A protocol to compare nestedness among submatrices

Abstract

Searching for nestedness has become a popular exercise in community ecology. Significance of a nestedness index is usually evaluated using z values, and finding that a matrix is nested is typically a common result. However, nestedness is not likely to be spread uniformly within a matrix of species presence/absence per site. Selected parts of the matrix may show a degree of nestedness significantly higher (or lower) than expected from the overall pattern. Here we describe a procedure to assess if a particular submatrix (i.e., a peculiar combination of rows and columns extracted from the complete matrix) is more or less nested than expected for an assortment of sites and species taken at random from the same overall matrix. The idea is to obtain several submatrices of different sizes from the same overall matrix and to calculate their z values. A regression is then performed between z values of submatrices and their sizes. A nestedness index independent of matrix size is suggested as the deviation of the z value of a particular submatrix from that expected according to the regression line. We applied our protocol to 55 matrices with different nestedness indices under various null‐models and, for purpose of demonstration, we discussed in detail a single case study regarding various animal groups of the Aegean Islands (Greece). The obtained results strongly encourage further research to focus not only on the question whether a matrix is nested or not, but also on where and why nestedness is confined.

Plant recording across two centuries reveals dramatic changes in species diversity of a Mediterranean archipelago

“…Although Z-values can be used to assess whether a matrix is significantly nested or not, they cannot provide information about the ‘magnitude’ of nestedness 61 . For this purpose, we also calculated ‘relative nestedness’ (RN) 62 , which is computed as [ Nr- mean( Ns )]/mean( Ns ).…”

On the methods to assess significance in nestedness analyses

“…This comparison is usually made using a Z value calculated as [Nr-mean(Ns)]/stdev(Ns), where Nr is the nestedness of the matrix under study, and mean(Ns) and stdev(Ns) are, respectively, the average and standard deviation of the nestedness values of the null matrices (Ulrich and Gotelli 2007;Ulrich et al 2009). Although Z values can assess whether a matrix is significantly nested or not, they cannot provide information about the 'magnitude' of nestedness (Strona et al 2011(Strona et al , 2013b. For this, Bascompte et al (2003) proposed a different way to standardize the nestedness value, introducing a concept of ''relative nestedness'' (RN) computed as [Nr-mean(Ns)]/mean(Ns).…”

Patterns and processes in the distribution of European centipedes (Chilopoda)

“…Consistent with previous studies (e.g. Dennis et al ., ; Fattorini, ; Hausdorf & Hennig, ; Simaiakis & Martínez‐Morales, ; Strona et al ., ; Parmakelis et al ., ) our results highlighted the role of palaeogeographical events and geographical configuration on biodiversity and species assemblage patterns.…”

“…Comparing nestedness degree between different modules could provide valuable insights into the biogeographical history of a taxon. In particular, a high degree of nestedness in a biogeographical module may be promoted by the presence of species-rich localities from which species disperse towards other areas (Strona et al, 2012).…”

“…Finally, the Z-values of biogeographical modules were ranked on the basis of their respective 'distance' from the Z-values predicted by the regression line for a matrix of the same size. For each biogeographical module, this distance was calculated as (Z r À UL)/(UL À LL), where Z r is the actual Z of the module matrix, and UL and LL are the upper and lower 95% confidence limits, respectively, of the regression line for a matrix the same size as the matrix of the module under study (see Strona et al, 2012).…”