Food webs, networks describing feeding relations in ecosystems, are
paradigmatic examples of complex systems in nature. Despite the
challenge posed by the intricacy of these networks, simple models have
been proposed for their topology that capture successfully particular
structural properties. Two of the most prominent, the niche and cascade
models, postulate the existence of a single dimension along which
species can be ordered, with the resulting hierarchy constraining
partially or completely the connections among species. The niche model
further generates interval networks, in which all prey of a predator are
adjacent on the niche axis, a property clearly related to the concept
of ecological niches. Recently, it has been shown that the empirical
food webs are close to being interval, a result interpreted as
supportive of the niche model. The degree of compatibility with data is
not, however, a good measure of the performance of a model, even if
multiple characteristics are taken into account. What is missing is an
evaluation based on the full topology of the networks. In order to
achieve this goal, we have developed a likelihood-based approach. Since
none of the two models is completely compatible with data, we first
extended both models, providing alternative formulations capable of
generating all empirical food webs. Given data from the best studied food
webs available, we find that our extension, the minimal potential niche model,
always yields better likelihoods. The central assumption of the niche model,
the fact that predators consume prey that share similar characteristics, is
well founded, even if it does not explain all consumer-resource links
in empirical webs. These results open the possibility for a quantitative
characterization of the nature of the niche axis and provide better null
models for the analysis of ecological networks.