Intervality and coherence in complex networks

TL;DR

This paper demonstrates that intervality in complex networks, including food webs, is a consequence of structural traits like trophic coherence rather than a cause, challenging traditional niche-based models.

Contribution

It shows that intervality arises from fundamental network properties and is present across various types of complex networks, not just food webs.

Findings

Empirical food webs exhibit predator intervality alongside prey intervality.

Intervality is common in diverse complex networks such as gene, neuron, and airport networks.

A simple model without a niche axis can generate significant intervality.

Abstract

Food webs -- networks of predators and prey -- have long been known to exhibit "intervality": species can generally be ordered along a single axis in such a way that the prey of any given predator tend to lie on unbroken compact intervals. Although the meaning of this axis -- identified with a "niche" dimension -- has remained a mystery, it is assumed to lie at the basis of the highly non-trivial structure of food webs. With this in mind, most trophic network modelling has for decades been based on assigning species a niche value by hand. However, we argue here that intervality should not be considered the cause but rather a consequence of food-web structure. First, analysing a set of $46$ empirical food webs, we find that they also exhibit {\it predator} intervality: the predators of any given species are as likely to be contiguous as the prey are, but in a different ordering. Furthermore, this property is not exclusive of trophic networks: several networks of genes, neurons, metabolites, cellular machines, airports, and words are found to be approximately as interval as food webs. We go on to show that a simple model of food-web assembly which does not make use of a niche axis can nevertheless generate significant intervality. Therefore, the niche dimension (in the sense used for food-web modelling) could in fact be the consequence of other, more fundamental structural traits, such as trophic coherence. We conclude that a new approach to food-web modelling is required for a deeper understanding of ecosystem assembly, structure and function, and propose that certain topological features thought to be specific of food webs are in fact common to many complex networks.