Biodiversity Simpson Index Calculator Formula
Understand the math behind the biodiversity simpson index calculator. Each variable explained with a worked example.
Formulas Used
Simpson D (dominance)
simpson_d = sum_n_n1 / (total_n * (total_n - 1))Simpson Diversity (1-D)
simpson_diversity = 1 - sum_n_n1 / (total_n * (total_n - 1))Reciprocal Index (1/D)
reciprocal_index = total_n * (total_n - 1) / sum_n_n1Variables
| Variable | Description | Default |
|---|---|---|
species_a | Species A Count | 40 |
species_b | Species B Count | 25 |
species_c | Species C Count | 20 |
species_d | Species D Count | 15 |
total_n | Derived value= species_a + species_b + species_c + species_d | calculated |
sum_n_n1 | Derived value= species_a * (species_a - 1) + species_b * (species_b - 1) + species_c * (species_c - 1) + species_d * (species_d - 1) | calculated |
How It Works
Simpson Diversity Index
The Simpson Index measures the probability that two randomly selected individuals belong to different species. Higher values mean greater diversity.
Formula
D = Sum of [n(n-1)] / [N(N-1)]
Where n is the count of each species and N is the total count. D ranges from 0 to 1, where 0 is infinite diversity and 1 is no diversity. The complement (1-D) is more intuitive: higher values mean more diversity.
Worked Example
A forest plot has 40 oaks, 25 maples, 20 birches, and 15 pines.
- 01Total N = 40 + 25 + 20 + 15 = 100
- 02Sum n(n-1) = 40x39 + 25x24 + 20x19 + 15x14 = 1560 + 600 + 380 + 210 = 2750
- 03D = 2750 / (100 x 99) = 2750 / 9900 = 0.2778
- 04Diversity (1-D) = 1 - 0.2778 = 0.7222
- 05Reciprocal = 1/0.2778 = 3.60
Frequently Asked Questions
What does a Simpson Index of 0.72 mean?
A 1-D value of 0.72 means there is a 72% chance that two randomly picked individuals will be from different species. This indicates moderate to good diversity.
How many species can this handle?
The formula works for any number of species. This calculator uses four inputs for simplicity, but the principle extends to dozens or hundreds of species.
Simpson vs Shannon index?
Simpson is more sensitive to dominant species, while Shannon gives more weight to rare species. Simpson is also easier to interpret as a probability.
Ready to run the numbers?
Open Biodiversity Simpson Index Calculator