A straightforward computational approach for measuring nestedness using quantitative matrices

Nestedness has been one of the most reported patterns of species distribution in metacommunities as well as of species interactions in bipartite networks. We propose here a straightforward approach for quantifying nestedness using quantitative instead of presence–absence data. We named our estimator WNODF because it is a simple modification of the nestedness index called NODF. We also introduce the NODF-Program that calculates the above described nestedness metrics as well as metrics for idiosyncratic species and sites. Statistical inference is done through a null model approach, in which the user can choose among five null models commonly used for presence–absence matrices as well as three randomization algorithms for matrices that contain quantitative data. The program performs multiple analyses using many matrices. Finally, the NODF-Program provides four sorting options that, together with the null algorithms, cover a range of possibilities to test hypotheses on the possible mechanisms producing nested patterns. By using a set of model matrices, we showed that WNODF differentiates nested matrices with distinct structures and correctly identifies matrices with no nested pattern as having zero degree of nestedness.

Research highlights
► A new index (WNODF) is proposed to quantify nestedness for quantitative data.
► WNODF yields distinct nestedness values for matrices with different nested patterns.
► WNODF expresses how the nested pattern resembles abundance gradients among species or sites.
► WNODF quantifies to what extent columns and rows contribute to the overall nested pattern.
► For now, it is the only quantitative index that is fully consistent with the nestedness concept.