Simpson Diversity Index Calculator
Free Simpson diversity index Calculator for ecology & environmental. Enter variables to compute results with formulas and detailed steps.
Formula
D = SUM(ni(ni-1)) / N(N-1) or D = SUM(pi^2)
Simpson's Index D is the probability that two randomly selected individuals belong to the same species. The finite form uses ni(ni-1)/N(N-1) for exact counts, while the proportion form uses SUM(pi^2). Diversity = 1-D (higher = more diverse). Reciprocal = 1/D (effective dominant species count). Evenness = (1/D)/S where S is species richness.
Worked Examples
Example 1: Coral Reef Fish Community
Problem: A coral reef transect counts 6 fish species: Clownfish (25), Damselfish (20), Wrasse (15), Parrotfish (10), Angelfish (5), Goby (5). Calculate all Simpson indices.
Solution: N = 25+20+15+10+5+5 = 80\nD (finite) = [25(24)+20(19)+15(14)+10(9)+5(4)+5(4)] / [80(79)]\nD = [600+380+210+90+20+20] / 6320 = 1320/6320 = 0.2089\n1-D = 0.7911 (79% chance two individuals differ)\n1/D = 4.79 (effective dominant species)\nEvenness = 4.79/6 = 0.798
Result: D=0.209 | 1-D=0.791 | 1/D=4.79 | Evenness=0.80 | High diversity
Example 2: Disturbed vs Pristine Habitat
Problem: Disturbed site: 90, 5, 3, 2 (4 spp). Pristine: 25, 25, 25, 25 (4 spp). Compare diversity.
Solution: Disturbed: D = SUM(pi^2) = 0.90^2 + 0.05^2 + 0.03^2 + 0.02^2 = 0.8138\n1-D = 0.186; 1/D = 1.23; Evenness = 1.23/4 = 0.31\nPristine: D = 4 x 0.25^2 = 0.25\n1-D = 0.75; 1/D = 4.00; Evenness = 4/4 = 1.00\nPristine is 4x more diverse (1-D: 0.75 vs 0.19)
Result: Disturbed: 1-D=0.19, 1/D=1.23 | Pristine: 1-D=0.75, 1/D=4.00 | Same richness, vastly different diversity
Frequently Asked Questions
What is the Simpson Diversity Index?
The Simpson Diversity Index measures the probability that two individuals randomly selected from a community belong to the same species. The original Simpson's Index (D) ranges from 0 to 1, where 0 represents infinite diversity and 1 represents no diversity (only one species). Because this is counterintuitive, ecologists commonly use two derived forms: Simpson's Diversity Index (1-D), where higher values mean more diversity, and Simpson's Reciprocal Index (1/D), which represents the effective number of dominant species. The index was introduced by Edward Simpson in 1949 and is one of the most robust diversity measures in ecology.
What is the difference between Simpson's D, 1-D, and 1/D?
Simpson's D (concentration index) is the probability that two randomly chosen individuals belong to the same species; it increases as diversity decreases, which is counterintuitive. Simpson's Diversity Index (1-D), also called the Gini-Simpson Index, flips this so higher values mean higher diversity, ranging from 0 to 1. Simpson's Reciprocal Index (1/D) converts to effective species count, ranging from 1 to S (total species). For example, if D=0.25, then 1-D=0.75 (75% chance two random individuals differ), and 1/D=4 (community behaves like one with 4 equally abundant species). Most ecological studies report 1-D or 1/D.
How does Simpson Index differ from Shannon Index?
Both measure species diversity but weight species differently. Simpson's Index gives more weight to dominant (common) species because it uses squared proportions (pi^2), making it relatively insensitive to rare species additions. Shannon's Index uses pi x ln(pi), giving more weight to rare species. In practice: if you add a rare species with 1 individual to a community of 1,000, Shannon's H' changes noticeably but Simpson's D barely moves. Simpson's Index is considered more robust with small sample sizes and is easier to interpret in its reciprocal form (1/D = effective dominant species). Shannon's is preferred when rare species are ecologically important.
What is a good Simpson Diversity Index value?
For the 1-D form, values closer to 1 indicate higher diversity. A value of 0.9 or above is generally considered high diversity, meaning there is a 90%+ chance that two randomly selected individuals belong to different species. Values of 0.7-0.9 represent moderate diversity. Values below 0.5 suggest low diversity with one or two dominant species. For the reciprocal form (1/D), values should be compared to species richness; a value close to the total number of species indicates high evenness. Agricultural monocultures approach 0 (1-D) or 1 (1/D), while tropical forests can exceed 0.95 (1-D) or have 1/D values of 20+.
How accurate are the results from Simpson Diversity Index Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.
What formula does Simpson Diversity Index Calculator use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.