Shannon Diversity Index Calculator

The Shannon Diversity Index (denoted as H') stems from information theory and is adapted in ecology to quantify uncertainty in predicting the species identity of a random individual. The mathematical formula is expressed as H' = - sum from i=1 to S of (p_i * ln(p_i)), where S represents the total number of species (species richness) and p_i represents the proportion of individuals made up of species i relative to the total number of all species. A higher value indicates a more diverse, evenly distributed ecosystem, while a lower value signals dominance by a single or few species.

Imagine surveying a woodland area and recording two dominant tree species: 80 oak trees and 20 maple trees. The total number of trees is 100. First, calculate the proportional abundance (p_i) for each species: oak is 80/100 = 0.8, and maple is 20/100 = 0.2. Next, multiply each proportion by its natural logarithm (ln): for oak, 0.8 * ln(0.8) = -0.1785; for maple, 0.2 * ln(0.2) = -0.3219. Sum these values and multiply by negative one to find H': H' = -(-0.1785 + -0.3219) = 0.5004. This provides a baseline metric of the woodland's localized biodiversity.

Ensure consistent sampling effort across all compared sites, as under-sampling rare species can artificially deflate your diversity score. Pay attention to your logarithmic base selection; while natural logarithms (ln) are standard in ecology, base-2 is sometimes used in information theory. Always pair your Shannon index with a richness count or Pielou's evenness metric to gain a complete picture of community structure.