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


Composite (or heterogeneous) indices



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Composite (or heterogeneous) indices

We computed heterogeneous indices (Peet, 1974 ; Buckland et al. 2005), which combine both the number of species and evenness components in a single value (Table 1). We computed both Shannon-Wiener index H’ (Shannon and Weaver, 1949) and the Simpson diversity 1-D (Simpson, 1949) for which there is extensive literature concerning their statistical properties, notably with regard to their sensitivity to rare and dominant species, their sensitivity to sampling size, and the relative influence of species number and evenness (Peet, 1974 ; Lande 1996 ; Lande et al. 2000 ; Buckland et al. 2005). We used Simpson diversity (1-D) which increases with diversity, and which is considered not to be sensitive to sample size (Lande 1996 ; Lande et al. 2000). H’ is assumed to be sensitive to the changes in abundance of relatively rare species while D is heavily weighted towards the dominant species and less sensitive to species richness than H’ (Peet, 1974; Boyle et al., 1990). Although H’ and 1-D are not focused on a single diversity component, we used these two very popular heterogeneous indices to facilitate comparisons of our results with previous studies and to compare their pattern with indices dedicated to a single diversity component, i.e. species number and evenness, in order to assess the respective influence of each of these components on the heterogeneous indices on our data set.


Of course, other indices could have been used. For instance, some authors (e.g. Jost 2006, Tuomisto, 2010) recently promoted the use of Hill’s numbers (Hill, 1973) Na, such as Hill N1 [i.e. exp(H’) ] rather than Shannon index (H’). This family of indices consists of a single mathematical formula from which various indices can be derived from an a parameter value (e.g. N1=exp(H’), N2=1/D, etc.). The resulting value of these indices corresponds to the equivalent number of species that would be in the sample in the case of perfect evenness, i.e. if all individuals are equally distributed among species. Jost (2006) proposed calling this concept and corresponding indices ‘true diversity’, also known as “effective number of species”. However, the concept and indices of “true diversity” have recently been contested in the literature both with regard to the terminology, the suitability of solely taking into account and applying the concept and the related indices when dealing with species diversity (e.g. Norton, 1994; Hoffmann and Hoffmann, 2008; Gorelick, 2011). Indeed, by considering a single concept of an “equivalent number of species”, this family of indices limits species diversity to being viewed simply as species richness, while species richness and evenness are two fundamentally different concepts and facets of species diversity. They are widely known to have different sensitivities to structuring factors, and different implications for the studied system (eg. Ma, 2005; Wilsey et al. 2005; Wilsey and Stirling, 2007; Moreno and Rodriguez, 2010). In contrast, the approach we have adopted in our paper enables us to differentiate between these two key components of species diversity. In addition, even authors that actively promoted the use of Hill numbers, based on Jost’s work (2006), such as Tuomisto (2010) recognized that “other measures [than true diversity] related to diversity (such as entropies and probabilities [ie. H’ and 1-D we used]) continue to be useful, but they represent different phenomena and should therefore be referred to by different names”.

Similarly, Hurlbert's PIE (Hurlbert, 1971) (probability of an interspecific encounter) could have been preferred to Simpson (1-D). Hurlbert's PIE measures the probability that two randomly drawn individuals represent different species. From a practical viewpoint it is calculated on the basis of 1-D (with an adjustment for small sample size)”. These two indices are mathematically identical at the following factor , with n the number of individuals in the sample. Consequently, because our data set is not affected by small size samples (1st quartile value is 147 individuals and median value is 332 individuals for the 1454 trawls analyzed), it is thus logical that we did not use the PIE index.


However, we have computed PIE and Hill N1 for our data in order to assess their empirical complementarity/redundancy with Simpson (1-D) and Shannon (H’), respectively (see Tables B and C). Our results unequivocally show that Hurlbert's PIE provides exactly the same information as 1-D, whether we used Pearson or Spearman correlation coefficients (see Tables B and C where r > 0.99 in both cases). The same point can be made about the use of the Shannon index and the N1 Hill number version.
Table B. Pairwise Pearson correlation coefficients between diversity indices

 

Shannon H'

Hill N1

( exp(H'))



Simpson

(1-D)



Hurlbert’s

PIE

H'

1.0000

0.9589

0.9632

0.9600

Hill N1

0.9589

1.0000

0.8703

0.8666

1-D

0.9632

0.8703

1.0000

0.9990

PIE

0.9600

0.8666

0.9990

1.0000

Table C. Pairwise Spearman correlation coefficient between diversity indices





Shannon H'

Hill N1

(exp(H'))



Simpson

(1-D)



Hurlsbert’s

PIE

H'

1.0000

1.0000

0.9709

0.9621

Hill N1

1.0000

1.0000

0.9709

0.9621

1-D

0.9709

0.9709

1.0000

0.9965

PIE

0.9621

0.9621

0.9965

1.0000




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