Partitioning abundance-basedmultiple-site dissimilarity into components: balanced variation in abundance and abundance gradients

1. Abundance-based assemblage dissimilarity can be partitioned into components accounting for (i) balanced variation in abundance, whereby the individuals of some species in one site are substituted by the same number of individuals of different species in another site, and (ii) abundance gradients, whereby some individuals are lost fromone site to the other. 2. Such amethod was available for pairwise dissimilarity, but not for multiple-site dissimilarity. 3. New multiple-site extensions of Bray-Curtis and Ruzicka indices based on the formulation of multiple-site analogues of matching components (i.e. the intersection and the relative complements among multiple sites in terms of species abundances) are introduced. 4. These new indices can be partitioned into balanced-variation and abundance-gradients components. 5. An example assessing multiple-site dissimilarity of birds and butterflies in a mosaic of habitats is shown to illustrate the usefulness of comparing incidence-and abundance-based multiple-site dissimilarity and its components to characterize biotic heterogeneity across multiple sites. 6. Themethodmay be generally useful when the question of interest is the overall abundance-based dissimilarity across multiple units (in space, time or other), as separating the balance-variation (i.e. substitution) and abundance-gradients (i.e. subsets) components of dissimilarity can shed light on the processes behind variation in species abundances.