Bray–Curtis dissimilarity

In ecology and biology, the Bray–Curtis dissimilarity, named after J. Roger Bray and John T. Curtis, 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 C i j 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

The Bray–Curtis dissimilarity is directly related to the Sørensen similarity index Q S i j 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.

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.