Bray–Curtis dissimilarity

In ecology and biology, the Bray–Curtis dissimilarity, named after J. Roger Bray and John T. Curtis,^[1] is a statistic used to quantify the compositional dissimilarity between two different sites, based on counts at each site. As defined by Bray and Curtis, the index of dissimilarity is:

$BC_{ij} = 1 - \frac{2C_{ij}}{S_i + S_j}$

Where $C_{ij}$ is the sum of the lesser values for only those species in common between both sites. $S_i$ and $S_j$ are the total number of specimens counted at both sites. The index reduces to 1-2C/2 = 1-C where abundances at each site are expressed as a percentage. Further treatment can be found in Legendre & Legendre^[2]

The Bray–Curtis dissimilarity is directly related to the Sørensen similarity index $QS_{ij}$ between the same sites:

$\overline{BC}_{ij} = 1 - QS_{ij}$.

The Bray–Curtis dissimilarity is bound between 0 and 1, where 0 means the two sites have the same composition (that is they share all the species), and 1 means the two sites do not share any species. At sites with where BC is intermediate (e.g. BC = 0.5) this index differs from other commonly used indices.^[3]

The Bray–Curtis dissimilarity is often erroneously called a distance. It is not a distance since it does not satisfy triangle inequality, and should always be called a dissimilarity to avoid confusion. A software implementation for large samples is provided as part of the mothur software package.^[4]

References

1. Bray, J. R. and J. T. Curtis. 1957. An ordination of upland forest communities of southern Wisconsin. Ecological Monographs 27:325-349.
2. Pierre Legendre & Louis Legendre. 1998. Numerical ecology. 2nd English edition. Elsevier Science BV, Amsterdam.
3. Bloom, S.A. 1981. Similarity indices in community studies: Potential Pitfalls. Marine Ecology--Progress Series 5: 125-128.
4. http://www.mothur.org/wiki/Braycurtis

5. Czekanowski J (1909) Zur Differentialdiagnose der Neandertalgruppe. Korrespbl dt Ges Anthrop 40:44–47

6. Somerfield, PJ (2008) Identification of Bray-Curtis similarity index: comment on Yoshioka (2008). Mar Ecol Prog Ser 372:303–306

7. Yoshioka PM (2008) Misidentification of the Bray-Curtis similarity index. Mar Ecol Prog Ser 368:309–310 http://doi.org/10.3354/meps07728