Foraging behaviours lead to spatiotemporal self-similar dynamics in grazing ecosystems.

Biological behaviour-driven self-organized patterns have recently been confirmed to play a key role in ecosystem functioning. Here, we develop a theoretical phase-separation model to describe spatiotemporal self-similar dynamics, which is a consequence of behaviour-driven trophic interactions in short-time scales. Our framework integrates scale-dependent feedback and density-dependent movement into grazing ecosystems. This model derives six types of selective foraging behaviours that trigger pattern formation for top-down grazing ecosystems, and one of which is consistent with existing foraging theories. Self-organized patterns nucleate under moderate grazing intensity and are destroyed by overgrazing, which suggests ecosystem degradation. Theoretical results qualitatively agree with observed grazing ecosystems that display spatial heterogeneities under variable grazing intensity. Our findings potentially provide new insights into self-organized patterns as an indicator of ecosystem transitions under a stressful environment.