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ABSTRACT 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 (βcc, overall beta diversity) in its two components, species replacement (β-3) and species richness differences (βrich) 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 (βsor) in replacement (βsim) and nestedness (βnes). The linear response of βcc contrasts with the curvilinear response of βsor to linear gradients of dissimilarity. When two sites did not share any species, βsim was always 1 and β-3 only reached 1 when the number of exclusive species of both sites was equal. β-3 remained constant along gradients of richness differences with constant replacement, while βsim decreased. βrich had a linear response to a linear gradient of richness differences with constant species replacement, whereas βnes exhibited a hump-shaped response. Moreover, βsim > βnes when clearly almost all species of one site were lost, whereas β-3 < βrich in the same circumstances. Main conclusions The behaviour of the partition of βcc into β-3 and βrich is consistent with the variation of replacement and richness differences. The partitioning of βsor into βsim and βnes 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. [ABSTRACT FROM AUTHOR]