Bray-Curtis Dissimilarity Calculator

Calculate Bray-Curtis dissimilarity and Jaccard index for community similarity analysis.

Species abundance in community 1 (sum) (total individuals)

Species abundance in community 2 (sum) (total individuals)

Shared minimum abundance (sum of min for shared species)

Sum of min(n1i, n2i) for each species

Shared species count (species)

Total unique species (both communities) (species)

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Abundance Versus Presence-Absence

Bray–Curtis and Jaccard answer different questions, and the choice changes conclusions. Bray–Curtis weights abundance; Jaccard counts only presence.

BC = 1 − 2C/(S₁ + S₂) J = shared / total

Index	Uses	Sensitive to	Range
Bray–Curtis	Abundances	Dominant species	0 (identical) to 1 (no overlap)
Jaccard	Presence only	Rare species	0 to 1 similarity
Sørensen	Presence, doubled shared weight	Rare species	Always > Jaccard

Because Bray–Curtis is driven by abundant taxa, two communities sharing all their rare species but differing in dominants appear dissimilar. Jaccard on the same data would call them nearly identical. Neither is wrong; they measure different things.

Note that Bray–Curtis is a dissimilarity — 0 means identical. Jaccard as normally reported is a similarity, where 1 means identical. Reversing them is a common reporting error.

Why It Is Not a Metric

Bray–Curtis violates the triangle inequality, so it is semi-metric. Ordination methods assuming a true metric — principal components analysis in particular — can distort the resulting picture.

Non-metric multidimensional scaling is the standard alternative, since it uses only the rank order of dissimilarities and makes no metric assumption. This is why NMDS dominates community ecology plots while PCA dominates elsewhere.

Sampling and Transformation

Issue	Effect	Handling
Unequal sample sizes	Inflates apparent dissimilarity	Rarefy or use relative abundance
One dominant taxon	Swamps the index	Square-root or fourth-root transform
Joint absences	Ignored by design	Usually desirable in ecology

Ignoring joint absences is a deliberate feature. Two sites both lacking a species are not thereby similar — most species are absent from most sites, so counting shared absences would make everything look alike.

Worked Examples

Example 1: Two forest plots: S1=50, S2=60, shared_abundance=35

BC=1-2×35/(50+60)=1-70/110

Result: BC=0.364 — moderate dissimilarity

30-40% dissimilarity common for nearby communities

Example 2: Jaccard: 8 shared species, 12 total

J=8/12=0.667

Result: 67% of species shared

High species overlap between communities

Example 3: Same data, opposite conclusions

Two sites sharing all rare species but differing in dominants

Result: Bray–Curtis high, Jaccard low dissimilarity

Abundance-weighted and presence-based indices disagree because they measure different aspects of community structure.

Example 4: Why joint absences are ignored

Two sites both lacking 200 species from the regional pool

Result: Contributes nothing to similarity

Most species are absent from most sites. Counting shared absences would make all communities appear similar regardless of what they contain.

Common Mistakes

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Reporting Bray–Curtis as similarity

It is a dissimilarity: 0 means identical communities and 1 means no shared abundance. Jaccard runs the opposite way.

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Comparing samples of unequal size

Larger samples detect more species, inflating apparent dissimilarity. Rarefy or convert to relative abundance first.

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Using PCA on Bray–Curtis distances

The index is semi-metric and violates the triangle inequality. Use NMDS, which relies only on rank order.

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Letting one dominant taxon drive the result

A single abundant species can determine the index. Square-root or fourth-root transformation moderates its influence.

Frequently Asked Questions

Bray-Curtis vs Jaccard?

Bray-Curtis (abundance-based): more informative, considers relative abundances. Jaccard/Sorensen (presence/absence): simpler, ignores rare vs dominant species. Bray-Curtis widely used in ecology ordination (NMDS, PCoA). Jaccard for species lists without counts.

Beta diversity?

Overall beta diversity = gamma/alpha. Bray-Curtis measures pairwise dissimilarity. Whittaker's beta = S_gamma/S_alpha - 1. Nestedness vs. turnover components. Used to understand community assembly, biogeography, conservation prioritization.

What is the difference between Bray–Curtis and Jaccard?

Bray–Curtis uses abundances and is driven by dominant species; Jaccard uses presence-absence and gives rare species equal weight.

Is Bray–Curtis a similarity or dissimilarity?

A dissimilarity. Zero means identical communities, and one means no shared abundance at all.

Why use NMDS rather than PCA?

Because Bray–Curtis violates the triangle inequality and is only semi-metric. NMDS uses rank order and makes no metric assumption.

Why are joint absences excluded?

Because most species are absent from most sites. Counting shared absences would make unrelated communities appear similar.