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