A stochastic theory of community food webs I. Models and aggregated data

Abstract Three recently discovered quantitative empirical generalizations describe major features of the structure of community food webs. These generalizations are: (i) a species scaling law: the mean proportions of basal, intermediate and top species remain invariant at approximately 0.19, 0.53, and 0.29, respectively, over the range of variation in the number of species in a web; (ii) a link scaling law : the mean proportions of trophic links in the categories basal-intermediate, basal-top, intermediate–intermediate, and intermediate–top remain invariant at approximately 0.27, 0.08, 0.30 and 0.35, respectively, over the range of variation in the number of species in a web; and (iii) a link-species scaling law: the ratio of mean trophic links to species remains invariant at approximately 1.86, over the range of variation in the number of species in a web. This paper presents a model, the only successful one among several attempts, in which the first two of these empirical generalizations can be derived as a consequence of the third. The model assumes that species are ordered in a cascade or hierarchy such that a given species can prey on only those species below it and can be preyed on by only those species above it in the hierarchy.