Résumé: * Two alternative frameworks have been proposed to partition compositional dissimilarity into replacement and nestedness-resultant component or into replacement and richness-difference components. These are, respectively, the BAS (Baselga 2010, Global Ecology and Biogeography, 19, 134–143) and POD (Podani & Schmera . Oikos, 120, 1625–1638) frameworks. * We conduct a systematic comparison of parallel components in alternative approaches. We test whether the replacement components derived from the BAS and POD frameworks are independent of richness difference. We also evaluate whether previously reported tests of monotonicity between indices and ecological processes are informative to assess the performance of indices. Finally, we illustrate the consequences of differences between the BAS and POD frameworks using the North American freshwater fish fauna as an empirical example. * In the BAS framework, the nestedness-resultant component (βjne or βsne) accounts only for richness differences derived from nested patterns while, in the POD framework, richness-difference dissimilarity (βrich or βrich.s) accounts for all kind of richness differences. Likewise, the replacement components of both alternative methods account for different concepts. Only the replacement component of the BAS framework (βjtu or βsim) is independent of richness difference, while the parallel component in the POD framework (β−3 or β−3.s) is not (i.e. it is mathematically constrained by richness difference). * Therefore, only the BAS framework allows separating (i) the variation in species composition derived from species replacement which is independent of richness difference (i.e. not mathematically constrained by it) and (ii) the variation in species composition derived from nested patterns.

Résumé: The impact of the variation of the number of functional traits on functional diversity assessment is still poorly known. Although the covariation between these two parameters may be desirable in some situations (e.g. if adding functional traits provides relevant new functional information), it may also result from mathematical artefacts and lead to misinterpretation of the results obtained. Here, we have tested the behaviour of a set of nine indices widely used for assessing the three main components of functional diversity (i.e. functional richness, evenness and divergence), according to the variation in the number of functional traits. We found that the number of functional traits may strongly impact the values of most of the indices considered, whatever the functional information they contain. The FRic, TOP and n-hypervolume indices that have been developed to characterize the functional richness component appeared to be highly sensitive to the variation in the number of traits considered. Regarding functional divergence, most of the indices considered (i.e. Q, FDis and FSpe) also showed a high degree of sensitivity to the number of traits considered. In contrast, we found that indices used to compute functional evenness (FEve and Ru), as well as one of the indices related to functional divergence (FDiv), are weakly influenced by the variation in the number of traits. All these results suggest that interpretation of most of the functional diversity indices considered cannot only be based on their values as they are, but requires taking into account the way in which they have been computed.

Résumé: Aim Two frameworks (BASVIL and PODCAR), based on two different functional representations (ordination and dendrogram), have been proposed for partitioning overall functional beta diversity into two analogous components: turnover and nestedness-resultant dissimilarity, or replacement and difference of functional richness, respectively. We compared the two frameworks by testing the influence of functional representations and partitioning methods on the measurement of overall functional beta diversity and its components. Innovation We computed beta-diversity indices from the two frameworks on a set of communities simulated according to five scenarios of assembly: random, richness gradient, pure nestedness, pure turnover and mixed turnover/loss scenarios. To disentangle the effects of the partitioning approach and those of the functional representation on measurement of functional beta diversity, we also computed PODCAR indices in multidimensional space. Main conclusions BASVIL and PODCAR frameworks led to different results for overall functional beta diversity and their analogous partitioning components. Most of the difference between the two frameworks was due to the functional representation used. The goodness-of-fit measure (mean squared deviation, mSD) to assess the quality of functional spaces showed that the one computed on the basis of the dendrogram used in PODCAR remained lower than that of the functional ordination considered in BASVIL. In addition, only functional turnover derived from the BASVIL framework is independent of difference in functional richness. Finally, BASVIL measured functional variations derived from nested phenomena while PODCAR did not allow separation of this variation derived from richness difference. However, the sensitivity of BASVIL to functionally extreme species may make it difficult to know whether variations of the nestedness-resultant dissimilarity components are due to a turnover with few extreme species or a loss in functional richness. Particular attention with regard to the properties of the two frameworks is required before drawing conclusions regarding processes that structure communities.