On some properties of the Bray-Curtis dissimilarity and their ecological meaning |
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| Affiliation: | 1. Department of Environmental Biology, University of Rome ‘La Sapienza’, Rome, Italy;2. Institute for Cereal Crops Improvement, Tel Aviv University, Tel Aviv, Israel;3. Department of Biosciences, University of Milano, Milano, Italy;4. Department of Biotechnology and Life Sciences, University of Insubria, Varese, Italy;5. Centre d''Ecologie et des Sciences de la Conservation (CESCO), Muséum National d''Histoire Naturelle, CNRS, Sorbonne Université, Paris, France;1. Plymouth Marine Laboratory, Prospect Place, West Hoe, Plymouth PL1 3DH, UK;2. Primer-E Ltd, c/o Plymouth Marine Laboratory, Prospect Place, West Hoe, Plymouth PL1 3DH, UK |
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| Abstract: | In this paper, we examine some basic properties of the Bray-Curtis dissimilarity as compared with other distance and dissimilarity functions applied to ecological abundance data. We argue that the ability of every coefficient to measure species-level contributions is a fundamental requirement. By suggesting an additive decomposition formula for the Bray-Curtis coefficient we derive a general formula of dissimilarity, which includes the Canberra distance and the Bray-Curtis dissimilarity as special cases. A similar general formula is also proposed for the Marczewski-Steinhaus coefficient. Finally, using a modified version of Dalton’s principle of transfers, we show that the Bray-Curtis coefficient and the city-block distance exhibit a linear response to the transfer of species abundances from an abundant plot to a less abundant plot. At the other extreme, the chord and the Hellinger distances show an irregular and non-monotonic behavior. |
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| Keywords: | Data standardization Generalized coefficients Multivariate dissimilarity measures Principle of transfers Species abundances |
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