On the methods to assess significance in nestedness analyses.

Use of Z values to evaluate nestedness significance is a common procedure. An appealing alternative to the use of Z values is that of using a value of relative nestedness (RN). However, there is no agreement on the preferable procedures to generate the null matrices needed to compute both Z and RN. In general, it is recommended to use restrictive null models that take into account row and column totals. The two most widely used null models of this kind, namely, FF and CE [that generate matrices with row and column sums equal (FF) or proportional (CE) to the row and column totals of the original matrix, respectively], are very different in terms of restrictiveness. We performed a set of comparative analyses on both theoretical and real matrices to investigate the differences between the use of Z and RN values, and between the use of FF and CE null models, when NODF (Nestedness metric based on overlap and decreasing fill) or ρ(A) (i.e., the largest eigenvalue of the adjacency matrix) are used to measure nestedness. We found no difference in the use of Z or RN values. On the other hand, we found that different combinations of nestedness measures and null models may lead to inconsistent outcomes. Our results offer some clarity on a few issues that, despite playing a central role in the practical application of nestedness analysis, have been little explored, and highlight the need for the definition of some commonly accepted standards.