Can we trust the chord (and the Hellinger) distance?

To avoid the problems associated with the Euclidean distance for the calculation of plot-to-plot dissimilarity, a variety of alternative measures have been proposed. Among them, the chord and the Hellinger distances are both obtained by first transforming separately the species abundances in each plot vector and then by calculating the Euclidean distance on the chord-transformed or the Hellinger-transformed data. However, although both measures are routinely used by ecologists as substitutes for the Euclidean distance, they have very different properties. In this paper, using a modified version of Dalton's principle of transfers, I will show that, unlike the Euclidean distance, the chord and the Hellinger distances are not monotonic to changes in absolute abundances. Therefore, they are not interchangeable with the Euclidean distance. The moral of this story is that although dissimilarity may appear an intuitively simple concept, the properties of even the best-known indices are not fully understood. Therefore, a clear understanding of old and new coefficients is needed to evaluate their ability to highlight relevant aspects of compositional dissimilarity among plots.