Calculate Simpson's Diversity Index, Shannon Index, evenness, richness, and Hill numbers for any categorical dataset. Includes visual distribution bars and detailed breakdown.
The Simpson's Diversity Index Calculator computes diversity metrics such as Simpson's D, Shannon-Wiener H', Pielou's evenness, Berger-Parker dominance, Margalef richness, and Hill numbers.
Diversity indices describe how evenly categories are represented. In ecology that might mean species counts, in business it can mean market concentration, and in demographics it can mean how a population is distributed across groups. Simpson's 1-D is especially intuitive because it is the probability that two randomly selected individuals belong to different categories.
The calculator shows the common indices together with proportion bars and a computation table, which makes it easier to compare richness, dominance, and evenness in one view.
Different diversity metrics emphasize different parts of the same distribution. Some respond mostly to common categories, while others give more weight to rare ones. Seeing the indices together makes it easier to understand whether a dataset is diverse, merely even, or dominated by a small number of categories.
The Hill numbers framework helps connect those measures instead of treating them as unrelated formulas.
Simpson's D = Σpᵢ². Diversity = 1 - D. Reciprocal = 1/D. Shannon H' = -Σ(pᵢ × ln pᵢ). Evenness J = H'/H'max. Margalef = (S-1)/ln(N).
Result: Simpson's 1-D = 0.7300, Shannon H' = 1.4405, Evenness J = 0.8947
Total = 100. Proportions: 0.40, 0.25, 0.20, 0.10, 0.05. D = 0.40² + 0.25² + 0.20² + 0.10² + 0.05² = 0.27. Diversity = 1 - 0.27 = 0.73 (73% probability two random individuals differ).
In ecology, Simpson's Diversity Index is used to compare species diversity across habitats, monitor biodiversity over time, and assess the impact of environmental changes. A declining index may indicate habitat degradation, invasive species, or pollution. Conservation biologists use these metrics to prioritize protection efforts.
Hill numbers, introduced by Mark Hill in 1973, provide a unified mathematical framework for diversity measurement. At order q=0, they reduce to species richness. At q=1, they equal the exponential of Shannon entropy. At q=2, they equal Simpson's reciprocal. This framework eliminates the apparent contradiction between different indices by showing they're all part of one family with different sensitivity to rare vs. common categories.
Despite sharing a name, Simpson's Diversity Index and Simpson's Paradox are unrelated — named after different statisticians (E.H. Simpson for the index, Edward Simpson for the paradox). However, both remind us that aggregated statistics can be misleading: a habitat with high overall diversity might have low diversity within each microhabitat.
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It measures the probability that two randomly selected individuals from the sample belong to different categories. Ranges from 0 (no diversity, one category dominates) to nearly 1 (maximum diversity, all categories equal). Higher values indicate more diversity.
Simpson's index is more sensitive to dominant categories (commons), while Shannon's is more sensitive to rare categories. Simpson's has a clear probability interpretation; Shannon's is measured in "nats" (information units). Both increase with diversity.
Evenness (Pielou's J) measures how equally individuals are distributed across categories, ranging from 0 (all individuals in one category) to 1 (perfectly equal distribution). It's calculated as H'/H'max, where H'max = ln(S).
Hill numbers unify diversity indices into a family parameterized by order q. q=0 gives richness (number of categories), q=1 gives exp(H') (Shannon diversity), q=2 gives 1/D (Simpson diversity). Higher q gives more weight to common categories.
Absolutely! Diversity indices apply to any categorical data: market concentration (companies), ethnic diversity (demographics), vocabulary richness (linguistics), or portfolio diversification (finance). The math is identical.
The Berger-Parker index equals the proportional abundance of the most dominant category. It ranges from 1/S (perfect evenness) to 1 (total dominance). Lower values indicate more even distributions.