Text S1 Selection of the set of indices considered: properties and complementarity/redundancy with others existing measures

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Taxonomic diversity component

While the above components and indices offer a complementary view of species diversity, all of them consider species as equivalent and do not take into account differences between species in their taxonomic relatedness, evolutionary history (phylogeny) or function. We did not have at our disposal phylogeny and function for the 76 species studied but “only” their taxonomy. For both their conceptual and statistical properties, we used the popular indices introduced by Warwick and Clarke (Warwick and Clarke 1995, Clarke and Warwick 1998, 2001) which for years have been widely computed in studies dealing with taxonomy (e.g. Tolimieri and Anderson 2010, and are also increasingly applied to phylogeny (e.g. Plazzi et al. 2010, Modica et al. 2011) or even functional diversity (e.g. Somerfield et al. 2008) in both marine and terrestrial ecosystems.

Consequently, we computed four taxonomic indices, widespread and recognized for their complementary properties, proposed by Warwick and Clarke (1995) and Clarke and Warwick (1998, 2001) that quantify the taxonomic diversity of a faunal assemblage in terms of average distance of all pairs of individuals (or species) in a sample by tracing their distances through the Linnaean taxonomic tree. Each of these four indices has specific statistical properties that were already established in Clarke and Warwick (1998, 2001).

In short, on the basis of species abundance data, Taxonomic diversity Δ is the average taxonomic distance (path length) traced through the taxonomic tree between two randomly chosen individuals in the assemblage, including the individuals which belong to the same species. Taxonomic distinctness Δ* considers only individuals belonging to different species and is less sensitive to dominant species. Δ can be seen as a generalization of the Simpson diversity index 1-D (see above) incorporating the pairwise taxonomic distance between species (Table 1 in the ms, Clarke and Warwick, 1998, Warwick and Clarke, 1995). Δ differs from Δ* in its sensitivity to species dominance (Clarke and Warwick, 1998).

Because collecting presence–absence data can be easier and less time consuming than collecting abundance data, we also investigated a third index Δ+ in order to study the possible “loss of information” with the previous taxonomic indices that require abundance data. Average taxonomic distinctness Δ+ can be defined as the average taxonomic distance between two randomly chosen species in the assemblage (Clarke and Warwick, 1998). In addition to complement Δ+, we applied the index of Variation in taxonomic distinctness Λ+ which is based on the evenness of the taxonomic level distribution in the taxonomic tree, being mathematically the variance of Δ+ (Clarke and Warwick, 2001).
There are two main methods to define ωij which is the weight given to the path length linking species i and j in the taxonomic tree (Clarke and Warwick, 1999), but Rogers et al. (1999) showed that Δ+ calculated with and without ωij modified to reflect the quantitative reduction in taxon richness was strongly correlated. Thus, we adopted the simplest form of ωij with equal step-lengths between each successive taxonomic level, setting the ωij at 100 for two species connected at the highest (taxonomically coarsest) possible level (Clarke and Warwick, 1999). In this study we have considered 6 hierarchical levels (individual, species, genus, family, class, and phylum) to build the taxonomic tree. Knowing the method adopted to define the weight given to the path length linking species i and j in the taxonomic tree, each of the 5 steps necessary to link the 6 hierarchical levels was worth 20 units (i.e. 100/5).
Finally, adopting the list of 11 selected indices in the present work was also driven by the need to draw direct comparisons with our previous works that analysed the multicomponent aspect of species diversity of fishes. Keeping constant both the list of initial indices and the statistical approach for assessing the degree of complementarity/redundancy between indices offers us a unique standardized framework for analyzing the degree of reproducibility of the empirical relationships between multiple indices for different fish communities and ecosystems. Although this topic, which is directly related to the reproducibility of the multicomponent aspect of diversity, is of major concern for both theoretical ecology and monitoring plans (see Purvis and Hector, 2000; Gaertner et al. 2010; Mouchet et al. 2010; Wilsey et al. 2010), it has been very poorly investigated. Here, the comparison made between our different studies provides an important basis for discussion of the feasibility of monitoring the complementary aspects of the diversity for a given taxon, and for different situations and different management scales, on the basis of a single shortlist of indices.

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