Figure 1: Propagation of the perturbation through the network.

(a) Trajectory of a perturbation through time. Reactivity (λ_H) measures whether perturbations grow before decaying; asymptotic resilience λ₁ indicates whether perturbations eventually decay; and the asymptotic perturbation amplitude describes the intensity of the perturbation for large time. The principal right eigenvector determines which species will be affected most by the perturbation after its propagation, while the left principal eigenvector controls which species are the most sensitive to the initial perturbation. The weighted degree heterogeneity affects the localization pattern in the network: (b) is a regular graph where each node is connected to six other nodes, while (c) is a power-law scale-free graph² of the same size and with similar connectance. In both cases, edge weights are randomly extracted from a Gamma distribution. The size and the colour of the nodes indicate the absolute values of the corresponding component of the leading right eigenvector. In b, all species are equally perturbed. In contrast, in c, only few species are affected.