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:

Where is the sum of the lesser values for only those species in common between both sites. and 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 between the same sites:

.

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


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