Sørensen Index Calculators

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The Sørensen similarity index (QS, also called the Sørensen-Dice coefficient or Dice coefficient) is a measure of species overlap between two communities based on presence-absence data: QS = 2C / (A + B), where A = species in community 1, B = species in community 2, and C = species shared by both. It ranges from 0 (no species in common) to 1 (identical species lists). The Sørensen index gives more weight to shared species than the Jaccard index and is generally preferred in ecology for community comparisons. The Sørensen dissimilarity = 1 − QS.

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Sørensen Index Formula

QS = 2C / (A + B)

A = total species in site 1; B = total species in site 2; C = species in common. Range: 0 (no overlap) to 1 (identical). Sørensen dissimilarity = 1 − QS (used as a beta diversity metric).

Example: Site 1: {oak, maple, birch, pine, elm} (A=5); Site 2: {maple, pine, spruce, alder, elm} (B=5); shared: {maple, pine, elm} (C=3). QS = 2×3/(5+5) = 6/10 = 0.60.

Sørensen vs. Jaccard

Jaccard: J = C / (A + B − C). Sørensen: QS = 2C / (A + B). Relationship: QS = 2J/(1+J); J = QS/(2−QS). Sørensen is equivalent to the F1-score in machine learning (harmonic mean of precision and recall). Sørensen weights shared species more heavily — generally preferred for community ecology comparisons.

Quantitative Sørensen (Bray-Curtis)

When abundance data available: QS_quant = 2 × Σ min(aᵢ, bᵢ) / (ΣAᵢ + ΣBᵢ). Equivalent to 1 − Bray-Curtis dissimilarity. Bray-Curtis dissimilarity = most commonly used for abundance-based community comparisons.

Glossary

Sørensen Index (QS)
QS = 2C/(A+B); presence-absence similarity between two communities; A and B = species counts in each site; C = shared species; ranges 0–1; QS = 2J/(1+J) where J = Jaccard index.
Sørensen Dissimilarity
1 − QS; beta diversity metric; 0 = identical communities; 1 = completely different; used in NMDS ordination and PERMANOVA; related to Bray-Curtis dissimilarity for abundance data.
Quantitative Sørensen
2 × Σmin(aᵢ,bᵢ)/(ΣAᵢ+ΣBᵢ); abundance-weighted version; equivalent to 1 − Bray-Curtis dissimilarity; accounts for dominance patterns rather than just species presence.

Frequently Asked Questions

QS = 2C/(A+B). A = species count in site 1; B = species count in site 2; C = number of species present in both sites. Range: 0 (no shared species) to 1 (identical species lists). Example: forest A has 20 species; forest B has 18 species; 12 species in common: QS = 2×12/(20+18) = 24/38 = 0.632. Sørensen dissimilarity = 1 − 0.632 = 0.368. Interpretation: QS > 0.75 = high similarity; 0.50–0.75 = moderate; < 0.50 = low similarity. These are rough guidelines — appropriate thresholds depend on the study context and organism group.

Both are presence-absence similarity measures: Jaccard: J = C/(A+B−C) = shared/(total unique). Sørensen: QS = 2C/(A+B) = 2×shared/(sum of both lists). Relationship: QS = 2J/(1+J); J = QS/(2−QS). Same underlying data, different weighting: Sørensen gives twice the weight to shared species relative to unshared species. Jaccard is more sensitive to differences in species richness between sites. For the same data, QS > J always (except when QS = J = 0 or 1). Sørensen is generally preferred in ecology because it is less sensitive to species richness imbalances. Example: A=5, B=5, C=3: J = 3/7 = 0.429; QS = 0.60 — Sørensen gives a higher, arguably more intuitive similarity value.

The quantitative Sørensen (abundance-weighted) uses species counts or biomass rather than presence-absence: QS_quant = 2 × Σ min(aᵢ, bᵢ) / (ΣAᵢ + ΣBᵢ). For each species i: take the minimum of the count in site 1 (aᵢ) and site 2 (bᵢ). Sum these minimums across all shared species; divide by the sum of all individuals in both sites. Equivalently: 1 − Bray-Curtis dissimilarity. The quantitative version accounts for abundance patterns — two sites may share many species but differ dramatically in which ones dominate. Use presence-absence Sørensen when abundance data are unreliable or when compositional identity (not dominance patterns) is the focus.

Use Sørensen (presence-absence) when: abundance data are unavailable or unreliable; comparing historic vs. current species lists (museum records, herbarium specimens); studying compositional turnover independent of abundance patterns; comparing species lists across literature sources with inconsistent sampling effort. Use quantitative Sørensen (or Bray-Curtis dissimilarity) when: reliable abundance or biomass data are available; dominance patterns are ecologically important (a community dominated by one invasive species vs. one with many equally abundant natives are very different). Both are commonly used as beta diversity metrics in ordination analyses (NMDS, PCoA) and PERMANOVA tests for community differences.