Abstract
Nestedness is a concept employed to describe a particular pattern of organization in species interaction networks and in site-by-species incidence matrices. Currently the most widely used nestedness index is the NODF (Nestedness metric based on Overlap and Decreasing Fill), initially presented for binary data and later extended to quantitative data, WNODF. In this manuscript we present a rigorous formulation of this index for both cases, NODF and WNODF. In addition, we characterize the matrices corresponding to the two extreme cases, (W)NODF=1 and (W)NODF=0, representing a perfectly nested pattern andthe absence of nestedness respectively. After permutations of rows and columns if necessary, the perfectly nested pattern is a full triangular matrix, which must of course besquare, with additional inequalities between the elements for WNODF. On the other hand there are many patterns characterized by the total absence of nestedness. Indeed, any binary matrix (whether square or rectangular) with uniform row and column sums (or marginals) satisfies this condition: the chessboard and a pattern reflecting an underlying annular ecological gradient, which we shall call gradient-like, are symmetrical or nearly symmetrical examples from this class.
Highlights
Observing nature is one of the most fascinating experiences in life
Nestedness is a concept used in ecology to study a specific formation pattern in species interaction networks and in site-by-species incidence matrices
The N ODF index, an acronym for Nestedness metric based on Overlap and Decreasing Fill, is an index that was introduced in [2] and that has been widely used in the literature
Summary
Observing nature is one of the most fascinating experiences in life. A honeybee visits a daisy, a rosemary, and other ten different species. Nestedness is a concept used in ecology to study a specific formation pattern in species interaction networks and in site-by-species incidence matrices. In order to assess an index a large set of empirical or artificial data is used as a data bank to explore its limitations and fragility This process has already been used to test a set of nestedness indices [22]. Null models are necessary because statistical tests are otherwise always questionable by limitation in the range of tested parameters, interpretation bias of the results, or equivocal choice of random models These studies emphasis the necessity of analytic results to strength confidence about nestedness indices and their applications.
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