Community area and food-chain length: theoretical predictions

In combination with the simplest forms of the species-area curve, the cascade model predicts that the maximal chain length of a community food web (the height) should increase more slowly than linearly as a function of the logarithm of area and asymptotically in islands with extremely large area and extremely large numbers of species. Average chain length, according to the cascade model, should exceed 3.5 as soon as islands are large enough to have ≥30 species and should approach a finite limit, c4.0 in webs from arbitrarily large islands. According to the superlinear homogeneous model, both the height and the average chain length increase as a power, less than one, of the number of species, and therefore as a power, less than one, of area. The ratio of maximal to average chain length in the superlinear homogeneous model asymptotically approaches the limit e in webs from very large islands with very large numbers of species. -from Authors