H' = -Σ(pᵢ × ln pᵢ)
The Shannon Diversity Index (H'), developed by Claude Shannon in information theory (1948) and adopted by ecologists, quantifies the uncertainty in predicting the species identity of a randomly chosen individual. It accounts for both species richness (number of species) and evenness (how equally abundant they are). H' = -Σ(pᵢ × ln pᵢ), where pᵢ is the proportion of individuals belonging to species i. Values typically range from 0 (single species) to about 4.5 (highly diverse tropical ecosystems). A temperate forest might score 1.5-3.0, while a coral reef scores 3.0-4.5. Evenness (J = H'/ln S) ranges from 0 to 1, where 1 means all species are equally abundant. Low evenness indicates dominance by one or few species. The index is widely used in conservation to monitor ecosystem health: declining H' values signal biodiversity loss. It's also applied in gut microbiome analysis, where higher diversity correlates with better health outcomes.