Text S1 - Selection of the set of indices considered: properties and complementarity/redundancy with others existing measures.
The question of defining and choosing methods for assessing biodiversity is still the focus of widespread and very lively debate (e.g. Chao et al. 2010; Jost, 2006; Gotelli and Colwell, 2010; Hoffmann and Hoffmann, 2008; Mérigot and Gaertner, 2011; Mouchet et al., 2010 ; Tuomisto 2010; Gorelick, 2011). We briefly discuss below our reasons for selecting a set of 11 indices, mentioning their main properties. We notably highlight the main differences/similarities with some other indices that are widely used in the literature and/or that have been recently promoted by several authors, in order to explain why we did not adopt them for our work.
Species richness component
The number of species is still the most widely used component for describing diversity in both marine and terrestrial ecosystems. Two main methods of expressing estimates of species richness have been extensively used in the literature: the number of species per specified number of individuals (numerical species richness), and the number of species per unit area (species density, Magurran, 2004).
Because species richness is sensitive to sample size , we have initially selected only hauls showing low variation in the surface area trawled. Among the 1515 hauls undertaken during the period studied, only 1454 have been included in the analyses (mean Sd : 0.08 0.004 km²). We checked that swept area variation within the 1454 selected hauls did not affect values in species richness through a Chi2 test of independence (p > 0.05). We analysed the mean number of species by means of two indices: i) the number of species per haul as a measure of species density S and ii) Margalef’s species richness index Dmg (Margalef 1958) (see Table 1). Among the various indices available to adjust the number of species according to the total number of individuals sampled in each haul, we chose Margalef’s species richness index for its ease of calculation and its widespread use (Magurran, 2004). In addition, we used sample-based rarefaction curves according to the number of hauls per area to allow comparison of total species richness between areas with different sampling effort (see  for detailed information on this extensively used technique).
Other approaches could have been used for estimating the number of species component, such as non-parametric estimators of true total species richness (e.g. Chao or Jacknife estimators. However, here our goal was clearly not to assess the “true” total species richness, but to compare reproducible estimations of species diversity (and notably species richness) in space in order to investigate diversity patterns. For that purpose we did not deal with all the species sampled, but we have restricted our analyses to a large sub-set of 76 species. Each of these 76 species has been properly identified and sampled by each of the scientific teams involved in the large-scale survey in such a way as to strictly limit the risk of a variability in accuracy of sampling identification between the different teams. For information, we have however computed some of the most popular non-parametric estimators (see Table A below). These estimators gave exactly - or almost exactly - the same values as those of the total observed species richness we had already used (with a maximum difference of 1 species).
Table A. Estimators of true total species richness. Total observed species richness is 76.