—
—
100
3
3
—
—
100
3
3
Simpson's Reciprocal Index Calculator computes 1/D, where D is the Simpson concentration index (SUM of pi squared). The reciprocal index directly represents the effective number of equally common species in the community. It ranges from 1 (complete dominance by one species) to S (the total number of species, when all are equally abundant).
Enter the abundance for up to three species. The calculator returns the reciprocal index (1/D), the underlying Simpson D, total individuals, species count, and the maximum possible 1/D value. This index is increasingly favored in ecology because it has a clear biological interpretation as an effective species number.
First, the Simpson concentration index D is calculated:
D = SUM(pi²)
Where pi = ni/N is the proportion of species i. Then the reciprocal is:
1/D = 1 / SUM(pi²)
The reciprocal represents the number of equally common species that would produce the same D value. For example, 1/D = 3.5 means the community's diversity is equivalent to 3.5 equally abundant species. The maximum value of 1/D equals S (total species), which occurs when all species have identical abundances (pi = 1/S for all i).
Inputs
Results
With nearly equal abundances (30, 30, 40), 1/D = 2.94 out of a maximum of 3. The community has an effective diversity of nearly 3 equally common species.
Inputs
Results
With one dominant species (80%), 1/D = 1.50, meaning the effective number of species is only 1.5 despite three species being present. The community is heavily dominated.
D (Simpson concentration) is counterintuitive because it decreases with increasing diversity. The reciprocal 1/D increases with diversity and has a direct ecological interpretation as the effective number of species. It is also a true diversity measure of order 2 in the Hill numbers framework, making it mathematically well-behaved for comparisons and decomposition into alpha and beta diversity.
Hill numbers are a family of diversity indices parameterized by order q. At q=0, the Hill number equals species richness (S). At q=1, it equals exp(H') (exponential of Shannon index). At q=2, it equals 1/D (Simpson reciprocal). All Hill numbers share the same units (effective number of species) and can be directly compared. This unified framework was popularized by Jost and Chao.
Both 1/D and exp(H') represent effective numbers of species, but they weight species differently. Exp(H') (Hill q=1) weights all species by their proportion, while 1/D (Hill q=2) gives more weight to common species and less to rare species. In communities with many rare species, exp(H') will be larger than 1/D. In very even communities, both converge toward S.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
How helpful was this calculator?
Be the first to rate!
