Bray–Curtis dissimilarity

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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 similarity is:

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

Where  C_{ij} is the sum of the lesser value 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 2C/2 = 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. The Bray–Curtis dissimilarity is not a distance since it does not satisfy triangle inequality, and should always be called a dissimilarity to avoid confusion.

References[edit]

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

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

6. Yoshioka PM (2008) Misidentification of the Bray-Curtis similarity index. Mar Ecol Prog Ser 368:309–310