On some properties of the Bray-Curtis dissimilarity and their ecological meaning

- We examine some basic properties of the Bray-Curtis (BC) dissimilarity.
- We first suggest an additive decomposition formula for the BC coefficient.
- Next we derive a general formula of dissimilarity which includes the BC dissimilarity as special case.
- Finally we show that the BC coefficient exhibits a linear response to the transfer of species abundances from an abundant plot to a less abundant plot.

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.