Understanding the behaviors of ecological systems is challenging given their multifaceted complexity. To proceed, theoretical models such as Lotka-Volterra dynamics with random interactions have been investigated by the dynamical mean-field theory to provide insights into underlying principles such as how biodiversity and stability depend on the randomness in interaction strength. Yet the fully connected structures assumed in these previous studies are not realistic, as revealed by a vast amount of empirical data. We derive a generic formula for the abundance distribution under an arbitrary distribution of degree, the number of interacting neighbors, which leads to degree-dependent abundance patterns of species. Notably, in contrast to the fully interacting systems, the number of surviving species can be reduced as the community becomes cooperative in heterogeneous interaction structures. Our study, therefore, demonstrates that properly taking into account heterogeneity in the interspecific interaction structure is indispensable to understanding the diversity in large ecosystems, and our general theoretical framework can apply to a much wider range of interacting many-body systems.

中文翻译：

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纳入异质相互作用以促进生态生物多样性


鉴于生态系统的多方面复杂性，了解生态系统的行为具有挑战性。为了继续进行，动力学平均场理论研究了具有随机交互作用的 Lotka-Volterra 动力学等理论模型，以深入了解基本原理，例如生物多样性和稳定性如何取决于交互强度的随机性。然而，正如大量经验数据所揭示的那样，这些先前研究中假设的完全连接结构并不现实。我们推导出了一个通用公式，用于在任意程度分布下的丰度分布，即相互作用的邻居的数量，这导致物种的丰度模式与度有关。值得注意的是，与完全相互作用的系统相比，随着群落在异质相互作用结构中变得合作，幸存物种的数量可以减少。因此，我们的研究表明，正确考虑种间相互作用结构的异质性对于理解大型生态系统的多样性是必不可少的，我们的一般理论框架可以适用于更广泛的相互作用多体系统。