Simpson Diversity Index Calculator (D, 1−D, and 1/D)
What this calculator does
Simpson’s diversity measures how evenly individuals are distributed among species in a community. It uses only species abundances (counts per species) and summarizes diversity in a single number. This page calculates three closely related outputs so you can use the version your course, lab, or paper expects:
- Simpson’s D (dominance / concentration): the probability that two individuals sampled at random without replacement belong to the same species.
- 1 − D (often called the Gini–Simpson index): the probability that two randomly selected individuals belong to different species.
- 1 / D (Simpson reciprocal index): an “effective number of species” style measure where larger values mean greater diversity.
How to use the calculator
- Enter your species counts as a comma-separated list (for example:
10, 5, 3, 2). - Click Calculate.
- Review D, 1 − D, and 1/D plus the parsed counts, total individuals N, and number of species S.
If your dataset is in a spreadsheet, you can usually copy a column of counts and paste it—this calculator accepts commas, spaces, tabs, and new lines.
Definitions and formulas
Suppose you observed S species. Let ni be the count (abundance) of species i, and let:
- N = total individuals =
The classical finite-sample form of Simpson’s dominance index is:
From that, the other common variants are:
- Gini–Simpson: 1 − D
- Reciprocal: 1 / D (defined only when D > 0)
How to interpret the results
- D (same-species probability): closer to 1 means one or a few species dominate; closer to 0 means the community is more even and diverse.
- 1 − D (different-species probability): closer to 1 means higher diversity; closer to 0 means lower diversity.
- 1/D: larger values indicate higher diversity; it can be easier to compare across sites because it increases roughly in proportion to “effective diversity.”
Important terminology note: Different textbooks and fields sometimes call different variants “Simpson’s diversity index.” Many ecology sources use D (dominance), while others use 1 − D (diversity). This calculator provides both so you can report the one required and cite the definition you used.
Worked example (complete)
Imagine a meadow with four plant species with counts:
10, 5, 3, 2
- Total individuals: N = 10 + 5 + 3 + 2 = 20
- Compute the numerator: 10×9 + 5×4 + 3×2 + 2×1 = 90 + 20 + 6 + 2 = 118
- Compute the denominator: N(N−1) = 20×19 = 380
So:
- D = 118 / 380 ≈ 0.3105
- 1 − D ≈ 0.6895
- 1 / D ≈ 3.22
Interpretation: There is about a 31% chance two randomly chosen individuals are the same species (dominance), and about a 69% chance they are different species (diversity). The reciprocal (~3.22) suggests diversity comparable to a perfectly even community of about 3.2 equally common species.
Comparison table: how the variants behave
| Variant | Formula | Range | Higher value means… | Best for |
|---|---|---|---|---|
| Simpson’s D (dominance) | ∑ ni(ni−1) / [N(N−1)] | 0 to 1 | Less diverse / more dominated | Quantifying dominance; probability interpretation |
| Gini–Simpson | 1 − D | 0 to 1 | More diverse | Intuitive “higher = more diverse” reporting |
| Reciprocal Simpson | 1 / D | 1 to ∞ (when D>0) | More diverse | Comparisons; “effective diversity” style scaling |
Assumptions & limitations (read before using)
- Counts should be non-negative integers. This calculator accepts decimals but Simpson’s index is defined for counts; if you use proportions or weights, interpret results cautiously.
- Requires N ≥ 2. If the total number of individuals is 0 or 1, D is undefined because the denominator N(N−1) is 0.
- Zeros are allowed but don’t add information. A species with count 0 contributes nothing; consider omitting absent species from the list.
- Sampling assumptions matter. The probability interpretation assumes random sampling from a fixed community. Biased sampling or unequal detectability can distort diversity estimates.
- Not a full biodiversity profile. Simpson’s index emphasizes common species and is less sensitive to rare species than metrics like Shannon entropy.
- Comparisons require consistent effort. Comparing across sites/studies is meaningful only when sampling intensity and methods are comparable (or standardized).
Tips for clean inputs
- Paste counts separated by commas, spaces, tabs, or new lines.
- Use only numbers (e.g.,
12, not12 individuals). - If you have a header row or species names, remove them before pasting.
FAQ
Why does a smaller D mean higher diversity?
D is a same-species probability. In a highly even community, picking two individuals is less likely to yield the same species, so D is smaller.
Which value should I report in a lab report?
Report the variant your instructions specify, and include the definition (D vs 1−D vs 1/D). If unsure, 1 − D is commonly preferred because “higher means more diverse.”
What happens if one species dominates?
If most individuals belong to one species, D increases toward 1, while 1 − D decreases toward 0, reflecting low evenness.
Can I enter proportions instead of counts?
Simpson’s index is typically defined on counts. If you enter proportions, the finite-sample formula on this page no longer has the strict probability interpretation; use counts whenever possible.