Abstract
Understanding the causes and effects of network structural features is a key task in deciphering complex systems. In this context, the property of network nestedness has aroused a fair amount of interest as regards ecological networks. Indeed, Bastolla et al. introduced a simple measure of network nestedness which opened the door to analytical understanding, allowing them to conclude that biodiversity is strongly enhanced in highly nested mutualistic networks. Here, we suggest a slightly refined version of such a measure of nestedness and study how it is influenced by the most basic structural properties of networks, such as degree distribution and degree-degree correlations (i.e. assortativity). We find that most of the empirically found nestedness stems from heterogeneity in the degree distribution. Once such an influence has been discounted – as a second factor – we find that nestedness is strongly correlated with disassortativity and hence – as random networks have been recently found to be naturally disassortative – they also tend to be naturally nested just as the result of chance.
Highlights
Networks have become a paradigm for understanding systems of interacting objects, providing us with a unifying framework for the study of diverse phenomena and fields, from molecular biology to social sciences [1]
A well-known effect leading to effective disassortativity, is that simple algorithms, which are supposed to generate uncorrelated networks, can instead lead to degree-degree anti-correlations when the desired degree distribution has a heavy tail and no more than one link is allowed between any two vertices [21,22]
Theoretical studies suggest that a nested structure minimizes competition and increases the number of coexisting species [13], and it makes the community more robust to random extinctions [26] and habitat loss [27]
Summary
Networks have become a paradigm for understanding systems of interacting objects, providing us with a unifying framework for the study of diverse phenomena and fields, from molecular biology to social sciences [1]. A paradigmatic case is that of ecosystems, in which species can be visualized as nodes of a network and their mutual interactions (predation, mutualism, etc) encoded in the edges or links In this context, the solution to May’s famous paradox [6] – the fact that large ecosystems seem to be especially stable, while random matrix theory predicts the contrary – is still not fully clear, but it is widely suspected that there are structural (non random) features of ecological networks at the basis of enhanced stability, which as yet elude us (see [7] for a recent challenge to this idea).
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