Fig. 4.

Dynamics of individual patches and ecological resilience to local disturbances. (A) The slow coarsening dynamics in aggregation patterns cause big patches to grow (green region) and small patches shrink over time (red region). (B) A comparison between the pattern at $t = 2,000$ and $t = 2,500$ shows the growth of large patches (green) and the shrinkage/disappearance of small patches (red). (C and D) Statistical properties of patch growth rate as a function of patch size, for the density-dependent aggregation and the scale-dependent feedbacks models. The reduced growth of small patches in C versus D implies that patches in systems with density-dependent aggregation may collapse once perturbed below a threshold level (the gray line), while this is not the case in models with scale-dependent feedback. Consequently, systems with density-dependent aggregation have a lower patch-scale resilience than those with scale-dependent feedback.