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Aim To propose a unified framework for quantifying taxon ( Tβ), phylogenetic ( Pβ) and functional ( Fβ) 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 (βtotal) into its replacement (turnover, βrepl) and richness difference (βrich) 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 Pβ and Fβ with the most commonly used Tβ revealed previously hidden patterns of beta diversity. More importantly, we demonstrate that partitioning Pβtotal and Fβtotal into their respective βrepl and βrich components facilitates the detection of more complex patterns than using the overall coefficients alone, further elucidating the different forces operating in community assembly. Main conclusions The methods presented here allow the integration and full comparison of Tβ, Pβ and Fβ. They provide a tool for effectively disentangling the replacement (turnover) and richness difference components of the different biodiversity facets within the same methodological framework. [ABSTRACT FROM AUTHOR]