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.
species_a = 40species_b = 25species_c = 20species_d = 15
- 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
Ready to run the numbers?
Open Biodiversity Simpson Index Calculator