  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.
