ORIGINAL ARTICLE Partitioning taxon, phylogenetic and functional beta diversity into replacement and richness difference components Pedro Cardoso 1,2 *, Franc ßois Rigal 2 , Jos e C. Carvalho 2,3 , Mikael Fortelius 1,4 , Paulo A. V. Borges 2 , Janos Podani 5,6 and Denes Schmera 7,8 1 Finnish Museum of Natural History, University of Helsinki, Helsinki, Finland, 2 Azorean Biodiversity Group (CITA-A) and Portuguese Platform for Enhancing Ecological Research & Sustainability (PEERS), University of the Azores, Angra do Hero  ısmo, Portugal, 3 Department of Biology, CBMA – Molecular and Environmental Centre, University of Minho, Braga, Portugal, 4 Department of Geosciences and Geography, University of Helsinki, Helsinki, Finland, 5 Department of Plant Systematics, Ecology and Theoretical Biology, Institute of Biology, E€ otv€ os University, Budapest, Hungary, 6 Ecology Research Group, Hungarian Academy of Sciences, Budapest, Hungary, 7 Section of Conservation Biology, University of Basel, Basel, Switzerland, 8 Balaton Limnological Institute, Centre for Ecological Research, Hungarian Academy of Sciences, Klebelsberg K. u. 3, Tihany, Hungary *Correspondence: Pedro Cardoso, Finnish Museum of Natural History, P.O. Box 17, 00014 Helsinki, Finland. E-mail: pedro.cardoso@helsinki.fi ABSTRACT Aim To propose a unified framework for quantifying taxon (Tb), phylogenetic (Pb) and functional (Fb) beta diversity via pairwise comparisons of communi- ties, which allows these types of beta diversity to be partitioned into ecologi- cally 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 conclusions The 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. Keywords Azores, arthropods, beta diversity metrics, differentiation, dissimilarity, Euro- pean mammals, functional diversity, phylogenetic diversity, taxonomic diver- sity, turnover. INTRODUCTION Assessing, measuring and interpreting biodiversity in space and time are challenging tasks in ecology, evolution, bioge- ography and conservation. The notion of taxon diversity (TD) is the most common and is quantified in many dif- ferent ways based on the number of taxa and, often, on the distribution of abundances. TD treats taxa as being equally distinct from one another and disregards the fact that communities are composed of species with different evolutionary histories (Webb et al., 2002; Graham & Fine, 2008) and a diverse array of ecological functions (Vill  eger et al., 2012, 2013). Thus, the last decade has seen a grow- ing interest in alternative representations of biodiversity, including phylogenetic diversity (PD) and functional diver- sity (FD) (Devictor et al., 2010; Meynard et al., 2011; Stegen & Hurlbert, 2011). Although TD, PD and FD may be correlated, they can reveal different mechanisms associ- ated with the origin and maintenance of biodiversity. Note that although the terms ‘phylogenetic diversity’ and ‘func- tional diversity’ have been used to refer to a specific class of measures, we use them as generic terms for any method for integrating phylogenetic or functional information into diversity measures. ª 2013 John Wiley & Sons Ltd http://wileyonlinelibrary.com/journal/jbi 749 doi:10.1111/jbi.12239 Journal of Biogeography (J. Biogeogr.) (2014) 41, 749–761