A stochastic theory of community food webs II. Individual webs

Abstract The species scaling law and the link scaling law of community food webs can be derived from a simple mathematical model, called the cascade model, which incorporates the link-species scaling law. In the previous test of this model against data on 62 community food webs, the ratio of links to species is estimated from aggregated data on all webs taken together, on the assumption that the ratio is independent of the number of species in the web. This paper demonstrates that the ratio of links to species shows no pronounced increasing or decreasing trend, but varies substantially, over the observed range of variation in the number of species in a web. However, the ratio is higher for webs in constant environments than for webs in fluctuating environments. When the ratio of links to species is estimated separately for each web, the cascade model provides a good description of the numbers of intermediate species and of basal─intermediate, intermediate─intermediate, and intermediate─top links, aside from a single outlying web. The cascade model provides a fair description of the numbers of top and basal species, and a rather poor description of the number of basal─top links. The model describes the kinds of species and kinds of links of constant and fluctuating webs about equally well.