Simpson's Diversity Index (SDI) Calculator
Calculate Simpson's Diversity Index (SDI) instantly. Enter species population counts to compute Simpson's Index D, diversity index 1-D, and reciprocal index with bar charts and species breakdown.
About This Calculator
Simpson's Diversity Index (SDI), also known as the Gini-Simpson index, is one of the most widely used measures of biodiversity in ecology. This calculator helps ecologists, conservation biologists, environmental scientists, and students quantify species diversity in any community by computing three related indices: Simpson's Index (D), Simpson's Diversity Index (1-D), and Simpson's Reciprocal Index (1/D).
The calculation uses the formula D = Σ nᵢ(nᵢ−1) / N(N−1), where nᵢ is the number of individuals in species i and N is the total number of individuals across all species. The diversity index (1−D) represents the probability that two randomly selected individuals belong to different species. A value close to 1 indicates high biodiversity, while a value near 0 suggests a community dominated by few species. The reciprocal index (1/D) represents the effective number of species in the community.
This tool also generates a species breakdown table showing individual counts, n(n−1) values, and proportional abundances for each species. The interactive bar chart visualizes species population distributions, and the diversity comparison chart shows the relationship between Simpson's Index and the Diversity Index, making it easy to interpret biodiversity patterns at a glance.
Frequently Asked Questions
What is Simpson's Diversity Index?
Simpson's Diversity Index (SDI), also called the Gini-Simpson index, measures the probability that two randomly selected individuals from a community belong to different species. It ranges from 0 (no diversity, single species) to 1 (infinite diversity). The formula is 1 − Σ nᵢ(nᵢ−1) / N(N−1), where nᵢ is the number of individuals in species i and N is the total number of individuals.
How is Simpson's Index (D) different from Simpson's Diversity Index (1-D)?
Simpson's Index (D) measures the probability that two randomly selected individuals belong to the same species, so a higher D means lower diversity. Simpson's Diversity Index (1-D) flips this: a higher value means greater diversity. Most ecologists and researchers report 1-D as the standard diversity metric. This calculator provides both D and 1-D for complete analysis.
What is a good Simpson's Diversity Index value?
Simpson's Diversity Index (1-D) ranges from 0 to 1. Values above 0.7 indicate high diversity, 0.4-0.7 indicate moderate diversity, and below 0.4 indicate low diversity. A value of 0 means only one species is present. In practice, tropical rainforests often score above 0.9, while temperate forests score 0.5-0.8, and agricultural monocultures score near 0.
What is the formula for Simpson's Diversity Index?
The formula for Simpson's Diversity Index (Gini-Simpson index) is 1 − D, where D = Σ nᵢ(nᵢ−1) / N(N−1). In this formula, nᵢ is the count of individuals in species i, N is the total count across all species, and the sum is over all species. The reciprocal Simpson index is calculated as 1/D.
What is the difference between Simpson index and Shannon index?
Simpson's Diversity Index and the Shannon Diversity Index are both measures of biodiversity but differ in their sensitivity. Simpson's (1-D) is more sensitive to changes in dominant species and gives more weight to common species, while Shannon's index is more sensitive to rare species. Simpson's ranges from 0 to 1, while Shannon's typically ranges from 1.5 to 3.5. Ecologists often report both for comprehensive analysis.
How do I calculate Simpson's Diversity Index?
To calculate Simpson's Diversity Index: 1) Count the number of individuals in each species (nᵢ), 2) Calculate total individuals N = Σ nᵢ, 3) Compute nᵢ(nᵢ−1) for each species, 4) Sum all these values, 5) Divide by N(N−1) to get D, 6) Subtract D from 1 to get the diversity index. For example, with species counts of 300, 335, and 365, D = 0.33 and 1-D = 0.67.
What does a low SDI value indicate?
A low Simpson's Diversity Index (1-D near 0) indicates the community is dominated by one or very few species, meaning low biodiversity. For example, a farm growing only wheat has SDI near 0. A moderate value (0.4-0.6) suggests some diversity but with uneven population distribution. Conservation biologists use SDI to monitor ecosystem health and detect biodiversity loss.
Can Simpson's Diversity Index be applied outside ecology?
Yes, Simpson's Diversity Index is widely used beyond ecology. Businesses use it to measure workforce diversity across demographics. Social scientists apply it to study income or ethnic diversity in neighborhoods. Economists use it to analyze market concentration. The index works on any categorical data where you want to measure how evenly distributed items are across categories.