Bray-Curtis Dissimilarity Calculators

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The Bray-Curtis dissimilarity index measures the compositional difference (beta diversity) between two ecological communities based on species abundances. It ranges from 0 (identical communities) to 1 (completely different communities). The formula is: BC = 1 − 2 × Σ min(Aᵢ, Bᵢ) / (ΣA + ΣB), where Aᵢ and Bᵢ are the abundances of species i in communities A and B. Bray-Curtis is widely used in ecology, microbiome research, and environmental monitoring because it is robust to differences in community size (total abundance) and gives appropriate weight to common species.

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Bray-Curtis Formula

BC = 1 − [2 × Σ min(Aᵢ, Bᵢ)] / (ΣA + ΣB)

Equivalently: BC = Σ|Aᵢ − Bᵢ| / (ΣA + ΣB).

Both formulations are equivalent. BC ranges 0 (completely identical) to 1 (no species in common or all shared species have zero in one site).

Example: Community A: species 1=10, 2=5, 3=0. Community B: species 1=8, 2=0, 3=6. ΣA = 15, ΣB = 14. Σmin(Aᵢ,Bᵢ) = min(10,8) + min(5,0) + min(0,6) = 8 + 0 + 0 = 8. BC = 1 − (2×8)/(15+14) = 1 − 16/29 = 0.448.

Properties

  • Range: 0–1 (bounded, intuitive)
  • Symmetric: BC(A,B) = BC(B,A)
  • Not a true metric: violates triangle inequality in some cases
  • Sensitive to abundant species; rare species have less influence
  • Not affected by joint absences (species absent in both sites don't increase similarity)

Applications

NMDS (Non-metric Multidimensional Scaling): ordination technique that arranges samples in 2D/3D space preserving BC rank order. Used to visualize community similarity patterns in ecology and microbiome data. PERMANOVA: tests whether community composition differs significantly between groups based on Bray-Curtis distance matrix.

R Code

vegan package: vegdist(community_matrix, method='bray'). Returns pairwise Bray-Curtis dissimilarity matrix.

Glossary

Bray-Curtis Dissimilarity
BC = 1 − 2Σmin(Aᵢ,Bᵢ)/(ΣA+ΣB); measures compositional difference between two communities; range 0 (identical) to 1 (completely different); accounts for species abundances.
NMDS (Non-metric MDS)
An ordination technique arranging samples in 2D/3D space preserving rank-order of Bray-Curtis dissimilarities; stress < 0.1 = good fit; implemented in vegan R package.
Beta Diversity
Variation in species composition between sites; measured by Bray-Curtis, Jaccard, or other dissimilarity indices; complementary to alpha (within-site) diversity.

Frequently Asked Questions

Bray-Curtis (BC) dissimilarity measures how different two communities are in species composition and abundance: BC = 1 − [2Σmin(Aᵢ,Bᵢ)] / (ΣA + ΣB). Values range 0 (identical) to 1 (completely different). It is widely used because: (1) It uses abundance data (not just presence/absence). (2) It is not affected by joint absences — species absent from both sites don't inflate similarity. (3) It is robust to differences in total abundance between sites. Used in ecology (plant, animal community comparisons), microbiome studies (comparing gut microbiome compositions), and environmental monitoring (before/after pollution assessments).

Step 1: List all species. Step 2: For each species, take the minimum abundance from the two communities. Step 3: Sum these minimums: Σmin(Aᵢ, Bᵢ). Step 4: Sum total abundances in each community: ΣA and ΣB. Step 5: BC = 1 − (2 × Σmin) / (ΣA + ΣB). Example: Site A: oak=20, pine=10, birch=5 (ΣA=35). Site B: oak=15, pine=0, birch=8 (ΣB=23). Σmin = 15+0+5 = 20. BC = 1 − (2×20)/(35+23) = 1 − 40/58 = 0.310. The sites share about 69% of their abundance-weighted composition.

NMDS (Non-metric Multidimensional Scaling) is an ordination technique that arranges samples in 2D or 3D space such that the rank order of pairwise distances in the plot matches the rank order of actual dissimilarities (typically Bray-Curtis). NMDS doesn't preserve actual distances — only ranks — making it non-metric and robust to non-normal, heteroscedastic data. Steps: (1) Calculate pairwise Bray-Curtis matrix. (2) Run NMDS to minimize 'stress' (mismatch between rank-ordered distances in the plot vs. actual dissimilarities). (3) Stress < 0.1 = good representation; < 0.05 = excellent; > 0.2 = poor fit. In R: metaMDS(community_matrix, distance='bray') in the vegan package.

Jaccard dissimilarity (presence/absence only): J_dis = 1 − |A∩B| / |A∪B| = 1 − (shared species) / (total species). Uses only whether species are present or absent. Bray-Curtis: uses species abundances, weighting shared species by how many individuals are shared. Practical differences: BC is preferred when you have count data and want to account for dominance patterns (dominant species drive BC). Jaccard is preferred when: abundances are unreliable; you want to emphasize species richness and presence patterns; analyzing presence/absence data from museum records or occurrence databases. For microbiome 16S rRNA data: BC is standard (uses sequence counts); for presence/absence or occurrence data: Jaccard.