Aim  Beta diversity (variation of the species composition of assemblages) may reflect two different phenomena, spatial species turnover and nestedness of assemblages, which result from two antithetic processes, namely species replacement and species loss, respectively. The aim of this paper is to provide a unified framework for the assessment of beta diversity, disentangling the contribution of spatial turnover and nestedness to beta‐diversity patterns.Innovation  I derive an additive partitioning of beta diversity that provides the two separate components of spatial turnover and nestedness underlying the total amount of beta diversity. I propose two families of measures of beta diversity for pairwise and multiple‐site situations. Each family comprises one measure accounting for all aspects of beta diversity, which is additively decomposed into two measures accounting for the pure spatial turnover and nestedness components, respectively. Finally, I provide a case study using European longhorn beetles to exemplify the relevance of disentangling spatial turnover and nestedness patterns.Main conclusion  Assigning the different beta‐diversity patterns to their respective biological phenomena is essential for analysing the causality of the processes underlying biodiversity. Thus, the differentiation of the spatial turnover and nestedness components of beta diversity is crucial for our understanding of central biogeographic, ecological and conservation issues.

Summary: 1. Beta diversity, that is, the variation in species composition among sites, can be the result of species replacement between sites (turnover) and species loss from site to site (nestedness).2. We present betapart, an R package for computing total dissimilarity as Sørensen or Jaccard indices, as well as their respective turnover and nestedness components.3. betapart allows the assessment of spatial patterns of beta diversity using multiple‐site dissimilarity measures accounting for compositional heterogeneity across several sites or pairwise measures providing distance matrices accounting for the multivariate structure of dissimilarity.4. betapart also allows computing patterns of temporal difference in assemblage composition, and its turnover and nestedness components.5. Several example analyses are shown, using the data included in the package, to illustrate the relevance of separating the turnover and nestedness components of beta diversity to infer different mechanisms behind biodiversity patterns.

Summary: 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.