Simpson Reciprocal Index Calculators

0 calculators tagged with “Simpson Reciprocal Index”

Simpson's reciprocal index (1/D) is a species diversity measure that gives the effective number of equally abundant species required to produce the same level of dominance as the observed community. It is the reciprocal of Simpson's dominance index D = Σpᵢ², where pᵢ is the proportional abundance of species i. The reciprocal form 1/D ranges from 1 (complete dominance by one species) to S (maximum diversity when all S species are equally abundant). It is the q=2 Hill number and is preferred over the raw D or (1−D) formulations because it is expressed in intuitive units (effective number of species).

All Calculators

No calculators found for this topic.

Simpson's Reciprocal Index Formula

D = Σpᵢ² (Simpson's dominance index)

1/D = 1 / Σpᵢ² (Simpson's reciprocal diversity index)

pᵢ = proportional abundance of species i = nᵢ/N.

Range of 1/D: minimum = 1 (one species dominates completely); maximum = S (number of species, when all are equally abundant).

Worked Example

Community: species A = 50, B = 30, C = 15, D = 5 (N = 100).

pA = 0.50, pB = 0.30, pC = 0.15, pD = 0.05.

D = 0.50² + 0.30² + 0.15² + 0.05² = 0.25 + 0.09 + 0.0225 + 0.0025 = 0.365.

1/D = 1/0.365 = 2.74. Interpretation: the community is as diverse as ~2.74 equally abundant species.

Simpson's Index Variants

  • D = Σpᵢ²: Probability that two randomly chosen individuals belong to the same species; higher = less diverse
  • 1 − D: Gini-Simpson index; probability that two random individuals belong to different species; ranges 0–1; not in species units
  • 1/D: Reciprocal Simpson (preferred); effective number of species; the q=2 Hill number

Comparison with Shannon-Wiener

Shannon H' is the q=1 Hill number; 1/D is the q=2 Hill number. 1/D weights dominant species more heavily than H'. Communities dominated by one species have 1/D close to 1, regardless of how many rare species are present. For two communities with the same S, 1/D < exp(H') always.

Glossary

Simpson's Reciprocal Index (1/D)
1/Σpᵢ²; expressed in effective number of equally abundant species; ranges from 1 (one dominant species) to S (all species equal); the q=2 Hill number; preferred over raw D or 1−D.
Simpson's Dominance Index (D)
D = Σpᵢ²; the probability that two randomly chosen individuals belong to the same species; ranges 0–1; high D = low diversity; counterintuitive direction — reciprocal (1/D) is preferred.
Gini-Simpson Index (1−D)
1 − Σpᵢ²; probability that two random individuals belong to different species; ranges 0–1; more intuitive direction than D but not expressed in species units; the q→1 limit is NOT Shannon.

Frequently Asked Questions

Simpson's reciprocal index = 1/D = 1/Σpᵢ², where pᵢ is the proportional abundance of each species. Step 1: count individuals per species; calculate proportions (pᵢ = nᵢ/N). Step 2: square each proportion and sum them (= D). Step 3: take the reciprocal (1/D). Example: 3 species, 60/30/10 individuals → p = 0.6, 0.3, 0.1 → D = 0.36+0.09+0.01 = 0.46 → 1/D = 2.17 effective species. Higher 1/D = more diverse community.

All three are based on D = Σpᵢ² (probability two random individuals are the same species): D itself: ranges 0 (max diversity) to 1 (one species) — counterintuitively, higher D = less diversity. (1−D) = Gini-Simpson index: ranges 0 to 1; probability two random individuals are different species; more intuitive direction but not in species units. 1/D = Simpson reciprocal: ranges 1 to S; expressed as 'effective number of species'; the most ecologically interpretable form and equals the q=2 Hill number.

Both measure diversity but differ in how they weight species: Shannon H' = −Σpᵢ ln(pᵢ) weights species by their proportional abundance (moderate weight to rare species). Simpson 1/D = 1/Σpᵢ² weights species by their squared abundance (heavily weights dominant species; rare species barely matter). For Hill number comparison: H' is the q=1 Hill number (e^H'); 1/D is the q=2 Hill number. For the same community: 1/D ≤ e^H'. Use both to understand whether diversity differences are driven by rare species (H' sensitive) or dominant species (1/D sensitive).

Use Simpson's reciprocal (1/D) when you want a diversity measure that is robust to rare species and more sensitive to dominant species. It is less affected by sampling incompleteness since rare species contribute little to Σpᵢ². 1/D is preferred when: you want to characterize dominance structure; comparing highly uneven communities; or sampling effort is unequal between sites (rare species are under-sampled with small effort). Shannon H' is preferred when all species (including rare ones) should be given more weight and when completeness of sampling is reasonably good.