental disturbances like pollution or habitat loss. A declining Shannon index often serves as an early warning sign of ecosystem degradation or the loss of niche stability.
Avoid these traps
Common Mistakes
- Using log base 10.
- Forgetting the negative sign.
One free problem
Practice Problem
In a perfectly balanced ecosystem with exactly two species, each species accounts for half of the total population (p = 0.5). Calculate the Shannon Diversity Index (H) for this community.
Solve for:
Hint: Calculate p × ln(p) for one species, then double it and take the negative value.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Shannon, C. E. (1948). A mathematical theory of communication. Bell System Technical Journal, 27(3), 379-423.
- Wikipedia: Shannon index
- Britannica: Shannon diversity index
- Magurran, A. E. (2004). Measuring Biological Diversity. Blackwell Publishing.
- Molles, M. C., & Sher, A. A. Ecology: Concepts and Applications. McGraw-Hill.
- Begon, M., Townsend, C. R., & Harper, J. L. Principles of Ecology. Blackwell Science.
- Standard curriculum — Ecology