Quantitative analysis of the local structure of food webs

We analyze the local structure of model and empirical food webs through the statistics of three-node subgraphs. We study analytically and numerically the number of appearances of each subgraph for a simple model of food web topology, the so-called generalized cascade model, and compare them with 17 empirical community food webs from a variety of environments, including aquatic, estuarine, and terrestrial ecosystems. We obtain analytical expressions for the probability of appearances of each subgraph in the model, and also for randomizations of the model that preserve species' numbers of prey and number of predators; their difference allows us to quantify which subgraphs are over- or under-represented in both the model and the empirical food webs. We find agreement between the model predictions and the empirical results. These results indicate that simple models such as the generalized cascade can provide a good description not only of the global topology of food webs, as recently shown, but also of its local structure.