Figure 3. Distribution of side lengths in random and empirical networks.

Left panels show the mean (a) and the s.d. (b) of cos(η), where η is the side length. Analytical predictions for the first two moments of cos(η) (Supplementary Note 10) perfectly match the numerical simulations. The two panels on the right show the s.d. of cos(η) for food webs (c) and mutualistic networks (d) compared with the expectations for the randomized cases. Both trophic and mutualistic interactions show larger fluctuations of side lengths, suggesting the existence of perturbation directions to which the system is more sensitive than to others. This effect is particularly pronounced and relevant for mutualistic networks. While mutualistic and random networks have a similar feasibility domain size Ξ, this result implies that the response of mutualistic networks to perturbations is in fact more heterogeneous than those of their random counterparts.