Separating the two components of abundance-based dissimilarity: balanced changes in abundance vs. abundance gradients

Dissimilarity measures can be formulated using matching components that can be defined as the intersection in terms of species composition of both sets (a) and the relative complements of each set (b and c respectively). Previous work has extended these matching components to abundance-based measures of dissimilarity. Using these matching components in terms of species abundances I provide a novel partition separating two components of abundance-based dissimilarity: (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 from one site to the other. New indices deriving from the additive partition of Bray-Curtis dissimilarity are presented, each one accounting separately for these two antithetic components of assemblage variation. An example comparing the patterns of increase of assemblage dissimilarity with spatial distance in two tropical forests is provided to illustrate the usefulness of the novel partition to discern the different sources of assemblage variation. The widely used Bray-Curtis index of dissimilarity is the result of summing these two sources of dissimilarity, and therefore might consider equivalent patterns that are markedly different. Therefore, the novel partition may be useful to assess biodiversity patterns and to explore their causes, as substitution and loss of individuals are patterns that can derive from completely different processes.