From the euclidean distance to compositional dissimilarity. What is gained and what is lost

A well-known problem of the Euclidean distance is that it is not always appropriate to explore the multivariate structure of community composition. This is because all distances of the ‘Euclidean family’ may lead to the paradoxical condition for which two samples with no species in common may be more similar than two samples with the same species list. This effect is generally known as the Orlóci paradox. To avoid this problem, some kind of data normalization has to be performed. Therefore, the main question of this short paper is: what is gained and what is lost by moving from the Euclidean distance to compositional dissimilarity? To answer this question, I first explore the causes of the Orlóci paradox. Next, I discuss how the normalization methods that are included in virtually all compositional dissimilarity measures affect the way in which species abundances are modeled.