Aim To determine the relative contribution of species replacement and species richness differences to the emergence of beta-diversity patterns.Innovation A novel method that disentangles all compositional differences (bcc, overall beta diversity) in its two components, species replacement (b-3) and species richness differences (brich) is proposed. The performance of the method was studied with ternary plots, which allow visualization of the influence of the relative proportions of shared and unique species of two sites over each metric. The method was also tested in different hypothetical gradients and with real datasets. The novel method was compared with a previous proposal based on the partitioning of overall compositional differences (bsor) in replacement (bsim) and nestedness (bnes). The linear response of bcc contrasts with the curvilinear response of bsor to linear gradients of dissimilarity. When two sites did not share any species, bsim was always 1 and b-3 only reached 1 when the number of exclusive species of both sites was equal. b-3 remained constant along gradients of richness differences with constant replacement, while bsim decreased. brich had a linear response to a linear gradient of richness differences with constant species replacement, whereas bnes exhibited a hump-shaped response. Moreover, bsim > bnes when clearly almost all species of one site were lost, whereas b-3 < brich in the same circumstances. Main conclusionsThe behaviour of the partition of bcc into b-3 and brich is consistent with the variation of replacement and richness differences. The partitioning of bsor into bsim and bnes overestimates the replacement component and underestimates richness differences. The novel methodology allows the discrimination of different causes of beta-diversity patterns along latitudinal, biogeographic or ecological gradients, by estimating correctly the relative contributions of replacement and richness differences.

1. Novel algorithms have been recently developed to estimate alpha and partition beta diversity in all their dimensions (taxon, phylogenetic and functional diversity -TD, PD and FD), whether communities are completely sampled or not. 2.The R package BAT -Biodiversity Assessment Tools -performs a number of analyses based on either species identities (TD) or trees depicting species relationships (PD and FD). Functions include building randomized accumulation curves for alpha and beta diversity, alpha diversity estimation from incomplete samples and the partitioning of beta diversity in its replacement and richness difference components. All functions allow the rarefaction of communities. Estimation methods include curve-fitting andnon-parametric algorithms. Beta diversity indices include the Jaccard and Sørensen families of measures and deal with both incidence and abundance data. Two auxiliary functions that allow judging the efficiency of the algorithms are also included. 4.Several examples are shown using the data included in the package, which demonstrate the usefulness of the different methods. The BAT package constitutes an open platform for further development of new biodiversity assessment tools.

Aim To propose a unified framework for quantifying taxon (Tb), phylogenetic (Pb) and functional (Fb) beta diversity via pairwise comparisons of communities, which allows these types of beta diversity to be partitioned into ecologically meaningful additive components.Location Global, with case studies in Europe and the Azores archipelago.Methods Using trees as a common representation for taxon, phylogenetic and functional diversity, we partition total beta diversity (b total ) into its replacement (turnover, b repl ) and richness difference (b rich ) components according to which part of a global tree was shared by or unique to communities that were being compared. We demonstrate the application of this framework using artificial and empirical examples (mammals in Europe and epigean arthropods in the Azores).Results Our empirical examples show that comparing Pb and Fb with the most commonly used Tb revealed previously hidden patterns of beta diversity.More importantly, we demonstrate that partitioning Pb total and Fb total into their respective b repl and b rich components facilitates the detection of more complex patterns than using the overall coefficients alone, further elucidating the different forces operating in community assembly. Main conclusionsThe methods presented here allow the integration and full comparison of Tb, Pb and Fb. They provide a tool for effectively disentangling the replacement (turnover) and richness difference components of the different biodiversity facets within the same methodological framework.