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.
Ecological network Matrix order Null models Species-area matrix
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We thank two anonymous reviewers for their useful comments and suggestions. The views expressed are purely those of the writer and may not in any circumstances be regarded as stating an official position of the European Commission.
Table S1–S3 Pearson product-moment correlation coefficients and their respective p values of the pairwise correlations between matrix properties (number of occurrences, size and fill), nestedness measures [NODF and ρ(A)] and standardized nestedness measures (Z, RN and p values) under different null models (EE, CE and FF) computed for the set of theoretical matrices, the set of species-area matrices, and the set of mutualistic networks. Correlation coefficients and p values are, respectively, shown below and above the main table diagonal (XLS 63 kb)
Bastolla U, Fortuna MA, Pascual-García A, Ferrera A, Luque B, Bascompte J (2009) The architecture of mutualistic networks minimizes competition and increases biodiversity. Nature 458:1018–1020. doi:10.1038/nature07950PubMedCrossRefGoogle Scholar
1.European Commission, Joint Research CentreInstitute for Environment and SustainabilityIspraItaly
2.Azorean Biodiversity Group (GBA, CITA-A) and Platform for Enhancing Ecological Research and Sustainability (PEERS), Departamento de Ciências AgráriasUniversidade dos AçoresAngra do HeroísmoAzores, Portugal