Measuring nestedness: A comparative study of the performance of different metrics.

Clàudia Payrató-Borràs,Yamir Moreno,Laura Hernández

doi:10.1002/ece3.6663

Abstract

Nestedness is a property of interaction networks widely observed in natural mutualistic communities, among other systems. A perfectly nested network is characterized by the peculiarity that the interactions of any node form a subset of the interactions of all nodes with higher degree. Despite a widespread interest on this pattern, no general consensus exists on how to measure it. Instead, several nestedness metrics, based on different but not necessarily independent properties of the networks, coexist in the literature, blurring the comparison between ecosystems. In this work, we present a detailed critical study of the behavior of six nestedness metrics and the variants of two of them. In order to evaluate their performance, we compare the obtained values of the nestedness of a large set of real networks among them and against a maximum‐entropy and maximum‐likelihood null model. We also analyze the dependencies of each metrics on different network parameters, as size, fill, and eccentricity. Our results point out, first, that the metrics do not rank networks universally in terms of their degree of nestedness. Furthermore, several metrics show significant dependencies on the network properties considered. The study of these dependencies allows us to understand some of the observed systematic shifts against the null model. Altogether, this paper intends to provide readers with a critical guide on how to measure nestedness patterns, by explaining the functioning of several metrics and disclosing their qualities and flaws. Besides, we also aim to extend the application of null models based on maximum entropy to the scarcely explored area of ecological networks. Finally, we provide a fully documented repository that allows constructing the null model and calculating the studied nestedness indexes. In addition, it provides the probability matrices to build the null model for a large dataset of more than 200 bipartite networks.

Highlights

We focus on the problem of measuring nestedness by presenting a comparative study of the behavior of six nestedness metrics, most of which are commonly included in popular packages and cited in the literature
We have quantified the influence of several network properties on various nestedness metrics, taking into account how each metrics measures the nestedness of empirical networks as well as how they compare to the null model of section 2.2
It has recently been shown that nestedness is not an emergent irreducible pattern of the network, it still remains an interesting quantity to measure, since it constitutes a global property that informs on the heterogeneity of the degree distributions of the guilds

Summary

| MATERIALS AND METHODS

We briefly describe here the principal characteristics of the indices used in this work in order to quantify nestedness. With the results obtained in Payrató-Borràs et al (2019) using NODF and the spectral radius, NIR and NMD show that the nestedness values of the empirical networks are statistically equivalent to the average of the corresponding randomized ensemble This leads to the conclusion that the observed nestedness measured by these indices is not significant. To compare the average nestedness over the ensemble with that corresponding to empirical networks, we have used the six metrics described above plus two variations (the stable-NODF and the normalized spectral radius) As it has been shown analytically and numerically (using NODF and the spectral radius) in Payrató-Borràs et al (2019), the nested structure of mutualistic networks is a consequence of the double heterogeneity in the degree sequence which results from entropic effects.

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| DISCUSSION

| CONCLUSIONS