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.

中文翻译：

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觅食行为导致放牧生态系统的时空自相似动态

生物行为驱动的自组织模式最近被证实在生态系统功能中发挥关键作用。在这里，我们开发了一个理论相分离模型来描述时空自相似动力学，这是短时间尺度内行为驱动的营养相互作用的结果。我们的框架将依赖于规模的反馈和依赖于密度的运动整合到放牧生态系统中。该模型推导出了六种触发自上而下放牧生态系统模式形成的选择性觅食行为，其中一种与现有的觅食理论一致。自组织模式在中等放牧强度下成核并被过度放牧破坏，这表明生态系统退化。理论结果在定性上与观察到的放牧生态系统一致，这些生态系统在不同放牧强度下显示出空间异质性。我们的研究结果可能为自组织模式提供新的见解，作为压力环境下生态系统转变的指标。